A hybrid numerical method for Navier-Stokes equations based on simple algorithm

A new numerical approach using both the finite-element method and the control-volume method is proposed for the Navier-Stokes equations. For the momentum equation, the segregated equal-order velocity-pressure formulation has been combined with the streamline upwind Petrov-Galerkin finite-element method using the four-node element. The pressure equation has been obtained by applying the mass conservation principle to an arbitrary-shaped control volume. The present method has been tested for lid-driven cavity flow and natural convection in a square cavity. With comparable computing cost to the finite-volume method, the proposed hybrid numerical method gives accurate results for the Navier-Stokes equations, which are free from the checkerboard-type pressure distribution and retain the merits of equal-order finite-element method.