Modification of the Numerical Code for Gas-Dynamical Flowsin Cylindrical Coordinates

The goal of this article is to develop a robust and accurate numerical method for solving hyperbolic conservation laws in three dimensions. The basic equations are the three-dimensional Euler equations describing the motion of an inviscid gas. The mathematical description of the model is represented by the system of equations of continuity, motion and energy (three dimensional nonstationary partial differential equations). We used the equation for adiabatic motion in this article. The numerical method for solution of the gas-dynamical equations in strict divergent form has been used in this work. The three-dimensional numerical code for perfect non-stationary gas-dynamical flows simulation in cylindrical coordinates is constructed. This code is based on the explicit quasimonotonic, first-order TVD scheme. This scheme admit introduction of the limits on the anti-diffusion flows, which enhances the approximation order (to third order in the spatial coordinates) with minimal numerical dissipation and preservation of the monotonicity of the scheme. In order to ensure numerical stability, the time step is restricted by a well-known Courant-Friedrich-Lewy stability condition. The proposed scheme is comparable to the high order over the classical TVD schemes. Our scheme has the added advantage of simplicity and computational efficiency. The numerical tests which were fulfiled by the author in additional researches, validated the robustness and effectiveness of the proposed scheme.

gas dynamics, numerical simulation