Numerical Simulation of Natural and Mixed Convection Flows by Galerkin-Characteristic Method

Abstract

A numerical investigation is performed to study the solution of natural and mixed convection flows by Galerkin-characteristic method. The method is based on combining the modified method of characteristics with a Galerkin finite element discretization in primitive variables. It can be interpreted as a fractional step technique where convective part and Stokes/Boussinesq part are treated separately. The main feature of the proposed method is that, due to the Lagrangian treatment of convection, the Courant-Friedrichs-Lewy (CFL) restriction is relaxed and the time truncation errors are reduced in the Stokes/Boussinesq part. Numerical simulations are carried out for a natural convection in squared cavity and for a mixed convection flow past a circular cylinder. The computed results are compared with those obtained using other Eulerian-based Galerkin finite element solvers, which are used for solving many convective flow models. The Galerkin-characteristic method has been found to be feasible and satisfactory.