The Numerical Solution of Hyperbolic Systems of Partial Differential Equations in Three Independent Variables

TLDR: In this article, a method of integration for quasi-linear hyperbolic equations in three independent variables is described by means of a step-by-step procedure, employing difference relations along four bicharacteristics and one time-like ordinary curve through each point.

Abstract: An original method of integration is described for quasi-linear hyperbolic equations in three independent variables. The solution is constructed by means of a step-by-step procedure, employing difference relations along four bicharacteristics and one time-like ordinary curve through each point. From these difference relations the derivatives of the dependent variables at the unknown point are eliminated. The solution at any point can then be com­puted, with an error proportional to the step size cubed, without referring to conditions outside its domain of dependence. The application of the method to the systems of equations governing unsteady plane motion and steady supersonic flow of an inviscid, non-conducting fluid is discussed in detail. As an example of the use of the method, the flow over a particular delta-shaped body has been computed.