TECHNIQUE FOR SOLVING 3-D TIME-DEPENDENT PROBLEMS IN GAS DYNAMICS USING LAGRANGE VARIABLES

A. Yu. Artemiev, V. I. Delov, L. V. Dmitrieva
VANT. Ser.: Mat. Mod. Fiz. Rroc. 1989. Вып.1. С. 30-39.

      Integral-interpolation method is used for developing an explicit difference scheme to solve numerically 3-D time-dependent problems in gas dynamics. Discretizing differential equations, written in Cartesian coordinates, takes velocity values at semi - integral times as in the 1-D CREST scheme. The resulting scheme, for smooth solution regions on uniform and orthogonal grids, has a second-order time and space approximation and is stable when the Courant condition is met. For grids formed by flow-isolines, the scheme retains the symmetry in three types of 1-D flow: plane, cylindrical and spherical ones. Calculations performed on coarse grids indicate that the scheme has good conservative properties. The difference scheme performance is illustrated by three test problems.