Application of the Method of Lines to Nonstationary Compressible Euler Equations

Within the general framework of Method of lines, numerical solution of the nonstationary compressible Euler equations in 1D, 2D and 3D is splitted into three steps: First, space discretization is performed by the rst order nite volume method using several approximate Riemann solvers. Second, smoothness and Lipschitz continuity of RHS of the arising system of ODE's is analyzed and its solvability is discussed. Finally, the system of ODE's is integrated in time by means of implicit and explicit higher-order adaptive schemes oered by ODE packages ODEPACK and DDASPK, by a backward Euler scheme based on the linearization of the RHS and by higher-order explicit Runge-Kutta methods. Time integrators are compared from several points of view, their applicability to various types of problems is discussed, and 1D, 2D and 3D numerical examples are presented. 1 Introduction Let the domain IR d occupied by the uid be bounded and have a piecewise smooth boundary @ The d-dimensional compr..