The space–time CE/SE method for solving ultra-relativistic Euler equations

Abstract

This paper reports the application of space–time conservation element and solution element (CE/SE) method for solving one- and two-dimensional special ultra-relativistic Euler equations. For a sufficiently large internal energy of fluid particles the rest-mass energy of the fluid can be ignored. Then, the fluid flow can be modeled by ultra-relativistic Euler equations consisting a pair of coupled first-order non-linear hyperbolic partial differential equations. The governing equations describe the flow of a perfect fluid in terms of the particle density ρ, the spatial part of the four-velocity u and the pressure p. The CE/SE method is capable to accurately captures the sharp propagating wavefront of relativistic fluid without excessive numerical diffusion or spurious oscillations. In contrast to the existing upwind finite volume schemes, the Riemann solver and reconstruction procedure are not the building block of the suggested method. The method differs from the previous techniques because of global and local flux conservation in a space–time domain without resorting to interpolation or extrapolation. In order to reveal the efficiency and performance of the approach, several numerical test cases are presented in this manuscript. For validation, the results of current method are compared with other finite-volume schemes.