Roe-type Riemann solvers for general hyperbolic systems

• Published in: International journal for numerical methods in fluids Vol. 75; no. 7; pp. 467 - 486
• Main Authors: Castro, Cristóbal E., Toro, Eleuterio F.
• Format: Journal Article
• Language: English
• Published: Bognor Regis Blackwell Publishing Ltd 10.07.2014; Wiley Subscription Services, Inc
• Subjects: Accuracy; Coefficients; Computation; conservative finite volumes; Consumer goods; general equation of state; high order; Hyperbolic systems; Mathematical models; path-conservative; Riemann solver; Roe-type solver; Solvers
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.3903

SUMMARYWe present a Roe‐type weak formulation Riemann solver where the average coefficient matrix is computed numerically. The novelty of this approach is that it is general enough that can be applied to any hyperbolic system while retaining the accuracy of the original Roe solver. We show applications to the compressible Euler equations with general equation of state. An alternative version of the method uses directly the eigenvectors in the averaging process, simplifying the algorithm. These new solvers are applied in conservative and path‐conservative schemes with high‐order accuracy and on unstructured meshes. Copyright © 2014 John Wiley & Sons, Ltd. We present a Roe‐type weak formulation Riemann solver where the average coefficient matrix is computed numerically. The novelty of this approach is that it is general enough that can be applied to any hyperbolic system while retaining the accuracy of the original Roe solver. Here, we show the solution of the Euler system using a third‐order accuracy finite volume method and our new solver used to compute the numerical flux. Left: ideal EOS. Right: van der Waals EOS.