Program generation method for solving differential equations using mesh

Abstract

A program generating method for automatically generating a program used in a simulation of a physical phenomenon by using computers, wherein inputted information such as the shape of a domain where the physical phenomenon such as that in a fluid takes place, mesh division information therefor, a partial differential equation dominantly representing the physical phenomenon and boundary conditions thereof are inputted, differential operators included in the inputted partial differential equation and an equation representing the boundary condition are expanded to generate discrete equations and the generated discrete equations are coded to automatically generate simulation programs. Information indicating whether discrete points which are evaluation points of the values of variables included in the inputted partial differential equation are located at mesh points or at intermediate points between mesh points is inputted the relative positional relations between mesh points and the discrete points of the variables, and relative discrete equations are generated in accordance with the inputted information by discretizing the differential operators included in the partial differential equation by using a conversion table or a conversion program, where the position of a variable to be solved in the partial differential equation is designated as a reference point relative discrete equations are converted to discrete equations for an absolute position in the region where the physical phenomenon takes place, thereby generating the simulation program.