A hybrid semi-primitive shock capturing scheme for conservation laws

• Main Author: Ritesh Kumar Dubey
• Format: Article
• Language: English
• Published: Texas State University 2010-09-01
• Series: Electronic Journal of Differential Equations
• Subjects: Hyperbolic conservation laws; primitive scheme; upwind difference; hybrid schemes
• Online Access: http://ejde.math.txstate.edu/conf-proc/19/d2/abstr.html

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.