A method for the generation of moving computational grids for the solution of hyperbolic equations

The construction of explicit-difference-method computational grids for the solution of the gas dynamics equations is investigated analytically. The differential approximation method is used to define the conditions which a moving irregular grid must fulfill if the time-mesh width is to attain its maximum. The nonlinear transport equation which represents the model equation for explicit-difference-method evaluation in gas dynamics is approximated by a class of differential equations. It is shown that the maximum permissible mesh width in cases in which the solution exhibits jumps is determined by the initiation time of the gradient catastrophe. The results of sample numerical calculations are presented in a graph, and good agreement between exact and approximate solutions is found.