Sonic-point capturing

A prototype scheme that produces perfectly smooth transonic solutions to nozzle-flow problems is derived and tested. The basic upwind scheme is described as well as satisfying the entropy condition, treatment of the source term, and numerical verification. The analysis yielded a numerical flux function for use near a sonic point, which is based on a full model of a transonic expansion wave, and a matched treatment for the source term.

[1]  Bram van Leer,et al.  On the Relation Between the Upwind-Differencing Schemes of Godunov, Engquist–Osher and Roe , 1984 .

[2]  P. Woodward,et al.  The numerical simulation of two-dimensional fluid flow with strong shocks , 1984 .

[3]  Phillip Colella,et al.  Glimm's Method for Gas Dynamics , 1982 .

[4]  Randall J. LeVeque,et al.  A geometric approach to high resolution TVD schemes , 1988 .

[5]  P. Roe.  CHARACTERISTIC-BASED SCHEMES FOR THE EULER EQUATIONS , 1986 .

[6]  S. Osher.  Riemann Solvers, the Entropy Condition, and Difference , 1984 .

[7]  S. Osher.  Riemann Solvers, the Entropy Condition and High Resolution Difference Approximations, , 1984 .

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

[9]  Thomas W. Roberts,et al.  The behavior of flux difference splitting schemes near slowly moving shock waves , 1990 .

[10]  S. F. Davis,et al.  A rotationally biased upwind difference scheme for the euler equations , 1984 .

[11]  Stanley Osher,et al.  Upwind schemes and boundary conditions with applications to Euler equations in general geometries , 1983 .

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

[13]  Bram van Leer,et al.  An Implementation of a Grid-Independent Upwind Scheme for the Euler Equations , 1989 .

[14]  P. L. Roe,et al.  A survey of upwind differencing techniques , 1989 .