Finite Volume Software for Gasdynamics and Magnetogasdynamics Equations

ELASKAR, SERGIO; MAGLIONE, LIVIO; TAMAGNO, JOSÉ

Congreso; Pan-American Congress of Applied Mechanics - PACAM XI,; 2010

  Two codes for computers have been developed. One, to study flows in which an electrically conducting gas moves in a magnetic field and the other one to solve Euler equations. The first code solves 2D, time-dependent, viscous and resistive MGD flows. Its numerical approach is based on a finite volume discretization technique and to compute the numerical fluxes across cells interfaces, an approximate Riemann solver coupled with the Total Variation Diminishing (TVD) scheme proposed by Harten and Yee is utilized.  The eigensystem introduced by Powell and the eigenvectors normalization by Zarachay et al. have also been used. To verify its accuracy, the MGD code has been applied to the simulations of a magnetogasdynamics Riemann problem and of the Hartmann flow. The results obtained show good agreement with those reported by other authors. In the second code, a TVD scheme has been implemented on a non structured 3D finite volume formulation for solving the Euler equations. To simultaneously, achieve adequate accuracy in smooth flows, high resolution at flow discontinuities and to avoid spurious oscillations, different flux limiter functions are applied in a wave-to-wave basis. In this paper are analyzed the numerical viscosity reduction resulting after using compressive limiter functions in waves from the families two to four, and the ability of  diffusive limiter functions for the family waves one and five to capture pressure discontinuities whereas preserving the robustness of the TVD scheme. This sort of adaptive scheme has satisfactorily been applied to the slip interface between two parallel flows, and to supersonic flows over and airfoil, a wedge and a blunted bi-conic body.