Space conservation law in finite volume calculations of fluid flow

TLDR

Numerical solutions of fluid flow in moving coordinates require solving an additional space conservation law alongside mass, momentum, and energy equations. The paper proposes incorporating the space conservation law into a finite volume scheme. The proposed method is applied to several test cases. The method yields efficient, accurate results across all grid velocities and time steps where temporal accuracy holds, but neglecting the space conservation law introduces artificial mass source errors that can only be reduced by choosing a time step smaller than that required for temporal accuracy.

Abstract

Abstract In the numerical solutions of fluid flow problems in moving co‐ordinates, an additional conservation equation, namely the space conservation law, has to be solved simultaneously with the mass, momentum and energy conservation equations. In this paper a method of incorporating the space conservation law into a finite volume procedure is proposed and applied to a number of test cases. The results show that the method is efficient and produces accurate results for all grid velocities and time steps for which temporal accuracy suffices. It is also demonstrated, by analysis and test calculations, that not satisfying the space conservation law in a numerical solution procedure introduces errors in the form of artificial mass sources. These errors can be made negligible only by choosing a sufficiently small time step, which sometimes may be smaller than required by the temporal discretization accuracy.