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  • 1.
    Gong, Jing
    et al.
    Uppsala Univ., IT dept..
    Svärd, Magnus
    Nordström, Jan
    Artificial Dissipation for Strictly Stable Finite Volume Methods on Unstructured Meshes2004Ingår i: Computational Mechanics Abstracts: Volume II, 2004, s. 7-7Konferensbidrag (Refereegranskat)
  • 2. Mattsson, K.
    et al.
    Svärd, Magnus
    Nordstrom, J.
    Stable and accurate artificial dissipation2004Ingår i: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 21, nr 1, s. 57-79Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Stability for nonlinear convection problems using centered difference schemes require the addition of artificial dissipation. In this paper we present dissipation operators that preserve both stability and accuracy for high order finite difference approximations of initial boundary value problems.

  • 3. Mattsson, Ken
    et al.
    Svärd, Magnus
    Carpenter, Mark
    Nordstrom, Jan
    High-order accurate computations for unsteady aerodynamics2007Ingår i: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 36, nr 3, s. 636-649Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A high-order accurate finite difference scheme is used to perform numerical studies on the benefit of high-order methods. The main advantage of the present technique is the possibility to prove stability for the linearized Euler equations on a multi-block domain, including the boundary conditions. The result is a robust high-order scheme for realistic applications. Convergence studies are presented, verifying design order of accuracy and the superior efficiency of high-order methods for applications dominated by wave propagation. Furthermore, numerical computations of a more complex problem, a vortex-airfoil interaction, show that high-order methods are necessary to capture the significant flow features for transient problems and realistic grid resolutions. This methodology is easy to parallelize due to the multi-block capability. Indeed, we show that the speedup of our numerical method scales almost linearly with the number of processors.

  • 4. Nordstrom, J.
    et al.
    Svärd, Magnus
    Well-posed boundary conditions for the Navier-Stokes equations2005Ingår i: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 43, nr 3, s. 1231-1255Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this article we propose a general procedure that allows us to determine both the number and type of boundary conditions for time dependent partial differentia equations. With those, well-posedness can be proven for a general initial-boundary value problem. The procedure is exemplifie on the linearized Navier-Stokes equations in two and three space dimensions on a general domain.

  • 5. Nordström, Jan
    et al.
    Ham, Frank
    Shoeybi, Mohammad
    van der Weide, Edwin
    Svärd, Magnus
    Mattsson, Ken
    Laccarino, Gianluca
    Gong, Jing
    Uppsala Univ., IT dept..
    A hybrid method for unsteady inviscid fluid flow2009Ingår i: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 38, nr 4, s. 875-882Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We show how a stable and accurate hybrid procedure for fluid flow can be constructed. Two separate solvers, one using high order finite difference methods and another using the node-centered unstructured finite volume method are coupled in a truly stable way. The two flow solvers run independently and receive and send information from each other by using a third coupling code. Exact solutions to the Euler equations are used to verify the accuracy and stability of the new computational procedure. We also demonstrate the capability of the new procedure in a calculation of the flow in and around a model of a coral.

  • 6. Svärd, Magnus
    On coordinate transformations for summation-by-parts operators2004Ingår i: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 20, nr 1, s. 29-42Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    High order finite difference methods obeying a summation-by-parts (SBP) rule are developed for equidistant grids. With curvilinear grids, a coordinate transformation operator that does not destroy the SBP property must be used. We show that it is impossible to construct such an operator without decreasing the order of accuracy of the method.

  • 7. Svärd, Magnus
    et al.
    Carpenter, Mark H.
    Nordstrom, Jan
    A stable high-order finite difference scheme for the compressible Navier-Stokes equations, far-field boundary conditions2007Ingår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 225, nr 1, s. 1020-1038Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We construct a stable high-order finite difference scheme for the compressible Navier-Stokes equations, that satisfy an energy estimate. The equations are discretized with high-order accurate finite difference methods that satisfy a Summation-By-Parts rule. The boundary conditions are imposed with penalty terms known as the Simultaneous Approximation Term technique. The main result is a stability proof for the full three-dimensional Navier-Stokes equations, including the boundary conditions. We show the theoretical third-, fourth-, and fifth-order convergence rate, for a viscous shock, where the analytic solution is known. We demonstrate the stability and discuss the non-reflecting properties of the outflow conditions for a vortex in free space. Furthermore, we compute the three-dimensional vortex shedding behind a circular cylinder in an oblique free stream for Mach number 0.5 and Reynolds number 500.

  • 8. Svärd, Magnus
    et al.
    Gong, Jing
    Uppsala Univ., IT dept..
    Nordstroem, Jan
    An accuracy evaluation of unstructured node-centred finite volume methods2008Ingår i: Applied Numerical Mathematics, ISSN 0168-9274, E-ISSN 1873-5460, Vol. 58, nr 8, s. 1142-1158Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Node-centred edge-based finite volume approximations are very common in computational fluid dynamics since they are assumed to run on structured, unstructured and even on mixed grids. We analyse the accuracy properties of both first and second derivative approximations and conclude that these schemes cannot be used on arbitrary grids as is often assumed. For the Euler equations first-order accuracy can be obtained if care is taken when constructing the grid. For the Navier-Stokes equations, the grid restrictions are so severe that these finite volume schemes have little advantage over structured finite difference schemes. Our theoretical results are verified through extensive computations.

  • 9. Svärd, Magnus
    et al.
    Gong, Jing
    Uppsala Univ., IT dept..
    Nordstrom, Jan
    Stable artificial dissipation operators for finite volume schemes on unstructured grids2006Ingår i: Applied Numerical Mathematics, ISSN 0168-9274, E-ISSN 1873-5460, Vol. 56, nr 12, s. 1481-1490Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Our objective is to derive stable first-, second- and fourth-order artificial dissipation operators for node based finite volume schemes. Of particular interest are general unstructured grids where the strength of the finite volume method is fully utilised. A commonly used finite volume approximation of the Laplacian will be the basis in the construction of the artificial dissipation. Both a homogeneous dissipation acting in all directions with equal strength and a modification that allows different amount of dissipation in different directions are derived. Stability and accuracy of the new operators are proved and the theoretical results are supported by numerical computations.

  • 10. Svärd, Magnus
    et al.
    Gong, Jing
    Uppsala Univ., IT dept..
    Nordström, Jan
    An Accuracy Evaluation of Unstructured Node-Centred Finite Volume Methods2005Rapport (Övrigt vetenskapligt)
  • 11. Svärd, Magnus
    et al.
    Gong, Jing
    Uppsala Univ., IT dept..
    Nordström, Jan
    Stable Artificial Dissipation Operators for Finite Volume Schemes on Unstructured Grids2005Rapport (Övrigt vetenskapligt)
  • 12. Svärd, Magnus
    et al.
    Mattsson, K.
    Nordstrom, J.
    Steady-state computations using summation-by-parts operators2005Ingår i: Journal of Scientific Computing, ISSN 0885-7474, E-ISSN 1573-7691, Vol. 24, nr 1, s. 647-663Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    This paper concerns energy stability on curvilinear grids and its impact on steady-state calulations. We have done computations for the Euler equations using fifth order summation-by-parts block and diagonal norm schemes. By imposing the boundary conditions weakly we obtain a fifth order energy-stable scheme. The calculations indicate the significance of energy stability in order to obtain convergence to steady state. Furthermore, the difference operators are improved such that faster convergence to steady state are obtained.

  • 13. Svärd, Magnus
    et al.
    Nordstrom, J.
    Stability of finite volume approximations for the Laplacian operator on quadrilateral and triangular grids2004Ingår i: Applied Numerical Mathematics, ISSN 0168-9274, E-ISSN 1873-5460, Vol. 51, nr 1, s. 101-125Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Our objective is to analyse a commonly used edge based finite volume approximation of the Laplacian and construct an accurate and stable way to implement boundary conditions for time dependent problems. Of particular interest are unstructured grids where the strength of the finite volume method is fully utilised. As a model problem we consider the heat equation. We analyse the Cauchy problem in one and several space dimensions and prove stability on unstructured grids. Next, the initial-boundary value problem is considered and a scheme is constructed in a summation-by-parts framework. The boundary conditions are imposed in a stable and accurate manner, using a penalty formulation. Numerical computations of the wave equation in two-dimensions are performed, verifying stability and order of accuracy for structured grids. However, the results are not satisfying for unstructured grids. Further investigation reveals that the approximation is not consistent for general unstructured grids. However, grids consisting of equilateral polygons recover the convergence.

  • 14. Svärd, Magnus
    et al.
    Nordstrom, Jan
    A stable high-order finite difference scheme for the compressible Navier-Stokes equations no-slip wall boundary conditions2008Ingår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 227, nr 10, s. 4805-4824Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A stable wall boundary procedure is derived for the discretized compressible Navier-Stokes equations. The procedure leads to an energy estimate for the linearized equations. We discretize the equations using high-order accurate finite difference summation-by-parts (SBP) operators. The boundary conditions are imposed weakly with penalty terms. We prove linear stability for the scheme including the wall boundary conditions. The penalty imposition of the boundary conditions is tested for the flow around a circular cylinder at Ma = 0.1 and Re = 100. We demonstrate the robustness of the SBP-SAT technique by imposing incompatible initial data and show the behavior of the boundary condition implementation. Using the errors at the wall we show that higher convergence rates are obtained for the high-order schemes. We compute the vortex shedding from a circular cylinder and obtain good agreement with previously published (computational and experimental) results for lift, drag and the Strouhal number. We use our results to compare the computational time for a given for a accuracy and show the superior efficiency of the 5th-order scheme.

  • 15. Svärd, Magnus
    et al.
    Nordstrom, Jan
    On the order of accuracy for difference approximations of initial-boundary value problems2006Ingår i: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 218, nr 1, s. 333-352Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Finite difference approximations of the second derivative in space appearing in, parabolic, incompletely parabolic systems of, and 2nd-order hyperbolic, partial differential equations are considered. If the solution is pointwise bounded, we prove that finite difference approximations of those classes of equations can be closed with two orders less accuracy at the boundary without reducing the global order of accuracy. This result is generalised to initial-boundary value problems with an mth-order principal part. Then, the boundary accuracy can be lowered m orders. Further, it is shown that schemes using summation-by-parts operators that approximate second derivatives are pointwise bounded. Linear and nonlinear computations, including the two-dimensional Navier-Stokes equations, corroborate the theoretical results.

1 - 15 av 15
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  • en-US
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