Accuracy and stability of a finite difference scheme for two-dimensional problems of soil dynamics

Abstract

Problems of numerical methods for calculating hyperbolic systems of equations with several variables are considered topical. At present, for most technical issues, the solution to one-dimensional non-stationary problems can be conducted with sufficient accuracy. It is too early to assert the mass solution of three-dimensional problems. Therefore, the present study is focused on the consideration of the accuracy and stability of the two-dimensional difference method for solving non-stationary dynamic problems. Unlike conventional difference schemes, the M. Wilkins difference scheme, based on the integral definition of partial derivatives, is considered here. The order of approximation error for arbitrary quadrangular cells is shown. Analytical methods are used to determine the accuracy and stability of the difference relations for the linear equations of the dynamics of a deformable rigid body, as applied to the problems of the interaction of rigid bodies with soil.