Numerical Simulation Using Finite-Difference Schemes with Continuous Symmetries for Processes of Gas Flow in Porous Media

Abstract

This article presents the applications of continuous symmetry groups to the computational fluid dynamics simulation of gas flow in porous media. The family of equations for one-phase flow in porous media, such as equations of gas flow with the Klinkenberg effect, is considered. This consideration has been made in terms of difference scheme constructions with the preservation of continuous symmetries, which are presented in original parabolic differential equations. A new method of numerical solution generation using continuous symmetry groups has been developed for the equation of gas flow in porous media. Four classes of invariant difference schemes have been found by using known group classifications of parabolic differential equations with partial derivatives. Invariance of necessary conditions for stability has been shown for the difference schemes from the presented classes. Comparison with the classical approach for seeking numerical solutions for a particular case from the presented classes has shown that the calculation speed is greater by several orders than for the classical approach. Analysis of the accuracy for the presented method of numerical solution generation on the basis of continuous symmetries shows that the accuracy of generated numerical solutions depends on the accuracy of initial solutions for generations.