An scheme for inviscid compressible ow, considering a gas in thermo chemical equilibrium

SALDÍA, JUAN; ELASKAR, SERGIO; TAMAGNO, JOSÉ

Córdoba

Congreso; IV CLAM, 2012 - Congreso Latinoamericano de Matemáticos; 2012

Universidad Nacional de Córdoba

In this work, a nite volume scheme for the solution of the unsteady one and two dimensionalEuler equations, considering the working gas in thermo-chemical equilibrium,is presented. With the aim of achieving Total Variation Diminishing (TVD) properties inthe numerical scheme, a technique proposed in [1], based on the adaptive use of dierentlimiter functions in each wave of the Riemann problem, is applied. With this techniquethe unwanted eects of the articial viscosity on the capture of contact discontinuitiesare reduced, but without losing robustness in shock waves resolution. The chemical equilibriumthermodynamical properties computation are carried out through a Gibbs energyminimization procedure. Regarding this issue, a data base that stores discrete values ofthermodynamical variables needed in the numerical scheme is builded. Then, an ecientinterpolation procedure of these values is used during the uid ow computations. Thisprocedure increase the accuracy at similar computational cost in comparison with a widelyused approach, the Tannehill curves t. With the aim of evaluating the developed numericalscheme, results obtained solving several one dimensional Riemann problems, speciallyselected for this specic purpose, are presented. Also, in order to test the scheme in thebidimensional case, results of the unsteady ow in cylindrical explosions, and of the steadystate solution of hypersonic ow over a doble wedge and a blunt body, are presented.