An adaptive Riemann solver using a two-shock approximation

• Published in: Computers & fluids Vol. 28; no. 6; pp. 741 - 777
• Main Author: Rider, W.J.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.07.1999; Elsevier Science
• Subjects: Compressible flows; shock and detonation phenomena; Equations of state; Exact sciences and technology; Fluid dynamics; Functions; Fundamental areas of phenomenology (including applications); General theory; Physics; Problem solving; Shock-wave interactions and shock effects; Shock-wave interactions and shockeffects; Velocity; Discontinuity; Shock waves; Approximation; Equations of state; Riemann problem; Gas dynamics; Rarefaction wave; Pressure distribution; Perfect gas; Adaptive method
• ISSN: 0045-7930; 1879-0747
• DOI: 10.1016/S0045-7930(98)00033-4

An approximate Riemann solver is developed using a linear approximation for the shock velocity in particle velocity. The approximation is a second-order Taylor expansion for the pressure in velocity. Bounds are established for the values of the linear coefficient while assuring a physical entropy satisfying solution. This is done rigorously for an ideal gas and is incorporated in a nonlinear function that recovers both the weak and strong shock limits. Extensions to more general equations of state are discussed through several examples (JWL and Mie-Grüneisen). For strong rarefactions, an exponential function is used for the wave curve that has appropriate asymptotic properties and is continuous to second-order with the shock curve at the centering point for the Riemann problem. This provides the Riemann solver with an adaptive character with an inexpensive, but accurate approximation for weak discontinuities, and asymptotically appropriate approximations for strong discontinuities.