UDC 519.63+532.5-1/-9 Modification of the Numerical Code for Gas-Dynamical Flows in Cylindrical Coordinates E. A. Filistov Department of Physics Moscow State University of Civil Engineering 26, Jaroslavskoje shosse, Moscow, Russia, 129337 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 CourantFriedrich-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. <...> Introduction scalar conservation laws and linear systems of conservation laws have been firmly established through the work of Harten [1], Sweby [2], and Roe [3–5]. <...> These TVD schemes seek to prevent an increase in the total variation of the numerical solution, and are successfully implemented in the form of flux-limiters or slope limiters for scalar conservation laws and systems. <...> However, their application to conservation laws in strict divergent form written in cylindrical coordinates is still not fully developed and can be improved. <...> In this work we construct the three-dimensional numerical code for simulation of a perfect non-stationary gas-dynamical flows. <...> The theoretical foundations of high-resolution TVD schemes for homogeneous 2. <...> Basic Equations of Gas Dynamics The basic equations of gas dynamics govern the motion of a perfect non-stationary, inviscid gas-dynamical flows by conserving mass, momentum and energy (three dimensional nonstationary partial differential <...>