The numerical method of characteristics for hyperbolic problems in three independent variables

Abstract

Introduction and Summary.--Recent advances in electronic computing devices suggest that it may soon be feasible to attempt numerical solutions of problems involving three independent variables. In this paper, preliminary consideration is given to the extension of the numerical method of characteristics for hyperbolic equations to the case of three independent variables. A general quasi-linear second order partial differential equation in three variables is first considered, and the characteristic surfaces and curves are derived, together with the differential relations which hold along them. It is shown that numerical integration should be possible along the faces or edges of a hexahedral grid. The equations are developed in more detail for two special cases of compressible flow, namely steady isentropic supersonic flow in three-dimensional space, and unsteady flow in two dimensions.