NUMERICAL SIMULATION OF 2D FLUID FLOW USING THE FINITE ELEMENT DISCRETIZATION ON UNSTRUCTURED GRID COMBINED WITH ADAPTIVE MESH REFINEMENT TECHNIQUE

Abstract

The finite element method (FEM) has been successful in simulating complex physical systems in science and
engineering. A big challenge of using the FEM is how to reduce computation time in large-scale problems. In this
paper, we propose combining the FEM and an Adaptive Mesh Refinement (AMR) technique for solving an
incompressible fluid flow on unstructured grids. We use the magnitude of the vorticity field as an indicator function
to detect the region that needs to be refined and then refine the original mesh using an element subdivision
technique. The governing equations are discretized using a finite element method based on the linear, equal order
P1P1 elements (linear order for both velocity and pressure). The Navier-Stokes equations for unsteady fluid flow are
solved using a three-step projection method with the Crank-Nicolson scheme employed for the temporal
discretization of diffusion term and the Adams-Bashforth scheme for convection term. The performance of the
present method is verified for several benchmark problems in 2D domains. It shows that the proposed method can
provide enough accuracy compared to the previous results. Moreover, the present method can significantly reduce
the CPU time compared to the traditional method without using the AMR technique.