A Unified Coordinate For Solving The Invisid Compressible Equations

A unified coordinate which is based on Eulerian description and La-grangian description is used to solve invisid compressible flow. The two-dimensional Euler equations are still conservative and hyperbolic (weakly hyperbilic,when h = 1) after a transformation from Cartesian coordinates (t, x, y) to unified coordinate (A, ?T;). The unified coordinate takes Eule-rian coordinates while h - 0 and Lagrangian coordiantes while h = 1 as its two special cases. After Strang splitting, the Riemann problem in A -plane can be solved if replace u and v, which are x, y components of fluid velocity by velocity and r ,which are in - and r;-direction. By applying Godunov scheme, it is possible for unified coordinate to avoid the disad-vantages of excessive diffusion across slip lines in the Eulerian description and of severe grid deformation in the Lagrangian description. The appli-cation of it in solving the discontinuous problem for the Euler equations in conservative form is as well as the result of the Riemann solver of Roe.