Projection- and characteristic-based operator-splitting simulation of mixed convection flow coupling heat transfer and fluid flow in a lid-driven square cavity

Mixed convection flow in a 2D rectangular cavity is simulated by a novel finite element method, namely the projection- and characteristic-based operator-splitting algorithm. In each time step, the Navier-Stokes equations are split as follows: the diffusion part, the convection part by applying operator-splitting method, and the Poisson's equation by adopting projection method. The implicit diffusion part is solved by the preconditioned conjugate gradient (PCG) method, whereas characteristic method is applied for the convection part in a multistep explicit scheme. The characteristic Galerkin approach is used to solve the energy equation. To validate the model, lid-driven cavity flow and natural convection flow are simulated.