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  • 1.
    Ghasemi, Fatemeh
    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.
    Coupling Requirements for Multiphysics Problems Posed on Two Domains2017In: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 55, no 6, p. 2885-2904Article in journal (Refereed)
    Abstract [en]

    We consider two hyperbolic systems in first order form of different size posed on two domains. Our ambition is to derive general conditions for when the two systems can and cannot be coupled. The adjoint equations are derived and well-posedness of the primal and dual problems is discussed. By applying the energy method, interface conditions for the primal and dual problems are derived such that the continuous problems are well posed. The equations are discretized using a high order finite difference method in summation-by-parts form and the interface conditions are imposed weakly in a stable way, using penalty formulations. It is shown that one specic choice of penalty matrices leads to a dual consistent scheme. By considering an example, it is shown that the correct physical coupling conditions are contained in the set of well posed coupling conditions. It is also shown that dual consistency leads to superconverging functionals and reduced stiffness.

  • 2. Kreiss, Gunilla
    et al.
    Efraimsson, Gunilla
    Nordström, Jan
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Elimination of first order errors in shock calculations2001In: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 38, p. 1986-1998Article in journal (Refereed)
  • 3.
    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.

  • 4.
    Nordström, Jan
    et al.
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Svärd, Magnus
    Uppsala universitet, Avdelningen för teknisk databehandling.
    Well-posed boundary conditions for the Navier-Stokes equations2005In: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 43, p. 1231-1255Article in journal (Refereed)
1 - 4 of 4
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