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  • 1.
    Appelö, Daniel
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk Analys och Datalogi, NADA.
    Hagstrom, Thomas
    Department of Mathematics and Statistics, University of New Mexico.
    Kreiss, Gunilla
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk Analys och Datalogi, NADA.
    Perfectly matched layers for hyperbolic systems: General formulation, well-posedness and stability2006Ingår i: SIAM Journal on Applied Mathematics, ISSN 0036-1399, E-ISSN 1095-712X, Vol. 67, nr 1, s. 1-23Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Since its introduction the perfectly matched layer (PML) has proven to be an accurate and robust method for domain truncation in computational electromagnetics. However, the mathematical analysis of PMLs has been limited to special cases. In particular, the basic question of whether or not a stable PML exists for arbitrary wave propagation problems remains unanswered. In this work we develop general tools for constructing PMLs for first order hyperbolic systems. We present a model with many parameters, which is applicable to all hyperbolic systems and which we prove is well-posed and perfectly matched. We also introduce an automatic method for analyzing the stability of the model and establishing energy inequalities. We illustrate our techniques with applications to Maxwell's equations, the linearized Euler equations, and arbitrary 2 x 2 systems in (2 + 1) dimensions.

  • 2.
    Appelö, Daniel
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk Analys och Datalogi, NADA.
    Kreiss, Gunilla
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk Analys och Datalogi, NADA.
    A New Absorbing Layer for Elastic Waves2006Ingår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 215, nr 2, s. 642-660Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A new perfectly matched layer (PML) for the simulation of elastic waves in anisotropic media on an unbounded domain is constructed. Theoretical and numerical results, showing that the stability properties of the present layer are better than previously suggested layers, are presented. In addition, the layer can be formulated with fewer auxiliary variables than the split-field PML.

  • 3.
    Appelö, Daniel
    et al.
    KTH, Tidigare Institutioner                               , Numerisk analys och datalogi, NADA.
    Kreiss, Gunilla
    KTH, Tidigare Institutioner                               , Numerisk analys och datalogi, NADA.
    Discretely nonreflecting boundary conditions for higher order centered schemes for wave equations2003Ingår i: Proceedings of the WAVES-2003 conference, Berlin: Springer Verlag , 2003, s. 130-135Kapitel i bok, del av antologi (Övrigt vetenskapligt)
    Abstract [en]

    Using the framework introduced by Rawley and Colonius [2] we construct a nonreflecting boundary condition for the one-way wave equation spatially discretized with a fourth order centered difference scheme. The boundary condition, which can be extended to arbitrary order accuracy, is shown to be well posed. Numerical simulations have been performed showing promising results.

  • 4. Bergström, L.
    et al.
    Edlund, C.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk Analys och Datalogi, NADA. Stockholm University, Sweden.
    Fairbairn, M.
    Järemo, Anna Karin
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk Analys och Datalogi, NADA.
    Kreiss, Gunilla
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk Analys och Datalogi, NADA.
    Pieri, L.
    Signals of WIMP annihilation into electrons at the galactic center2005Ingår i: Proceedings of the 29th International Cosmic Ray Conference, Vol 4: OG 2.1, 2.2 & 2.3, Tata Institute of Fundamental Research , 2005, s. 57-60Konferensbidrag (Refereegranskat)
    Abstract [en]

    Photons from the annihilation of dark matter in the center of our Galaxy are expected to provide a promising way to find out the nature and distribution of the dark matter itself. These photons can be either produced directly and/or through successive decays of annihilation products, or radiated from electrons and positrons. This ends up in a multi-wavelength production of photons whose expected intensity can be compared to observational data. Assuming that the Lightest Supersymmetric Particle makes the dark matter, we derive the expected photon signal from a given dark matter model and compare it with present available data.

  • 5.
    Henningson, Dan Stefan
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Mekanik.
    Kreiss, Gunilla
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk analys, NA (stängd 2012-06-30).
    Threshold amplitudes in subcritical shear flows - Non-linear stability bonds2005Ingår i: IUTAM Symposium on Laminar-Turbulent Transition and Finite Amplitude Solutions / [ed] Mullin, T; Kerswell, R, DORDRECHT: SPRINGER , 2005, Vol. 77, s. 233-249Konferensbidrag (Refereegranskat)
    Abstract [en]

    Non-linear stability bounds are derived for subcritical shear flows. First the methodology is exemplified using a model problem and then it is applied to plane Couette flow. The result is a lower bound which scales as Re-4. Upper bounds based on numerical simulations are found to be about Re-1, depending slightly on the transition scenario investigated. Bounds for plane Poiseuille flow are also presented.

  • 6.
    Kreiss, Gunilla
    et al.
    KTH, Tidigare Institutioner, Numerisk analys och datalogi, NADA.
    Efraimsson, Gunilla
    KTH, Tidigare Institutioner, Farkost- och flygteknik.
    Approximate solutions to slightly viscous conservation laws2004Ingår i: Quarterly of Applied Mathematics, ISSN 0033-569X, E-ISSN 1552-4485, Vol. 62, nr 1, s. 117-133Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We study an approximate solution of a slightly viscous conservation law in one dimension, constructed by two asymptotic expansions that are cut off after the third order terms. In the shock layer, an inner solution is valid and an outer solution is valid elsewhere. Based on the stability results in [10], we show that for a given time interval the difference between the approximate solution and the true solution is not larger than o(epsilon), where epsilon is the viscosity coefficient. The result holds for shocks of any strength.

  • 7.
    Kreiss, Gunilla
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk Analys och Datalogi, NADA.
    Kreiss, Heinz-Otto
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk Analys och Datalogi, NADA.
    Lorenz, Jens
    Stability of viscous shocks on finite intervals2008Ingår i: Archive for Rational Mechanics and Analysis, ISSN 0003-9527, E-ISSN 1432-0673, Vol. 187, nr 1, s. 157-183Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Consider the Cauchy problem for a system of viscous conservation laws with a solution consisting of a thin, viscous shock layer connecting smooth regions. We expect the time-dependent behavior of such a solution to involve two processes. One process consists of the large-scale evolution of the solution. This process is well modeled by the corresponding inviscid equations. The other process is the adjustment in shape and position of the shock layer to the large-scale solution. The time scale of the second process is much faster than the first, 1/nu compared to 1. The second process can be divided into two parts, adjustment of the shape and of the position. During this adjustment the end states are essentially constant. In order to answer the question of stability we have developed a technique where the two processes can be separated. To isolate the fast process, we consider the region in the vicinity of the shock layer. The equations are augmented with special boundary conditions that reflect the slow change of the end states. We show that, for the isolated fast process, the perturbations decay exponentially in time.

  • 8.
    Olsson, Elin
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk Analys och Datalogi, NADA.
    Kreiss, Gunilla
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk Analys och Datalogi, NADA.
    A conservative level set method for two phase flow2005Ingår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 210, nr 1, s. 225-246Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A conservative method of level set type for moving interfaces in divergence free velocity fields is presented. The interface is represented implicitly by the 0.5 level set of a function Phi being a smeared out Heaviside function, i.e., a function being zero on one side of the interface and one on the other. In a transition layer of finite, constant thickness Phi goes smoothly from zero to one. The interface is moved implicitly by the advection of Phi, which is split into two steps. First Phi is advected using a standard numerical method. Then an intermediate step is performed to make sure that the smooth profile of Phi and the thickness of the transition layer is preserved. Both these steps are performed using conservative second order approximations and thus conserving integral Phi. In this way good conservation of the area bounded by the 0.5 contour of Phi is obtained.

    Numerical tests shows up to second order accuracy and very good conservation of the area bounded by the interface.

    The method was also coupled to a Navier-Stokes solver for incompressible two phase flow with surface tension. Results with and without topological changes are presented.

  • 9.
    Olsson, Elin
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk Analys och Datalogi, NADA.
    Kreiss, Gunilla
    Zahedi, Sara
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk Analys och Datalogi, NADA.
    A conservative level set method for two phase flow II2007Ingår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 225, nr 1, s. 785-807Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, we continue to develop and study the conservative level set method for incompressible two phase flow with surface tension introduced in [J. Comput. Phys. 210 (2005) 225-246]. We formulate a modification of the reinitialization and present a theoretical study of what kind of conservation we can expect of the method. A finite element discretization is presented as well as an adaptive mesh control procedure. Numerical experiments relevant for problems in petroleum engineering and material science are presented. For these problems the surface tension is strong and conservation of mass is important. Problems in both two and three dimensions with uniform as well as non-uniform grids are studied. From these calculations convergence and conservation is studied. Good conservation and convergence are observed.

  • 10.
    Siklosi, Malin
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk Analys och Datalogi, NADA.
    Batzorig, Begzsuren
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk Analys och Datalogi, NADA.
    Kreiss, Gunilla
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk Analys och Datalogi, NADA.
    An investigation of the internal structure of shock profiles for shock capturing schemes2007Ingår i: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 201, nr 1, s. 8-29Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The theoretical understanding of discrete shock transitions obtained by shock capturing schemes is very incomplete. Previous experimental studies indicate that discrete shock transitions obtained by shock capturing schemes can be modeled by continuous functions, so called continuum shock profiles. However, the previous papers have focused on linear methods. We have experimentally studied the trajectories of discrete shock profiles in phase space for a range of different high resolution shock capturing schemes, including Riemann solver based flux limiter methods, high resolution central schemes and ENO type methods. In some cases, no continuum profiles exists. However, in these cases the point values in the shock transitions remain bounded and appear to converge toward a stable limit cycle. The possibility of such behavior was anticipated in Bultelle, Grassin and Serre, 1998, but no specific examples, or other evidence, of this behavior have previously been given. In other cases, our results indicate that continuum shock profiles exist, but are very complicated. We also study phase space orbits with regard to post shock oscillations.

  • 11. 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)
  • 12.
    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.

  • 13.
    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.

  • 14.
    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.

  • 15.
    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.

  • 16.
    Åsén, Per-Olov
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk Analys och Datalogi, NADA.
    Kreiss, Gunilla
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk Analys och Datalogi, NADA.
    On a Rigorous Resolvent Estimate for Plane Couette Flow2007Ingår i: Journal of Mathematical Fluid Mechanics, ISSN 1422-6928, E-ISSN 1422-6952, Vol. 9, nr 2, s. 153-180Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We derive a rigorous bound of the solution of the resolvent equation for plane Couette flow in three space dimensions. We combine analytical techniques with numerical computations. Compared to earlier results, our analytical techniques cover a larger part of the parameter domain consisting of wave numbers in two space directions and the Reynolds number. Numerical computations are needed only in a compact subset of the parameter domain.

  • 17.
    Åsén, Per-Olov
    et al.
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk Analys och Datalogi, NADA.
    Kreiss, Gunilla
    KTH, Skolan för datavetenskap och kommunikation (CSC), Numerisk Analys och Datalogi, NADA.
    Resolvent bounds for pipe Poiseuille flow2006Ingår i: Journal of Fluid Mechanics, ISSN 0022-1120, E-ISSN 1469-7645, Vol. 568, s. 451-471Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We derive an analytical bound on the resolvent of pipe Poiseuille flow in large parts of the unstable half-plane. We also consider the linearized equations, Fourier transformed in axial and azimuthal directions. For certain combinations of the wavenumbers and the Reynolds number, we derive an analytical bound on the resolvent of the Fourier transformed problem. In particular, this bound is valid for the perturbation which numerical computations indicate to be the perturbation that gives the largest transient growth. Our bound has the same dependence on the Reynolds number as given by the computations.

  • 18.
    Åsén, Per-Olov
    et al.
    KTH, Skolan för teknikvetenskap (SCI), Centra, Linné Flow Center, FLOW.
    Kreiss, Gunilla
    Uppsala Univ, Dept Informat Technol..
    Rempfer, Dietmar
    IIT, Chicago.
    Direct numerical simulations of localized disturbances in pipe Poiseuille flow2010Ingår i: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 39, nr 6, s. 926-935Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider pipe Poiseuille flow subjected to a disturbance which is highly localized in space. Experiments by Peixinho and Mullin have shown this disturbance to be efficient in triggering turbulence, yielding a threshold dependence on the required amplitude as R-1.5 on the Reynolds number, R. The experiments also indicate an initial formation of hairpin vortices, with each hairpin having a length of approximately one pipe radius, independent of the Reynolds number in the range of R = 2000-3000. We perform direct numerical simulations for R = 5000. The results show a packet of hairpin vortices traveling downstream, each having a length of approximately one pipe radius. The perturbation remains highly localized in space while being advected downstream for approximately 10 pipe diameters. Beyond that distance from the disturbance origin, the flow becomes severely disordered.

1 - 18 av 18
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