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  • 251.
    Ruhe, Axel
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Introduction to the contents of issue 51:32011Ingår i: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 51, nr 3, s. 481-482Artikel i tidskrift (Refereegranskat)
  • 252.
    Ruhe, Axel
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Introduction to the contents of issue 52:22012Ingår i: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 52, nr 2, s. 271-272Artikel i tidskrift (Övrigt vetenskapligt)
  • 253.
    Ruhe, Axel
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Introduction to the contents of issue 52:32012Ingår i: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 52, nr 3, s. 537-538Artikel i tidskrift (Övrigt vetenskapligt)
  • 254.
    Ruhe, Axel
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Preface to BIT 52:12012Ingår i: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 52, nr 1, s. 1-2Artikel i tidskrift (Övrigt vetenskapligt)
  • 255.
    Runborg, Olof
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    FAST INTERFACE TRACKING VIA A MULTIRESOLUTION REPRESENTATION OF CURVES AND SURFACES2009Ingår i: Communications in Mathematical Sciences, ISSN 1539-6746, E-ISSN 1945-0796, Vol. 7, nr 2, s. 365-398Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider the propagation of an interface in a velocity field. The initial interface is described by a normal mesh [Guskov, et al, SIGGRAPH Proc., 259-268, 2000] which gives us a multiresolution decomposition of the interface and the related wavelet vectors. Instead of tracking marker points on the interface we track the wavelet vectors, which like the markers satisfy ordinary differential equations. We show that the finer the spatial scale, the slower the wavelet vectors evolve. By designing a numerical method which takes longer time steps for finer spatial scales weareable to track the interface with the same overall accuracy as when directly tracking the markers, but at a computational cost of O(logN/Delta t) rather than O(N/Delta t) for N markers and timestep Delta t. We prove this rigorously and give numerical examples supporting the theory. We also consider extensions to higher dimensions and co-dimensions.

  • 256.
    Runborg, Olof
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30).
    Wavelets and wavelet based numerical homogenization2009Ingår i: Multiscale Modeling and Simulation in Science, Springer Berlin/Heidelberg, 2009, s. 195-235Konferensbidrag (Refereegranskat)
    Abstract [en]

    Wavelets is a tool for describing functions on different scales or level of detail. In mathematical terms, wavelets are functions that form a basis for with special properties; the basis functions are spatially localized and correspond to different scale levels. Finding the representation of a function in this basis amounts to making a multiresolution decomposition of the function. Such a wavelet representation lends itself naturally to analyzing the fine and coarse scales as well as the localization properties of a function.Wavelets have been used in many applications, from image and signal analysis to numerical methods for partial differential equations (PDEs). In this tutorial we first go through the basic wavelet theory and then show a more specific application where wavelets are used for numerical homogenization.We will mostly give references to the original sources of ideas presented. There are also a large number of books and review articles that cover the topic of wavelets, where the interested reader can find further information, e.g. [25, 51, 48, 7, 39, 26, 23], just to mention a few.

  • 257. Sjögreen, B
    et al.
    Engquist, Björn
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Numerical approximation of hyperbolic conservation laws with stiff terms1991Konferensbidrag (Refereegranskat)
  • 258.
    Sjögreen, Björn
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk Analys och Datalogi, NADA.
    Gustavsson, Katarina
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Gudmundsson, Reynir Levi
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk Analys och Datalogi, NADA.
    A model for peak formation in the two-phase equations2007Ingår i: Mathematics of Computation, ISSN 0025-5718, E-ISSN 1088-6842, Vol. 76, nr 260, s. 1925-1940Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We present a hyperbolic-elliptic model problem related to the equations of two-phase fluid flow. The model problem is solved numerically, and properties of its solution are presented. The model equation is well-posed when linearized around a constant state, but there is a strong focusing effect, and very large solutions exist at certain times. We prove that the model problem has a smooth solution for bounded times.

  • 259. Strömgren, Magnus
    et al.
    Hanke, Michael
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    On the numerical approximation of a degenerated hyperbolic system2009Ingår i: Mathematics and Computers in Simulation, ISSN 0378-4754, E-ISSN 1872-7166, Vol. 79, nr 5, s. 1585-1602Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The heat exchanger in a heat pump system may be conveniently described by a degenerated hyperbolic system, namely the zero Mach-number limit of the Euler equations. This leads to a mixed hyperbolic/parabolic system with coupled time-dependent boundary conditions. We propose a method-of-lines discretisation by using an upwinding scheme. We derive stability estimates for the linearisation with frozen coefficients. The resulting differential-algebraic equation has a perturbation index of 2 and a weak instability with respect to the space step size. The latter property is validated experimentally even for the nonlinear system. In contrast, the perturbation index did not exceed one in the numerical experiments.

  • 260.
    Szepessy, Anders
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Atomistic and continuum models for phase change dynamics2006Ingår i: Proceedings of the International Congress of Mathematicians, 2006, s. 1563-1582Konferensbidrag (Refereegranskat)
    Abstract [en]

    The dynamics of dendritic growth of a crystal in an undercooled melt is determined by macroscopic diffusion-convection of heat and capillary forces acting on length scales compared to the nanometer width of the solid-liquid interface. Its modeling is useful for instance in processing techniques based on casting. The phase field method is widely used to study evolution of such microstructures of phase transformations on a continuum level; it couples the energy equation to a phenomenological Allen�Cahn/Ginzburg�Landau equation modeling the dynamics of an order parameter determining the solid and liquid phases, including also stochastic fluctuations to obtain the qualitative correct result of dendritic side branching. This lecture presents some ideas to derive stochastic phase field models from atomistic formulations by coarse-graining molecular dynamics and kinetic Monte Carlo methods.

  • 261.
    Szepessy, Anders
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Convergence of a streamline diffusion finite element method for a conservation law with boundary conditions1991Ingår i: RAIRO Modelling and numercial analysis modelisations, Vol. 25, nr 5, s. 749-783Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A higher order accurate shock-capturing streamline diffusion finite element method for general scalar conservation laws is analysed; convergence towards the unique solution is proved for several space dimensions with initial and boundary conditions, using a uniqueness theorem for measure valued solutions. Furthermore, some numerical results are given.

  • 262.
    Szepessy, Anders
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    On shock wave stability1992Ingår i: / [ed] V. Bo, F. Bampi and G. Toscani, 1992Konferensbidrag (Refereegranskat)
  • 263.
    Szepessy, Anders
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    On the stability of Broadwell shocks1993Konferensbidrag (Refereegranskat)
    Abstract [en]

    Introduction We study the asymptotic behavior of perturbations of traveling shock waves of the Broadwell model, Gamma @ @t + @ @x Delta f + = f 2 0 Gamma f + f Gamma ; x 2 R I 1 ; t ? 0; @ @t f 0 = Gamma 1 2 (f 2 0 Gamma f + f Gamma ); (1:1a) Gamma @ @t Gamma @ @x Delta f Gamma = f 2 0 Gamma f + f Gamma ; with initial data (1:1b) (f + ; f 0 ; f Gamma )(Delta; 0) = f I (Delta) ;<F13.54

  • 264.
    Szepessy, Anders
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30).
    Zumbrun, K
    On the stability of rarefaction waves in viscous media1994Ingår i: / [ed] J. Glimm, M.J. Graham, J.W. Grove and B.J. Plohr, 1994Konferensbidrag (Refereegranskat)
    Abstract [en]

    We study the time-asymptotic behavior of weak rarefaction waves of systems of conservation laws describing one-dimensional viscous media, with strictly hyperbolic flux functions. Our main result is to show that solutions of perturbed rarefaction data converge to an approximate, ''Burgers'' rarefaction wave, for initial perturbations w(o) with small mass and localized as w(o)(x)= O(\x\(-1)). The proof proceeds by iteration of a pointwise ansatz for the error, using integral representations of its various components, based on Green's functions. We estimate the Green's functions by careful use of the Hopf-Cole transformation, combined with a refined parametrix method. As a consequence of our method, we also obtain rates of decay and detailed pointwise estimates for the error. This pointwise method has been used successfully in studying stability of shock and constant-state solutions. New features in the rarefaction case are time-varying coefficients in the linearized equations and error waves of unbounded mass O(log(t)). These ''diffusion waves'' have amplitude O(t(-1/2) log t) in linear degenerate transversal fields and O(t(-1/2)) in genuinely nonlinear transversal fields, a distinction which is critical in the stability proof

  • 265.
    Tomac, Maxmillian
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Farkost och flyg.
    Rizzi, Arthur
    KTH, Skolan för teknikvetenskap (SCI), Farkost och flyg.
    Oppelstrup, Jesper
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30).
    From geometry to CFD grids - An automated approach for conceptual design2010Ingår i: AIAA Atmospheric Flight Mechanics Conference 2010, 2010Konferensbidrag (Refereegranskat)
  • 266. Ton, V
    et al.
    Karagozian, A
    Marble, F
    Osher, S
    Engquist, Björn
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Numerical simulation of high speed chemically reacting flow1994Ingår i: Theoretical and Computational Fluid Dynamics, ISSN 0935-4964, E-ISSN 1432-2250, Vol. 6, nr 2-3, s. 161-179Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The essentially nonoscillatory (ENO) shock-capturing scheme for the solution of hyperbolic equations is extended to solve a system of coupled conservation equations governing two-dimensional, time-dependent, compressible chemically reacing flow with full chemistry. The thermodynamic properties of the mixture are modeled accurately, and stiff kinetic terms are separated from the fluid motion by a fractional step algorithm. The methodology is used to study the concept of shock-induced mixing and combustion, a process by which the interaction of a shock wave with a jet of low-density hydrogen fuel enhances mixing through streamwise vorticity generation. Test cases with and without chemical reaction are explored here. Our results indicate that, in the temperature range examined, vorticity generation as well as the distribution of atomic species do not change significantly with the introduction of a chemical reaction and subsequent heat release. The actual diffusion of hydrogen is also relatively unaffected by the reaction process. This suggests that the fluid mechanics of this problem may be successfully decoupled from the combustion processes, and that computation of the mixing problem (without combustion chemistry) can elucidate much of the important physical features of the flow.

  • 267. Tornberg, Anna Karin
    et al.
    Engquist, Björn
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    A finite element based level-set method for multi-phase flow applications2000Ingår i: Computing and Visualization in Science, ISSN 1432-9360, E-ISSN 1433-0369, Vol. 3, nr 1-2, s. 93-101Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A numerical method for simulating incompressibletwo-dimensional multiphase flow is presented. The methodis based on a level-set formulation discretized by a finiteelementtechnique. The treatment of the specific features ofthis problem, such as surface tension forces acting at the interfacesseparating two immiscible fluids, as well as the densityand viscosity jumps that in general occur across such interfaces,have been integrated into the finite-element framework.Using a method based on the weak formulation of the Navier-Stokes equations has its advantages. In this formulation, thesingular surface tension forces are included through line integralsalong the interfaces, which are easily approximatedquantities. In addition, differentiation of the discontinuousviscosity is avoided. The discontinuous density and viscosityare included in the finite element integrals. A strategy forthe evaluation of integrals with discontinuous integrands hasbeen developed based on a rigorous analysis of the errors associatedwith the evaluation of such integrals. Numerical testshave been performed. For the case of a rising buoyant bubblethe results are in good agreement with results from a fronttrackingmethod. The run presented here is a run includingtopology changes, where initially separated areas of one fluidmerge in different stages due to buoyancy effects.

  • 268.
    Tornberg, Anna Karin
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30).
    Engquist, Björn
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30).
    A Finite Element Based Level-Set Method for Multiphase Flows2002Konferensbidrag (Refereegranskat)
    Abstract [en]

    A numerical method for simulating incompressible two-dimensional multiphase flow is presented. The method is based on a level-set formulation discretized by a finite-element technique. The treatment of the specific features of this problem, such as surface tension forces acting at the interfaces separating two immiscible fluids, as well as the density and viscosity jumps that in general occur across such interfaces, have been integrated into the finite-element framework. Using a method based on the weak formulation of the Navier-Stokes equations has its advantages. In this formulation, the singular surface tension forces are included through line integrals along the interfaces, which are easily approximated quantities. In addition, differentiation of the discontinuous viscosity is avoided. The discontinuous density and viscosity are included in the finite element integrals. A strategy for the evaluation of integrals with discontinuous integrands has been developed based on a rigorous analysis of the errors associated with the evaluation of such integrals. Numerical tests have been performed. For the case of a rising buoyant bubble the results are in good agreement with results from a front-tracking method. The run presented here is a run including topology changes, where initially separated areas of one fluid merge in different stages due to buoyancy effects.

  • 269.
    Tornberg, Anna Karin
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Engquist, Björn
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Interface Tracking in Two-Phase Flows2000Ingår i: State of the Art: Multifield Problems, Springer Berlin/Heidelberg, 2000, s. 58-66Kapitel i bok, del av antologi (Refereegranskat)
  • 270. Tornberg, Anna Karin
    et al.
    Engquist, Björn
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Interface tracking in two-phase flows2000Konferensbidrag (Refereegranskat)
  • 271. Tornberg, Anna Karin
    et al.
    Engquist, Björn
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Regularization techniques for numerical approximations of PDEs with singularities2003Ingår i: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 19, nr 1-3, s. 527-552Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The rate of convergence for numerical methods approximating differential equations are often drastically reduced from lack of regularity in the solution. Typical examples are problems with singular source terms or discontinuous material coefficients. We shall discuss the technique of local regularization for handling these problems. New numerical methods are presented and analyzed and numerical examples are given. Some serious deficiencies in existing regularization methods are also pointed out.

  • 272.
    Tornberg, Anna-Karin
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Regularization techniques for singular source terms in differential equations2005Ingår i: European Congress of Mathematics: Stockholm, June 27-July 2, 2004 / [ed] Ari Laptev, Zurich: European Mathematical Society Publishing House, 2005, s. 477-499Kapitel i bok, del av antologi (Refereegranskat)
  • 273.
    Tornberg, Anna-Karin
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Engquist, Björn
    KTH, Skolan för datavetenskap och kommunikation (CSC).
    Consistent boundary conditions for the Yee scheme2008Ingår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 227, nr 14, s. 6922-6943Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A new set of consistent boundary conditions for Yee scheme approximations of wave equations in two space dimensions are developed and analyzed. We show how the classical staircase boundary conditions for hard reflections or, in the electromagnetic case, conducting surfaces in certain cases give 0(l) errors. The proposed conditions keep the structure of the Yee scheme and are thus well suited for high performance computing. The higher accuracy is achieved by modifying the coefficients in the difference stencils near the boundary. This generalizes our earlier results with Gustafsson and Wahlund in one space dimension. We study stability and convergence and we present numerical examples.

  • 274.
    Tornberg, Anna-Karin
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Engquist, Björn
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Regularization for accurate numerical wave propagation in discontinuous media2006Ingår i: Methods and Applications of Analysis, ISSN 1073-2772, E-ISSN 1945-0001, Vol. 13, nr 3, s. 247-274Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Structured computational grids are the basis for highly efficient numerical approximations of wave propagation. When there are discontinuous material coefficients the accuracy is typically reduced and there may also be stability problems. In a sequence of recent papers Gustafsson et al. proved stability of the Yee scheme and a higher order difference approximation based on a similar staggered structure, for the wave equation with general coefficients. In this paper, the Yee discretization is improved from first to second order by modifying the material coefficients close to the material interface. This is proven in the $L^2$ norm. The modified higher order discretization yields a second order error component originating from the discontinuities, and a fourth order error from the smooth regions. The efficiency of each original method is retained since there is no special structure in the difference stencil at the interface. The main focus of this paper is on one spatial dimension, with the derivation of a second order algorithm for a two dimensional example given in the last section

  • 275.
    Tornberg, Anna-Karin
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Greengard, Leslie
    A fast multipole method for the three-dimensional Stokes equations2008Ingår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 227, nr 3, s. 1613-1619Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Many problems in Stokes flow (and linear elasticity) require the evaluation of vector fields defined in terms of sums involving large numbers of fundamental solutions. In the fluid mechanics setting, these are typically the Stokeslet (the kernel of the single layer potential) or the Stresslet (the kernel of the double layer potential). In this paper, we present a simple and efficient method for the rapid evaluation of such fields, using a decomposition into a small number of Coulombic N-body problems, following an approach similar to that of Fu and Rodin [Y. Fu, G.J. Rodin, Fast solution methods for three-dimensional Stokesian many-particle problems, Commun. Numer. Meth. En. 16 (2000) 145-149]. While any fast summation algorithm for Coulombic interactions can be employed, we present numerical results from a scheme based on the most modern version of the fast multipole method [H. Cheng, L. Greengard, V. Rokhlin, A fast adaptive multipole algorithm in three dimensions, J. Comput. Phys. 155 (1999) 468-498]. This approach should be of value in both the solution of boundary integral equations and multiparticle dynamics.

  • 276.
    Tornberg, Anna-Karin
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Gustavsson, Katarina
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk Analys och Datalogi, NADA.
    A numerical method for simulations of rigid fiber suspensions2006Ingår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 215, nr 1, s. 172-196Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, we present a numerical method designed to simulate the challenging problem of the dynamics of slender fibers immersed in an incompressible fluid. Specifically, we consider microscopic, rigid fibers, that sediment due to gravity. Such fibers make up the micro-structure of many suspensions for which the macroscopic dynamics are not well understood. Our numerical algorithm is based on a non-local slender body approximation that yields a system of coupled integral equations, relating the forces exerted on the fibers to their velocities, which takes into account the hydrodynamic interactions of the fluid and the fibers. The system is closed by imposing the constraints of rigid body motions. The fact that the fibers are straight have been further exploited in the design of the numerical method, expanding the force on Legendre polynomials to take advantage of the specific mathematical structure of a finite-part integral operator, as well as introducing analytical quadrature in a manner possible only for straight fibers. We have carefully treated issues of accuracy, and present convergence results for all numerical parameters before we finally discuss the results from simulations including a larger number of fibers.

  • 277. Vanbiervliet, J.
    et al.
    Michiels, W.
    Jarlebring, Elias
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Using spectral discretization for the optimal H2 design of time-delay systems2011Ingår i: International Journal of Control, ISSN 0020-7179, E-ISSN 1366-5820, Vol. 84, nr 2, s. 228-241Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The stabilization and robustification of a time-delay system is the topic of this paper. More precisely, we want to minimize the H2 norm of the transfer function corresponding to this class of linear time-invariant input-output systems with fixed time delays in the states. Due to the presence of the delays, the transfer function is a nonrational, nonlinear function, and the classical procedure which involves solving Lyapunov equations is no longer applicable. We therefore propose an approach based on a spectral discretization applied to a reformulation of the time-delay system as an infinite-dimensional standard linear system. In this way, we obtain a large delay-free system, which serves as an approximation to the original time-delay system, and which allows the application of standard H2 norm optimization techniques. We give an interpretation of this approach in the frequency domain and relate it to the approximation of the nonlinear terms in the time-delay transfer function by means of a rational function. Using this property, we can provide some insight in the convergence be- haviour of the approximation, justifying its use for the purpose of H2 norm computation. Along with this, the easy availibility of derivatives with respect to the original matrices allows for an efficient integration into any standard optimization framework. A numerical example finally illustrates how the presented method can be employed to perform optimal H2 norm design using smooth optimization techniques.

  • 278.
    Vilela de Abreu, Rodrigo
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30).
    Hoffman, Johan
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30).
    Jansson, Niclas
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30).
    Towards the development of adaptive finite element methods for aeroacousticsManuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    We report the latest results obtained in the development of an adaptive nite ele- ment method for computational aeroacoustics (CAA). The new methodology is based on the General Galerkin (G2) method, which has been successfully used for the computation of incompressible, turbulent ow. Here, we simulate the ow past an in-duct mixer plate and compare the results with available experimental data. The compar- isons include mean velocity pro les and frequency content of the turbulent signal. No direct simulation of sound or sound wave propagation has been performed; instead, simple analogy arguments have been used to extract acoustic results from incompressible simulations by assuming a direct correlation between the computed pressure drop signal and the sound at the far eld. We were able to reproduce the sound signal from experiments with our incompressible simulation and our results compared well with both the level and the broadband frequency peak of the measured sound. We suggest that the methodology presented here is mainly suitable for the prediction of sound in low Mach number pipe flows.

  • 279.
    Vilela de Abreu, Rodrigo
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Jansson, Niclas
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Hoffman, Johan
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Adaptive computation of aeroacoustic sources for a 4-wheel rudimentary landing gear benchmark problem2010Konferensbidrag (Refereegranskat)
    Abstract [en]

    We present our simulation results for the benchmark Rudimentary Landing Gear using a General Galerkin (G2) nite element method, also referred to as Adaptive DNS/LES. In G2 no explicit subgrid model is used, instead the computational mesh is adaptively re ned with respect to an a posteriori error estimate of a quantity of interest in the computation, in this case drag force. Turbulent boundary layers are modeled using a simple wall shear stress proportional to the skin friction, which here is assumed to be small and is approximated by zero skin friction, resulting in a slip velocity boundary condition. We compare our results with experimental data and other state of the art computations, where we nd good agreement in sound pressure levels, surface velocities and ow separation. We also compare with detailed surface pressure experimental data where we nd largely good agreement, apart from some local dierences for which we discuss possible explanations.

  • 280. Wadbro, Eddie
    et al.
    Zahedi, Sara
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30).
    Kreiss, Gunilla
    Berggren, Martin
    A uniformly well-conditioned, unfitted Nitsche method for interface problems2013Ingår i: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 53, s. 791-820Artikel i tidskrift (Refereegranskat)
  • 281. Weinan, E
    et al.
    Engquist, Björn
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Blowup of solutions of the unsteady Prandtl's equation1997Ingår i: Communications on Pure and Applied Mathematics, ISSN 0010-3640, E-ISSN 1097-0312, Vol. 50, s. 1287-1293Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We prove that for certain class of compactly supported C˜ initial data, smooth solutions of the unsteady Prandtl's equation blow up in nite time

  • 282. Weinan, E
    et al.
    Engquist, Björn
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Multi-scale Modeling and Computation2003Ingår i: Notices of the American Mathematical Society, ISSN 0002-9920, E-ISSN 1088-9477, Vol. 50, s. 1062-1070Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Many applications involve phenomena that act at scales of more than one order of magnitude. This article discusses developments in numerical and analytical techniques for handling such multiscale discussions.

  • 283. Weinan, E
    et al.
    Engquist, Björn
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    The heterogeneous multi-scale method2003Ingår i: Computational materials science, ISSN 0927-0256, E-ISSN 1879-0801, Vol. 1, s. 87-133Artikel i tidskrift (Refereegranskat)
  • 284. Weinan, E
    et al.
    Engquist, Björn
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Huang, Z
    Heterogeneous multi-scale method – a general methodology for multi-scale modelling2003Ingår i: Reviews of Physiology, Biochemistry, ISSN 0303-4240, E-ISSN 1617-5786, Vol. 67, nr 9, s. 2-5Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The heterogeneous multiscale method, is presented as a general methodology for an efficient numerical computation of problems with multiple scales. The method relies on an efficient coupling between the macroscopic and microscopic models. In case the macroscopic model is not explicitly available or is invalid in part of the domain, the microscopic model is used to supply the necessary data for the macroscopic model. Scale separation is exploited so that coarse-grained variables can be evolved on macroscopic spatial/temporal scales using data that are predicted based on the simulation of the microscopic process on microscale spatial/temporal domains. Applications to homogenization, dislocation dynamics and crack propagation are discussed.

  • 285. Yee, H. C.
    et al.
    Sjögreen, Björn
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Nonlinear filtering in compact high-order schemes2006Ingår i: Journal of Plasma Physics, ISSN 0022-3778, E-ISSN 1469-7807, Vol. 72, s. 833-836Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The adaptive nonlinear filtering approach for shock/turbulence gas dynamics and magnetohydrodynamics (MHD) flows adopted in our previous world is employed in conjunction with compact high-order methods as the spatial base scheme. The objective is to compare the performance of nonlinear filtering in compact high-order schemes with nonlinear filtering in standard central (non-compact) schemes for multiseale problems containing shock waves.

  • 286.
    Zahedi, Sara
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Numerical Methods for Fluid Interface Problems2011Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    This thesis concerns numerical techniques for two phase flowsimulations; the two phases are immiscible and incompressible fluids. Strategies for accurate simulations are suggested. In particular, accurate approximations of the weakly discontinuousvelocity field, the discontinuous pressure, and the surface tension force and a new model for simulations of contact line dynamics are proposed.

    In two phase flow problems discontinuities arise in the pressure and the gradient of the velocity field due to surface tension forces and differences in the fluids' viscosity. In this thesis, a new finite element method which allows for discontinuities along an interface that can be arbitrarily located with respect to the mesh is presented. Using standard linear finite elements, the method is for an elliptic PDE proven to have optimal convergence order and a system matrix with condition number bounded independently of the position of the interface.The new finite element method is extended to the incompressible Stokes equations for two fluid systemsand enables accurate approximations of the weakly discontinuous velocity field and the discontinuous pressure.

    An alternative way to handle discontinuities is regularization. In this thesis, consistent regularizations of Dirac delta functions with support on interfaces are proposed. These regularized delta functions make it easy to approximate surface tension forces in level set methods.

    A new model for simulating contact line dynamics is also proposed. Capillary dominated flows are considered and it is assumed that contact line movement is driven by the deviation of the contact angle from its static value. This idea is used together with the conservative level set method. The need for fluid slip at the boundary is eliminated by providing a diffusive mechanism for contact line movement. Numerical experiments in two space dimensions show that the method is able to qualitatively correctly capture contact line dynamics.

  • 287.
    Zahedi, Sara
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Numerical Modeling of Fluid Interface Phenomena2009Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)
  • 288.
    Zahedi, Sara
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Gustavsson, Katarina
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Kreiss, Gunilla
    Division of Scientific Computing, Department of Information Technology, Uppsala University.
    A Conservative Level Set Method for Contact Line Dynamics2009Ingår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 228, nr 17, s. 6361-6375Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A new model for simulating contact line dynamics is proposed. We apply the idea of driving contact-line movement by enforcing the equilibrium contact angle at the boundary, to the conservative level set method for incompressible two-phase flow [E. Olsson, G. Kreiss, A conservative level set method for two phase flow, J. Comput. Phys. 210 (2005) 225-246]. A modified reinitialization procedure provides a diffusive mechanism for contact-line movement, and results in a smooth transition of the interface near the contact line without explicit reconstruction of the interface. We are able to capture contact-line movement without loosing the conservation. Numerical simulations of capillary dominated flows in two space dimensions demonstrate that the model is able to capture contact line dynamics qualitatively correct.

  • 289.
    Zahedi, Sara
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30).
    Knonbichler, Martin
    Uppsala Univ, Uppsala, Sweden .
    Kreiss, Gunilla
    Uppsala University.
    Spurious currents in finite element based level set methods for two-phase flow2012Ingår i: International Journal for Numerical Methods in Fluids, ISSN 0271-2091, E-ISSN 1097-0363, Vol. 69, nr 9, s. 1433-1456Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A study of spurious currents in continuous finite element based simulations of the incompressible Navier-Stokes equations for two-phase flows is presented on the basis of computations on a circular drop in equilibrium. The conservative and the standard level set methods are used. It is shown that a sharp surface tension force, expressed as a line integral along the interface, can give rise to large spurious currents and oscillations in the pressure that do not decrease with mesh refinement. If instead a regularized surface tension representation is used, exact force balance at the interface is possible, both for a fully coupled discretization approach and for a fractional step projection method. However, the numerical curvature calculation introduces errors that cause spurious currents. Different ways to extend the curvature from the interface to the whole domain are discussed and investigated. The impact of using different finite element spaces and stabilization methods is also considered.

  • 290.
    Zahedi, Sara
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Kreiss, Gunilla
    An unfitted Nitsche method for the incompressible two fluid Stokes systemManuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    An easy-to-use finite element method for two fluid Stokes flow, with accurate treatment of jumps in pressure and in velocity gradients at the fluid-fluid interface, is presented. The method allows for an interface not aligned with the grid, and is based on continuous linear finite elements. The jumps at the interface are enforced by a variant of Nitsche's method. Numerical experiments demonstrate optimal convergence order.

  • 291.
    Zahedi, Sara
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Kreiss, Gunilla
    Gustavsson, Katarina
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    An Interface Capturing Method for Two-Phase Flow with Moving Contact Lines2008Ingår i: Proccedings of the 1st European Conference on Microfluidics 2008, SOCIETE HYDROTECHNIQUE DE FRANCE , 2008Konferensbidrag (Refereegranskat)
  • 292.
    Zahedi, Sara
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Tornberg, Anna-Karin
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Delta Function Approximations in Level Set Methods by Distance Function Extension2010Ingår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 229, nr 6, s. 2199-2219Artikel i tidskrift (Refereegranskat)
    Abstract [en]

     In [A.-K. Tornberg, B. Engquist, Numerical approximations of singular source terms in differential equations, J. Comput. Phys. 200 (2004) 462-488], it was shown for simple examples that the then most common way to regularize delta functions in connection to level set methods produces inconsistent approximations with errors that are not reduced with grid refinement. Since then, several clever approximations have been derived to overcome this problem. However, the great appeal of the old method was its simplicity. In this paper it is shown that the old method - a one-dimensional delta function approximation extended to higher dimensions by a distance function - can be made accurate with a different class of one-dimensional delta function approximations. The prize to pay is a wider support of the resulting delta function approximations.

  • 293.
    Zahedi, Sara
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA.
    Wadbro, Eddie
    Kreiss, Gunilla
    Berggren, Martin
    A uniformly well-conditioned, unfitted Nitsche method for interface problems: PartIIngår i: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170Artikel i tidskrift (Övrigt vetenskapligt)
    Abstract [en]

    A finite element method for elliptic partial differential equations that allows for discontinuities along an interface not aligned with the mesh is presented.The solution on each side of the interface is separately expanded in standard continuous, piecewise-linear functions, and a variant of Nitsche's method enforces the jump conditions at the interface.In this method, the solutions on each side of the interface are extended to the entire domain, which results in a fixed number of unknowns independent of the location of the interface. A stabilization procedure is included to ensure well-defined extensions. Numerical experiments are presented showing optimal convergence order in the energy and $L^2$ norms, and also for pointwise errors. The presented results also show that the condition number of the system matrix is independent of the position of the interface relative to the grid.

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