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

Title: A hybrid semi-primitive shock capturing scheme for conservation laws

Author: Ritesh Kumar Dubey (Univ. Paul  Sabatier, Toulouse Cedex 9, Fance)
 
Abstract: 
  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.