A time marching boundary element method for two-dimensional incompressible thermally coupled flows Original Research Article

A time marching boundary element method is developed for the solution of two-dimensional incompressible thermally coupled flows. By applying the operator splitting technique and time difference discretization, semi-discretized semi-implicit differential equations are obtained and then Greenʹs function method is used to derive time marching integral equations and time marching boundary integral equations. The relation between the time marching boundary integral equation and an explicit time integration scheme is brought to light. The boundary element and finite element approaches are employed to solve the resulting time marching boundary integral equations. Numerical calculations have been carried out for the free convection flow in a unit square cavity for testing the accuracy and efficiency of the present method.