Fluid flow analysis by finite element method using arbitrarily deformed elements (Proposal of the GMSR‐method)

Abstract

SUMMARYThe generalized MSR-method (GMSR-method) is proposed as a ÿnite element uid analysis algorithm for arbitrarily deformed elements using the error analysis approach. The MSR-method was originally developed by one of the authors in our previous research works using a modiÿed Galerkin method (MGM) for a convection-di usion equation and the SIMPLER-approach. In this paper, this MGM is developed theoretically in the case of arbitrarily deformed elements using the error analysis approach. In the GMSR-method, since the inertia term and the pressure term are considered explicitly, only symmetrical matrices appear. Hence, it helps us reduce computational memory and computation time. Moreover, artiÿcial viscosity and di usivity are introduced through an error analysis approach to improve the accuracy and stability. This GMSR-method is applied for two-and three-dimensional natural convection problems in a cavity. In the computations at di erent Rayleigh numbers, it is shown that this method gives reasonable results compared to other research works. Thus, it is found that the GMSR-method is applicable to thermal-uid ow problems with complicated boundaries.