A Second-Order Finite-Volume Scheme for Euler Equations: Kinetic Energy Preserving and Staggering Effects

摘要

A finite-volume method for Euler equations is presented. Interfaces fluxes are reconstructed with a linear interpolation, which leads to a second order approximation of the spatial derivatives. Since shocked flows have been considered as test cases, a Rusanov-like artificial dissipation is used in order to prevent spurious oscillations. The conservative form of a scheme does not ensure the correct balance of quantities like kinetic energy and inner energy because they are embedded into the total energy, which is instead conserved. We present how to define the fluxes of a conservative scheme taking also into account the kinetic energy balance. Moreover, two grid arrangements are used. One with all conserved variables collocated at the center of the volume, the other one with kinetic quantities collocated at the edges. We discuss the effect of the kinetic energy preservation constraint and of the kinetic variables staggering analyzing two shock tube problems: the modified Sod's problem and the Shu-Osher's problem.