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  • 1.
    Eriksson, Sofia
    et al.
    Uppsala University.
    Abbas, Qaisar
    Uppsala University.
    Nordström, Jan
    Linköping University.
    A stable and conservative method for locally adapting the design order of finite difference schemes2011In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 230, no 11, p. 4216-4231Article in journal (Refereed)
    Abstract [en]

    A procedure to locally change the order of accuracy of finite difference schemes is developed. The development is based on existing Summation-By-Parts operators and a weak interface treatment. The resulting scheme is proven to be accurate and stable.

    Numerical experiments verify the theoretical accuracy for smooth solutions. In addition, shock calculations are performed, using a scheme where the developed switching procedure is combined with the MUSCL technique.

  • 2.
    Eriksson, Sofia
    et al.
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Nordström, Jan
    Linköping University.
    Finite difference schemes with transferable interfaces for parabolic problems2018In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 375, p. 935-949Article in journal (Refereed)
    Abstract [en]

    We derive a method to locally change the order of accuracy of finite difference schemes that approximate the second derivative. The derivation is based on summation-by-parts operators, which are connected at interfaces using penalty terms. At such interfaces, the numerical solution has a double representation, with one representation in each domain. We merge this double representation into a single one, yielding a new scheme with unique solution values in all grid points. The resulting scheme is proven to be stable, accurate and dual consistent. (C) 2018 Elsevier Inc. All rights reserved.

  • 3.
    Nordström, Jan
    et al.
    Linköping University.
    Eriksson, Sofia
    Uppsala University.
    Eliasson, Peter
    The Swedish Defense Research Agency.
    Weak and strong wall boundary procedures and convergence to steady-state of the Navier-Stokes equations2012In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 231, no 14, p. 4867-4884Article in journal (Refereed)
    Abstract [en]

    We study the influence of different implementations of no-slip solid wall boundary conditions on the convergence to steady-state of the Navier–Stokes equations. The various approaches are investigated using the energy method and an eigenvalue analysis. It is shown that the weak implementation is superior and enhances the convergence to steady-state for coarse meshes. It is also demonstrated that all the stable approaches produce the same convergence rate as the mesh size goes to zero. The numerical results obtained by using a fully nonlinear finite volume solver support the theoretical findings from the linear analysis.

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