Eighth Mississippi State - UAB Conference on Differential Equations and Computational Simulations. Electron. J. Diff. Eqns., Conference 19 (2010), pp. 65-73.

A hybrid semi-primitive shock capturing scheme for conservation laws

Ritesh Kumar Dubey

A hybrid semi-primitive shock capturing scheme is presented for hyperbolic problems. Upwind based construction is done using explicit information on the wave propagation direction associated with the problem. This scheme captures the shock waves at right location but shows unphysical sonic expansion shock. This phenomena of unphysical expansion shock in the presence of expensive sonic point is not surprising and it is common for the wave based upwind schemes. A hybrid scheme approach using an iteration criteria based on sonic entropy fix is proposed to avoid such expansion shocks. Numerical results for scalar test problems are presented which show that proposed scheme captures the shock accurately.

Published September 25, 2010.
Math Subject Classifications: 35L65, 65M06, 65M12.
Key Words: Hyperbolic conservation laws; primitive scheme; upwind difference; hybrid schemes.

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Ritesh Kumar Dubey
Institut de Mathématiques de Toulouse
Université Paul Sabatier, 118 route de Narbonne
F-31062 Toulouse Cedex 9, Fance
email: riteshkd@gmail.com

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