An entropy satisfying relaxation/HLLC solver for gas dynamics that computes vacuum without correction
نویسندگان
چکیده
The limit of vanishing ratio of the electron mass to the ion mass in the isentropic transient Euler-Poisson equations with periodic boundary conditions is proved. The equations consist of the conservation laws for the electron density and current density for given ion density, coupled to the Poisson equation for the electrostatic potential. The limit is related to the low-Mach-number limit of Klainerman and Majda. In particular, the limit velocity satisfies the incompressible Euler equation with damping. The difference to the zero-Mach-number limit comes from the electrostatic potential which needs to be controlled. This is done by a reformulation of the equations in terms of the enthalpy, higher-order energy estimates and a careful use of the Poisson equation.
منابع مشابه
A multiwave approximate Riemann solver for ideal MHD based on relaxation. I: theoretical framework
We present a relaxation system for ideal MHD that is an extension of the Suliciu relaxation system for the Euler equations of gas dynamics. From it one can derive approximate Riemann solvers with three or seven waves, that generalize the HLLC solver for gas dynamics. Under some subcharacteristic conditions, the solvers satisfy discrete entropy inequalities, and preserve positivity of density an...
متن کاملEntropy satisfying flux vector splittings and kinetic BGK models
We establish forward and backward relations between entropy satisfying BGK relaxation models such as those introduced previously by the author and the rst order ux vector splitting numerical methods for general systems of conservation laws. Classically, to a kinetic BGK model that is compatible with some family of entropies we can associate an entropy ux vector splitting. We prove that the conv...
متن کاملSemi-discrete Entropy Satisfying Approximate Riemann Solvers. The Case of the Suliciu Relaxation Approximation
In this work we establish conditions for an approximate simple Riemann solver to satisfy a semi-discrete entropy inequality. The semi-discrete approach is less restrictive than the fully-discrete case and allows to grant some other good properties for numerical schemes. First, conditions are established in an abstract framework for simple Riemann solvers to satisfy a semi-discrete entropy inequ...
متن کاملA Robust and Entropy-Satisfying Numerical Scheme for Fluid Flows in Discontinuous Nozzles
We propose in this work an original finite volume scheme for the system of gas dynamics in a nozzle. Our numerical method is based on a piecewise constant discretization of the crosssection and on a approximate Riemann solver in the sense of Harten, Lax and van Leer. The solver is obtained by the use of a relaxation approximation that leads to a positive and entropy satisfying numerical scheme ...
متن کاملRelaxation of fluid systems
We propose a relaxation framework for general fluid models which can be understood as a natural extension of the Suliciu approach in the Euler setting. In particular, the relaxation system may be totally degenerate. Several stability properties are proved. The relaxation procedure is shown to be efficient in the numerical approximation of the entropy weak solutions of the original PDEs. The num...
متن کامل