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  • 1.
    Delorme, Yann T.
    et al.
    Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa, Israel.
    Puri, Kunal
    Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa, Israel.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Linders, Viktor
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Dong, Suchuan
    Department of Mathematics, Purdue University, West Lafayette, IN, USA.
    Frankel, Steven H.
    Faculty of Mechanical Engineering, Technion-Israel Institute of Technology, Haifa, Israel.
    A simple and efficient incompressible Navier-Stokes solver for unsteady complex geometry flows on truncated domains2017In: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 150, p. 84-94Article in journal (Refereed)
    Abstract [en]

    Incompressible Navier-Stokes solvers based on the projection method often require an expensive numerical solution of a Poisson equation for a pressure-like variable. This often involves linear system solvers based on iterative and multigrid methods which may limit the ability to scale to large numbers of processors. The artificial compressibility method (ACM) [6] introduces a time derivative of the pressure into the incompressible form of the continuity equation creating a coupled closed hyperbolic system that does not require a Poisson equation solution and allows for explicit time-marching and localized stencil numerical methods. Such a scheme should theoretically scale well on large numbers of CPUs, GPU'€™s, or hybrid CPU-GPU architectures. The original ACM was only valid for steady flows and dual-time stepping was often used for time-accurate simulations. Recently, Clausen [7] has proposed the entropically damped artificial compressibility (EDAC) method which is applicable to both steady and unsteady flows without the need for dual-time stepping. The EDAC scheme was successfully tested with both a finite-difference MacCormack'€™s method for the two-dimensional lid driven cavity and periodic double shear layer problem and a finite-element method for flow over a square cylinder, with scaling studies on the latter to large numbers of processors. In this study, we discretize the EDAC formulation with a new optimized high-order centered finite-difference scheme and an explicit fourth-order Runge-€“Kutta method. This is combined with an immersed boundary method to efficiently treat complex geometries and a new robust outflow boundary condition to enable higher Reynolds number simulations on truncated domains. Validation studies for the Taylor-€“Green Vortex problem and the lid driven cavity problem in both 2D and 3D are presented. An eddy viscosity subgrid-scale model is used to enable large eddy simulations for the 3D cases. Finally, an application to flow over a sphere is presented to highlight the boundary condition and performance comparisons to a traditional incompressible Navier-€“Stokes solver is shown for the 3D lid driven cavity. Overall, the combined EDAC formulation and discretization is shown to be both effective and affordable.

  • 2.
    Linders, Viktor
    et al.
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Kupiainen, Marco
    Rossby Centre SMHI, Norrköping, Sweden.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Summation-by-Parts Operators with Minimal Dispersion Error for Coarse Grid Flow Calculations2016Report (Other academic)
    Abstract [en]

    We present a procedure for constructing Summation-by-Parts operators with minimal dispersion error both near and far from numerical interfaces. Examples of such operators are constructed and compared with purely periodic stencils as well as non-optimised Summation-by-Parts operators of higher order. Experiments show that the optimised operators are superior for wave propagation and turbulent flows involving large wavenumbers, long solution times and large ranges of resolution scales.

  • 3.
    Linders, Viktor
    et al.
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Kupiainen, Marko
    SMHI, SE-601 76 Norrköping, Sweden.
    Frankel, Steven H.
    Technion, Haifa, Israel 320003.
    Delorme, Yann
    Technion, Haifa, Israel 320003.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Summation-by-parts Operators with Minimal Dispersion Error for Accurate and Efficient Flow Calculations2016Conference paper (Refereed)
    Abstract [en]

    We develop summation-by-parts operators with minimal dispersion errors both near and far from boundaries and interfaces. Such operators are superior to classical stencils for problems involving high frequency waves or multi-frequency solutions over long time intervals with a relatively coarse spatial mesh. This is demonstrated by solving the Taylor-Green vortex flow with optimised and classical operators both in a purely periodic setting as well as in the presence of numerical interfaces.

  • 4.
    Linders, Viktor
    et al.
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Lundquist, Tomas
    University of Cape Town, South Africa.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    On the order of Accuracy of Finite Difference Operators on Diagonal Norm Based Summation-By-Parts Form2017Report (Other academic)
    Abstract [en]

    In this paper we generalise results regarding the order of accuracy of finite difference operators on Summation-By-Parts (SBP) form, previously known to hold on uniform grids, to grids with arbitrary point distributions near domain boundaries. We give a definite proof that the order of accuracy in the interior of a diagonal norm based SBP operator must be at least twice that of the boundary stencil, irrespective of the grid point distribution near the boundary. Additionally, we prove that if the order of accuracy in the interior is precisely twice that of the boundary, then the diagonal norm defines a quadrature rule of the same order as the interior stencil. Again, this result is independent of the grid point distribution near the domain boundaries.

  • 5.
    Linders, Viktor
    et al.
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Lundquist, Tomas
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    On the order of Accuracy of Finite Difference Operators on Diagonal Norm Based Summation-by-Parts Form2018In: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 56, no 2, p. 1048-1063Article in journal (Refereed)
    Abstract [en]

    In this paper we generalize results regarding the order of accuracy of finite difference operators on summation-by-parts (SBP) form, previously known to hold on uniform grids, to grids with arbitrary point distributions near domain boundaries. We give a definite proof that the order of accuracy in the interior of a diagonal norm based SBP operator must be at least twice that of the boundary stencil, irrespective of the grid point distribution near the boundary. Additionally, we prove that if the order of accuracy in the interior is precisely twice that of the boundary, then the diagonal norm defines a quadrature rule of the same order as the interior stencil. Again, this result is independent of the grid point distribution near the domain boundaries.

  • 6.
    Linders, Viktor
    et al.
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, The Institute of Technology.
    Uniformly Best Wavenumber Approximations by Spatial Central Difference Operators2015Report (Other academic)
    Abstract [en]

    We construct accurate central difference stencils for problems involving high frequency waves or multi-frequency solutions over long time intervals with a relatively coarse spatial mesh, and with an easily obtained bound on the dispersion error. This is done by demonstrating that the problem of constructing central difference stencils that have minimal dispersion error in the infinity norm can be recast into a problem of approximating a continuous function from a finite dimensional subspace with a basis forming a Chebyshev set. In this new formulation, characterising and numerically obtaining optimised schemes can be done using established theory.

  • 7.
    Linders, Viktor
    et al.
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Uniformly Best Wavenumber Approximations by Spatial Central Difference Operators2015In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 300, p. 695-709Article in journal (Refereed)
    Abstract [en]

    We construct accurate central difference stencils for problems involving high frequency waves or multi-frequency solutions over long time intervals with a relatively coarse spatial mesh, and with an easily obtained bound on the dispersion error. This is done by demonstrating that the problem of constructing central difference stencils that have minimal dispersion error in the infinity norm can be recast into a problem of approximating a continuous function from a finite dimensional subspace with a basis forming a Chebyshev set. In this new formulation, characterising and numerically obtaining optimised schemes can be done using established theory.

  • 8.
    Linders, Viktor
    et al.
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Uniformly Best Wavenumber Approximations by Spatial Central Difference Operators: An Initial Investigation2015In: Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014 / [ed] Mejdi Azaïez, Henda El Fekih, Jan S. Hesthaven, Springer, 2015, p. 325-333Chapter in book (Refereed)
    Abstract [en]

    A characterisation theorem for best uniform wavenumber approximations by central difference schemes is presented. A central difference stencil is derived based on the theorem and is compared with dispersion relation preserving schemes and with classical central differences for a relevant test problem.

  • 9.
    Linders, Viktor
    et al.
    Facultyof, Mechanica, Engineering,Technion, Israel Institute of Technology, Haifa, Israel.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Frankel, Steven H.
    Facultyof, Mechanica, Engineering,Technion, Israel Institute of Technology, Haifa, Israel.
    Convergence and stability properties of summation-by-parts in time2019Report (Other academic)
    Abstract [en]

    We extend the list of stability properties satisfied by Summation-By-Parts (SBP) in time to include strong S-stability, dissipative stability and stiff accuracy. Further, it is shown that SBP in time is B-convergent for strictly contractive non-linear problems and weakly convergent for non-linear problems that are both contractive and dissipative

  • 10.
    Linders, Viktor
    et al.
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Kupiainen, Marco
    Rossby Centre SMHI, Norrköping, Sweden.
    Nordström, Jan
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Summation-by-Parts Operators with Minimal Dispersion Error for Coarse Grid Flow Calculations2017In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 340, p. 34p. 160-176Article in journal (Refereed)
    Abstract [en]

    We present a procedure for constructing Summation-by-Parts operators with minimal dispersion error both near and far from numerical interfaces. Examples of such operators are constructed and compared with a higher order non-optimised Summation-by-Parts operator. Experiments show that the optimised operators are superior for wave propagation and turbulent flows involving large wavenumbers, long solution times and large ranges of resolution scales.

  • 11.
    Nordström, Jan
    et al.
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Linders, Viktor
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Well-posed and Stable Transmission Problems2017Report (Other academic)
    Abstract [en]

    We introduce the notion of a transmission problem to describe a general class of problems where different dynamics are coupled in time. Well-posedness and stability is analysed for continuous and discrete problems using both strong and weak formulations, and a general transmission condition is obtained. The theory is applied to several examples including the coupling of fluid flow models, multi-grid implementations, multi-block formulations and numerical filtering.

  • 12.
    Nordström, Jan
    et al.
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Linders, Viktor
    Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.
    Well-posed and stable transmission problems2018In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 364, p. 95-110Article in journal (Refereed)
    Abstract [en]

    We introduce the notion of a transmission problem to describe a general class of problems where different dynamics are coupled in time. Well-posedness and stability are analysed for continuous and discrete problems using both strong and weak formulations, and a general transmission condition is obtained. The theory is applied to the coupling of fluid-acoustic models, multi-grid implementations, adaptive mesh refinements, multi-block formulations and numerical filtering.

    The full text will be freely available from 2020-03-28 16:03
1 - 12 of 12
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