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  • 1.
    af Klinteberg, Ludvig
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Tornberg, Anna-Karin
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Fast Ewald summation for Stokesian particle suspensions2014In: International Journal for Numerical Methods in Fluids, ISSN 0271-2091, E-ISSN 1097-0363, Vol. 76, no 10, p. 669-698Article in journal (Refereed)
    Abstract [en]

    We present a numerical method for suspensions of spheroids of arbitrary aspect ratio, which sediment under gravity. The method is based on a periodized boundary integral formulation using the Stokes double layer potential. The resulting discrete system is solved iteratively using generalized minimal residual accelerated by the spectral Ewald method, which reduces the computational complexity to O(N log N), where N is the number of points used to discretize the particle surfaces. We develop predictive error estimates, which can be used to optimize the choice of parameters in the Ewald summation. Numerical tests show that the method is well conditioned and provides good accuracy when validated against reference solutions. 

  • 2.
    Brüger, Armin
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Gustafsson, B.
    Lötstedt, P.
    Nilsson, J.
    Splitting methods for high order solution of the incompressible Navier-Stokes equations in 3D2005In: International Journal for Numerical Methods in Fluids, ISSN 0271-2091, E-ISSN 1097-0363, Vol. 47, no 10-11, p. 1157-1163Article in journal (Refereed)
    Abstract [en]

    The incompressible Navier-Stokes equations are discretized in space by a hybrid method and integrated in time by the method of lines. The solution is determined on a staggered curvilinear grid in two space dimensions and by a Fourier expansion in the third dimension. The space derivatives are approximated by a compact finite difference scheme of fourth-order on the grid. The solution is advanced in time by a semi-implicit method. In each time step, systems of linear equations have to be solved for the velocity and the pressure. The iterations are split into one outer iteration and three inner iterations. The accuracy and efficiency of the method are demonstrated in a numerical experiment with rotated Poiseuille flow perturbed by Off-Sommerfeld modes in a channel.

  • 3. Gullbrand, J.
    et al.
    Bai, X. S.
    Fuchs, Laszlo
    High-order Cartesian grid method for calculation of incompressible turbulent flows2001In: International Journal for Numerical Methods in Fluids, ISSN 0271-2091, E-ISSN 1097-0363, Vol. 36, no 6, p. 687-709Article in journal (Refereed)
    Abstract [en]

    A high-order wall treatment is proposed and implemented into a Cartesian grid method and the wall treatment is evaluated for incompressible turbulent flows. The Cartesian grid method employs a sequence of locally refined, uniformly spaced, Cartesian grids. In order to achieve a high-order accuracy, a wall treatment procedure has been developed for arbitrarily shaped geometries. The procedure consists of high-order Lagrangian polynomial interpolations and extrapolations for determining the dependent variables around the wall boundaries. The wall treatment procedure and the Cartesian grid method are used together with a highly efficient multi-grid acceleration method and a local grid refinement strategy for optimal distribution of the grid points. The high-order Cartesian grid method is evaluated using test functions as well as for laminar and turbulent flows. The proposed approach maintains the high-order discretization and yields high-order accuracy of the numerical results. Large eddy simulation of a turbulent swirling flow indicates that the high-order wall treatment leads to significantly different results from those calculated using a low-order piecewise constant wall description. The differences in the results are smaller at a low level of turbulence near the inlet region, but become significant in the region far away from the inlet where the turbulence is more intense. In the latter situation the effect of the wall treatment is as important as the choice of the subgrid scale stress model.

  • 4.
    Hoffman, Johan
    Chalmers, Mathematics.
    Dynamic subgrid modelling for time dependent convection-diffusion-reaction equations with fractal solutions2002In: International Journal for Numerical Methods in Fluids, ISSN 0271-2091, E-ISSN 1097-0363, Vol. 40, no 3-4, p. 583-592Article in journal (Refereed)
    Abstract [en]

    A dynamic scale similarity model is proposed. The subgrid model is tested for model problems related to time dependent non-linear convection-diffusion-reaction systems with fractal solutions. The error of an approximate solution with subgrid model on a scale h is typically smaller than that of a solution without subgrid model on the scale h/2. We also consider the problem of a posteriori error estimation for fractal solutions, splitting the total computational error into a numerical error, related to the discretization of the continuous equations, and a modelling error, taking into account the quality of the subgrid model.

  • 5.
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Efficient computation of mean drag for the subcritical flow past a circular cylinder using general Galerkin G22009In: International Journal for Numerical Methods in Fluids, ISSN 0271-2091, E-ISSN 1097-0363, Vol. 59, no 11, p. 1241-1258Article in journal (Refereed)
    Abstract [en]

    General Galerkin (G2) is a new computational method for turbulent flow. where a stabilized Galerkin finite element method is used to compute approximate weak solutions to the Navier-Stokes equations directly, without any filtering of the equations as in a standard approach to turbulence simulation. such as large eddy simulation, and thus no Reynolds stresses are introduced, which need modelling. In this paper, G2 is used to compute the drag coefficient c(D) for the flow Past a circular cylinder at Reynolds number Re=3900, for which the flow is turbulent. It is found that it is possible to approximate c(D) to an accuracy of a few percent, corresponding to the accuracy in experimental results for this problem, using less than 10(5) mesh points, which makes the simulations possible using a standard PC. The mesh adaptively refined until a stopping criterion is reached with respect to the error in a chosen output of interest, which in this paper is c(D). Both the stopping criterion and the mesh-refinement strategy are based on a posteriori error estimates, in the form of a space-time integral of residuals times derivatives of the solution of it dual problem, linearized at the approximate solution, and with data coupling to the output of interest.

  • 6. Holmvall, M.
    et al.
    Lindström, Stefan B.
    KTH, School of Chemical Science and Engineering (CHE), Fibre and Polymer Technology.
    Uesaka, T.
    Simulation of two-phase flow with moving immersed boundaries2011In: International Journal for Numerical Methods in Fluids, ISSN 0271-2091, E-ISSN 1097-0363, Vol. 67, no 12, p. 2062-2080Article in journal (Refereed)
    Abstract [en]

    A two-dimensional multi-phase model for immiscible binary fluid flow including moving immersed objects is presented. The fluid motion is described by the incompressible NavierStokes equation coupled with a phase-field model based on van der Waals' free energy density and the CahnHilliard equation. A new phase-field boundary condition was implemented with minimization of the free energy in a direct way, to specifically improve the physical behavior of the contact line dynamics for moving immersed objects. Numerical stability and execution time were significantly improved by the use of the new boundary condition. Convergence toward the analytical solution was demonstrated for equilibrium contact angle, the LucasWashburn theory and Stefan's problem. The proposed model may be used for multi-phase flow problems with moving boundaries of complex geometry, such as the penetration of fluid into a deformable, porous medium.

  • 7.
    Izbassarov, Daulet
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Rosti, Marco E.
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Niazi Ardekani, Mehdi
    KTH, School of Engineering Sciences (SCI), Mechanics.
    Sarabian, Mohammad
    Hormozi, Sarah
    Brandt, Luca
    KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Engineering Sciences (SCI), Mechanics, Stability, Transition and Control. KTH, Centres, SeRC - Swedish e-Science Research Centre. KTH, School of Engineering Sciences (SCI), Mechanics, Physicochemical Fluid Mechanics. KTH, School of Engineering Sciences (SCI), Mechanics, Fluid Mechanics of Industrial Processes.
    Tammisola, Outi
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, Centres, SeRC - Swedish e-Science Research Centre.
    Computational modeling of multiphase viscoelastic and elastoviscoplastic flows2018In: International Journal for Numerical Methods in Fluids, ISSN 0271-2091, E-ISSN 1097-0363, Vol. 88, no 12, p. 521-543Article in journal (Refereed)
  • 8. Lorstad, D.
    et al.
    Francois, M.
    Shyy, W.
    Fuchs, Laszlo
    Assessment of volume of fluid and immersed boundary methods for droplet computations2004In: International Journal for Numerical Methods in Fluids, ISSN 0271-2091, E-ISSN 1097-0363, Vol. 46, no 2, p. 109-125Article in journal (Refereed)
    Abstract [en]

    The volume of fluid (VOF) and immersed boundary (IB) methods are two popular computational techniques for multi-fluid dynamics. To help shed light on the performance of both techniques, we present accuracy assessment, which includes interfacial geometry, detailed and global fluid flow characteristics, and computational robustness. The investigation includes the simulations of a droplet under static equilibrium as a limiting test case and a droplet rising due to gravity for Re less than or equal to 1000. Surface tension force models are key issues in both VOF and IB and alternative treatments are examined resulting in improved solution accuracy. A refined curvature model for VOF is also presented. With the newly developed interfacial treatments incorporated, both IB and VOF perform comparably well for the droplet dynamics under different flow parameters and fluid properties.

  • 9. Nazarov, M.
    et al.
    Hoffman, Johan
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Residual-based artificial viscosity for simulation of turbulent compressible flow using adaptive finite element methods2013In: International Journal for Numerical Methods in Fluids, ISSN 0271-2091, E-ISSN 1097-0363, Vol. 71, no 3, p. 339-357Article in journal (Refereed)
    Abstract [en]

    In this paper, we present a finite element method with a residual-based artificial viscosity for simulation of turbulent compressible flow, with adaptive mesh refinement based on a posteriori error estimation with sensitivity information from an associated dual problem. The artificial viscosity acts as a numerical stabilization, as shock capturing, and as turbulence capturing for large eddy simulation of turbulent flow. The adaptive method resolves parts of the flow indicated by the a posteriori error estimates but leaves shocks and turbulence under-resolved in a large eddy simulation. The method is tested for examples in 2D and 3D and is validated against experimental data.

  • 10.
    Nazarov, Murtazo
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    An adaptive finite element method for inviscid compressible flow2010In: International Journal for Numerical Methods in Fluids, ISSN 0271-2091, E-ISSN 1097-0363, Vol. 64, no 10-12, p. 1102-1128Article in journal (Refereed)
    Abstract [en]

    We present an adaptive finite element method for the compressible Euler equations, based on a posteriori error estimation of a quantity of interest in terms of a dual problem for the linearized equations. Continuous piecewise linear approximation is used in space and time, with componentwise weighted least-squares stabilization of convection terms and residual-based shock-capturing. The adaptive algorithm is demonstrated numerically for the quantity of interest being the drag force on a body.

  • 11.
    Pal, Mayur
    et al.
    Carbonate Research Shell International Exploration and Production, Rijswijk, Netherlands.
    Jönsson, Pär
    KTH, School of Industrial Engineering and Management (ITM), Materials Science and Engineering, Applied Process Metallurgy.
    Multiphysics modeling of an induction-stirred ladle in two and three dimensions2012In: International Journal for Numerical Methods in Fluids, ISSN 0271-2091, E-ISSN 1097-0363, Vol. 70, no 11, p. 1378-1392Article in journal (Refereed)
    Abstract [en]

    A unified model of an induction-stirred ladle in two and three dimensions is presented. Induction stirring of molten steel is a coupled multiphysics phenomena involving electromagnetic and fluid flow. Models presented in this paper gives a more accurate description of the real stirring conditions and flow pattern by taking into account the multiphysics behavior of the induction-stirring process in an induction-stirred ladle. This paper presents formulation of coupled electromagnetic and fluid flow equations. The coupled electromagnetic and fluid flow equations are solved with the use of the finite element method in two and three dimensions. The model is used to predict values of steel velocities and magnetic flux density. The model is also used to predict the effect of increased current density on flow velocity. Magnetic flux density values obtained from the model are verified against the experimental values.

  • 12. Revstedt, J.
    et al.
    Fuchs, Laszlo
    Handling complex boundaries on a Cartesian grid using surface singularities2001In: International Journal for Numerical Methods in Fluids, ISSN 0271-2091, E-ISSN 1097-0363, Vol. 35, no 2, p. 125-150Article in journal (Refereed)
    Abstract [en]

    This paper considers flow around arbitrarily shaped objects. The boundary conditions on the solid boundaries have been applied by replacing the boundary with a surface force distribution on the surface, such that the required boundary conditions are satisfied. The velocity on the boundary is determined by interpolation or by local (Gaussian space) average. The source terms are determined iteratively as part of the solution. They are then averaged and are smoothed out to nearby computational grid points. The method has been applied both to test problems as well as to more complex engineering problems, where there are not many real competitive alternatives to the proposed method. Simulations of creeping flow around a sphere were studied in order to evaluate the performance of different, competitive approaches of imposing boundary conditions. Using local averaging first-order accuracy is obtained; this can be improved by using a Lagrangian polynomial instead, although the convergence is then considerably slower. Simulations of flows around spheres in the Reynolds number range 1-1000 have been carried out. Finally, the approach was used to describe the impellers in a turbine agitated mixer. For these cases, the results show overall good agreement with other computational and experimental results.

  • 13.
    Vilela de Abreu, Rodrigo
    et al.
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz). KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Jansson, Niclas
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Hoffman, Johan
    KTH, School of Computer Science and Communication (CSC), High Performance Computing and Visualization (HPCViz).
    Adaptive Computation of Aeroacoustic Sources for a Rudimentary Landing Gear2014In: International Journal for Numerical Methods in Fluids, ISSN 0271-2091, E-ISSN 1097-0363, Vol. 74, no 6, p. 406-421Article in journal (Refereed)
    Abstract [en]

    We present our simulation results for the benchmark problem of the flow past a rudimentary landing gear using a General Galerkin FEM, also referred to as adaptive DNS/LES. In General Galerkin, no explicit subgrid model is used; instead, the computational mesh is adaptively refined with respect to an a posteriori error estimate of a quantity of interest in the computation, in this case, the drag force on the rudimentary landing gear. Turbulent boundary layers are modeled using a simple wall-layer model with the shear stress at walls proportional to the skin friction, which here is assumed to be small and, therefore, can be approximated by zero skin friction. We compare our results with experimental data and other state of the art computations, where we find good agreement in sound pressure levels, surface velocities, and flow separation. We also compare with detailed surface pressure experimental data where we find largely good agreement, apart from some local differences for which we discuss possible explanations.

  • 14.
    Zahedi, Sara
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 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 flow2012In: International Journal for Numerical Methods in Fluids, ISSN 0271-2091, E-ISSN 1097-0363, Vol. 69, no 9, p. 1433-1456Article in journal (Refereed)
    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.

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