A second-order time accurate finite element formulation for quasi-incompressible viscous flow and heat transfer stabilized by local time-steps

A stabilized finite element method for the solution of viscous flow and heat transfer is presented. An equation for pressure is derived from a second-order time accurate Taylor-Galerkin procedure that combines the mass and the momentum conservation laws. At each time-step, once the pressure has been determined, the velocity field and the temperature field are computed solving discretized equations obtained from another second-order time accurate scheme and a least-squares minimization of momentum and energy residual. Thus, the procedure leads to a stabilized finite element method suitable for the simulation of heat transfer problems in free, mixed and forced convection. The terms that stabilize the finite element method arise naturally from the process, rather than being introduced a priori in the variational formulation. Local time-steps, chosen according to the time-scales of convection-difusion of momentum and energy, play the role of stabilization parameters. Numerical solutions of some representative examples demonstrate the application of the proposed stabilized formulation, where good agreement with previously published experimental and computational results have been obtained.A stabilized finite element method for the solution of viscous flow and heat transfer is presented. An equation for pressure is derived from a second-order time accurate Taylor-Galerkin procedure that combines the mass and the momentum conservation laws. At each time-step, once the pressure has been determined, the velocity field and the temperature field are computed solving discretized equations obtained from another second-order time accurate scheme and a least-squares minimization of momentum and energy residual. Thus, the procedure leads to a stabilized finite element method suitable for the simulation of heat transfer problems in free, mixed and forced convection. The terms that stabilize the finite element method arise naturally from the process, rather than being introduced a priori in the variational formulation. Local time-steps, chosen according to the time-scales of convection-difusion of momentum and energy, play the role of stabilization parameters. Numerical solutions of some representative examples demonstrate the application of the proposed stabilized formulation, where good agreement with previously published experimental and computational results have been obtained