An upwind second-order scheme for compressible duct flows
SIAM Journal on Scientific and Statistical Computing
The generalized Riemann problem for reactive flows
Journal of Computational Physics
Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
A direct Eulerian GRP scheme for compressible fluid flows
Journal of Computational Physics
Journal of Computational Physics
Implementation of the GRP scheme for computing radially symmetric compressible fluid flows
Journal of Computational Physics
Journal of Computational Physics
An adaptive GRP scheme for compressible fluid flows
Journal of Computational Physics
Journal of Computational Physics
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The generalized Riemann problem (GRP) method was proposed for compressible fluid flows based on the Lagrangian formulation [M. Ben-Artzi, J. Falcovitz, A second-order Godunov-type scheme for compressible fluid dynamics, J. Comput. Phys., 55(1) (1984) 1-32], and a direct Eulerian version was developed in [M. Ben-Artzi, J. Li, G. Warnecke, A direct Eulerian GRP scheme for compressible fluid flows, J. Comput. Phys., 28 (2006) 19-43] by using the concept of Riemann invariants. The central feature of the GRP method is the resolution of centered rarefaction waves. In this note we show how to use the concept of Riemann invariants in order to resolve the rarefaction waves in the Lagrangian coordinate system and result in the GRP scheme.