An algorithm for calculating two-dimensional problems of gas dynamics in Lagrange variables

The numerical solution of two-dimensional equations of gas dynamics in a Lagrangian coordinate system on quadrangular grids is examined. A grid restructuring approach based on the integration of the continuity equation is used to prevent the formation of 'inside-out' cells; the mass distribution between cells remains unchanged. This method is applied to two examples: (1) hot-gas expansion leading to the generation of a shock wave; and (2) the effect of laser radiation on a gas initially at rest.