Recent Developments of the GRP Method

A review of about a decade of development of the generalized Riemann problem (GRP) scheme is presented. The method is briefly outlined, followed by various numerical and physical extensions. The range of versatile applications of the GRP method is illustrated through numerous examples.

[1]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method , 1979 .

[2]  R. D. Richtmyer,et al.  Difference methods for initial-value problems , 1959 .

[3]  J. Falcovitz,et al.  An upwind second-order scheme for compressible duct flows , 1986 .

[4]  O. Igra,et al.  Numerical Solution to Rarefaction or Shock Wave/Duct Area-Change Interaction , 1986 .

[5]  J. Falcovitz,et al.  A Singularities Tracking Conservation Laws Scheme for Compressible Duct Flows , 1994 .

[6]  GRP — An analytic approach to high-resolution upwind schemes for compressible fluid flow , 1985 .

[7]  Matania Ben-Artzi,et al.  Computation of reactive duct flows in external fields , 1990 .

[8]  P. Raviart,et al.  An asymptotic expansion for the solution of the generalized Riemann problem Part I: General theory , 1988 .

[9]  P. Colella,et al.  Theoretical and numerical structure for reacting shock waves , 1986 .

[10]  Numerical simulation of the head‐on reflection of a regular reflection , 1993 .

[11]  J. Haas,et al.  Interaction of weak shock waves with cylindrical and spherical gas inhomogeneities , 1987, Journal of Fluid Mechanics.

[12]  Matania Ben-Artzi,et al.  Application of the “generalized Riemann problem” method to 1-D compressible flows with material interfaces , 1986 .

[13]  On Majda's model for dynamic combustion , 1992 .

[14]  R. Hillier,et al.  Computation of shock wave diffraction at a ninety degrees convex edge , 1991 .

[15]  J. Falcovitz,et al.  A second-order Godunov-type scheme for compressible fluid dynamics , 1984 .

[16]  THE GENERALIZED RIEMANN PROBLEM IN COMPRESSIBLE DUCT FLOW , 1985 .

[17]  Li Ta-Tsien,et al.  A global asymptotic expansion for the solution to the generalized Riemann problem , 1991 .

[18]  P. Raviart,et al.  An asymptotic expansion for the solution of the generalized Riemann problem. Part 2 : application to the equations of gas dynamics , 1989 .

[19]  P. Raviart,et al.  Approximate solution of the generalized Riemann problem and applications , 1987 .

[20]  G. Strang On the Construction and Comparison of Difference Schemes , 1968 .

[21]  Matania Ben-Artzi,et al.  The generalized Riemann problem for reactive flows , 1989 .

[22]  I. Bohachevsky,et al.  Finite difference method for numerical computation of discontinuous solutions of the equations of fluid dynamics , 1959 .