A finite-difference method for solving the equations of gas dynamics using adaptive nets which are dynamically associated with the solution

Abstract

A finite-difference method for solving non-stationary, spatially one-dimensional problems of gas dynamics is proposed. The method is based on the use of grids which are adapted and obtained by a coordinate transformation which, in its turn, is determined by the required solution. An efficient numerical algorithm has been constructed on the basis of the proposed method which enables the accuracy of the calculations to be increased considerably with a simultaneous reduction in the total number of mesh points in the net by a factor of 2–5 compared with other methods.