Contribution to the Theoretical Study and Finite-Element Approximation of theMultidimensional, Multispecies, Hyperbolic System of Gas Dynamics

摘要

A number of points relating to the change of variables in thermodynamics(extensive, intensive variables) and in gas dynamics (conservative, entropic variables) are clarified. The system of compressible Euler equations for gas mixtures is described from the thermodynamic viewpoint without regard to any particular equation of state for the pressure. The concept of a K-diagonalizable system conveys in a single formalism the at once symmetric and kinetic aspects of the Euler equation system and permits generalization of the splitting of the Jacobian for the equations through the sign of the eigenvalues in a kinetic type splitting. A discontinuous Galerkin type finite element method of approximation involving entropic variables and a kinetic type splitting is proposed. Some of its properties are elucidated. The case of Friedrichs system is also considered. A method of mesh refinement is then implemented in two dimensions.