An explicit finite element algorithm for convection heat transfer problems

A finite element algorithm is presented for the simulation of steady incompressible fluid flow with heat transfer using triangular meshes. The continuity equation is modified by employing the artificial compressibility concept to provide coupling between the pressure and velocity fields of the fluid. A standard Galerkin finite element method is used for spatial discretization and an explicit multistage Runge‐Kutta scheme is used to march in the time domain. The resulting procedure is stabilized using an artificial dissipation technique. To demonstrate the performance of the proposed algorithm a wide range of test cases is solved including applications with and without heat transfer. Both natural and forced convection applications are studied.