A NEW APPROXIMATE RIEMANN SOLVER APPLIED TO HLLC METHOD

ELASKAR, SERGIO; FALCINELLI, OSCAR; TAMAGNO, JOSÉ

Sao Pablo

Congreso; World Congress on Computational Mechanics 2012; 2012

International Asociation on Computational Mechanics

In solving Euler equations applying finite volume techniques, the calculations ofnumerical fluxes across cell interfaces, have become an essential item. The numerical schemeexactitude, the ability of handle discontinuities and the correct prediction of the propagatingwaves velocity, are strongly dependent on such numerical fluxes. The pioneer work ofGodunov [1] was the starting point to solve the Euler equations by means of Riemann solvers.The excellent results obtained with Godunov technique, motivated several lines of researchwith the purpose of extending it to three dimensional flows, to achieve higher order ofaccuracy, etc. All calculating schemes that incorporate Riemann solvers are very precise, butunfortunately, computational demands are intense because of the non linear system ofalgebraic equations which must be solved in an iterative manner. An alternative which willdemand less computational effort, could be provided by the use of approximate Riemannsolvers, although less accurate and also, less robust. In this paper, an approximate Riemannsolver which does not require iterations, possesses a high degree of accuracy and a lowercomputational demand in solving the Euler equations, is described. It is based on the use ofdimensional analysis to reduce the number of independent variables needed to outline thephysics of the problem. The scheme here presented is compared in accuracy as well as incomputational effort with an exact iterative solver and with three well known approximatedsolvers: the Two Rarefactions Riemann Solver, the Two Shocks Riemann Solver, and anAdaptive version of these two. Substantially smaller mean errors have been found with theapproximation here presented than those found with the best of all the above mentionedapproximated solvers. Finally, a finite volume computer code to solve one-dimensional Eulerequations using the Harten, Lax and van Leer Contact (HLLC) scheme, was developed.Results obtained solving the Shock Tube problem with the HLLC scheme, have shown nosignificant differences in accuracy and robustness when either the new approximate Riemannsolver or the exact solver, are used. From the point of view of computer resources, the new approximate solver offers advantages.