CONICET | Buscador de Institutos y Recursos Humanos

In solving the unsteady Euler equations applying the finite volume technique, the precision of the whole numerical scheme, its ability to handle discontinuities and the correct prediction of the velocity of propagating waves, are strongly dependent on how good are the calculation of numerical fluxes at cells interfaces. Early attempts to develop these fluxes being only based on numerical considerations did not perform well on handling discontinuous solutions of the equations of fluid dynamics. Most of the inconveniences arisen from this way of doing things were overcome when Godunov in 1959, published his work. This new approach, in striking difference to previous ones, it is fully supported by physical considerations and its principal tool is the Riemann solver. The success of Godunov´s technique motivated many lines of research with the purpose of extending its applications to complex three-dimensional flows and achieving higher accuracy. All calculation schemes that incorporate Riemann solvers are by itself precise, but unfortunately, computational demands are intense. This is mainly originated on the system of non linear algebraic equations which must be solved in an iterative manner to find, at each point of the computational domain, an exact solution of a Riemann problem. Alternatives which will demand less computational effort, are provided by the use of approximate Riemann solvers, although less accurate and also, less robust. In this chapter, however, an approximate Riemann solver which does not require iterations, possesses a high degree of exactitude and a much lower computational demand on its use for solving the Euler equations, is described. Furthermore, it is proved that it can replace to the exact Riemann solver with no significant differences in accuracy and/or robustness, but offering appreciable advantages from the point of view of computer resources.

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