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

V. Dolejší ()
Additional contact information
V. Dolejší: Charles University

A chapter in Hyperbolic Problems: Theory, Numerics, Applications, 2008, pp 77-88 from Springer

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.

Keywords: Euler Equation; Hyperbolic System; Riemann Problem; Discontinuous Galerkin Method; Stabilization Technique (search for similar items in EconPapers)
Date: 2008
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-75712-2_6

Ordering information: This item can be ordered from
http://www.springer.com/9783540757122

DOI: 10.1007/978-3-540-75712-2_6

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().