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Higher Order Numerical Schemes for Hyperbolic Systems with an Application in Fluid Dynamics

In: Hyperbolic Problems: Theory, Numerics, Applications

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  • V. Dolejší

    (Charles University)

Abstract

We deal with a numerical solution of the (nonlinear hyperbolic) system of the Euler equations, which describe a motion of inviscid compressible flow. We present a higher order numerical scheme with respect to the space as well as time coordinates. This scheme is based on the discontinuous Galerkin method for the space semi-discretization and the backward difference formula for the time discretization. We employ a suitable linearization of inviscid fluxes and an explicit extrapolation in nonlinear terms, which preserve a high order of accuracy and lead to a linear algebraic problem at each time step. Moreover, we discuss a use of non-reflecting boundary conditions at inflow/outflow parts of boundary and present a stabilization technique that avoid spurious oscillations of numerical solution in vicinity of shock waves. Finally, two numerical examples of unsteady compressible flow demonstrating an efficiency of the scheme are presented.

Suggested Citation

  • V. Dolejší, 2008. "Higher Order Numerical Schemes for Hyperbolic Systems with an Application in Fluid Dynamics," Springer Books, in: Sylvie Benzoni-Gavage & Denis Serre (ed.), Hyperbolic Problems: Theory, Numerics, Applications, pages 77-88, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-75712-2_6
    DOI: 10.1007/978-3-540-75712-2_6
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