Accurate 3D viscous incompressible flow calculations with the FEM

Abstract

Summary: A second-order-accurate (in both time and space) formulation is developed and implemented for solution of the three-dimensional incompressible Navier-Stokes equations involving high-Reynolds-number flows past complex configurations. For stabilization, only a fourth-order-accurate artificial dissipation term in the momentum equations is used. The finite element method with an explicit time-marching scheme based on two-fractional-step integration is used for solution of the momentum equations. The element-by-element technique is employed for solution of the auxiliary potential function equation in order to ease the memory requirements for matrix. The cubic cavity problem, the laminar flow past a sphere at various Reynolds numbers and the flow around the fuselage of a helicopter are solved. Comparison of the results with the low-order solutions indicates that the flow details are depicted clearly even with coarse grids.