Solution of the Multi-Dimensional, Incompressible Navier-Stokes Equations Using Low-Order Finite Elements and One-Point Quadrature

摘要

The modeling goal is to develop accurate and efficient, yet reasonably versatile numerical models for simulating the evolution of the velocity, temperature, and pollutant concentration fields associated with air flow over complex terrain in the planetary boundary layer. Since both the physics (e.g., stratified shear flows) and the geometry are complex, fairly fine spatial resolution (say, approx. 10 exp 4 nodes) will often be required. The longer-term goal is to be able to do faster than real time simulations in response to emergency situations. It is with these points in mind that a finite element code was developed which entails many short-cuts and simplifications compared to the conventional Galerkin finite element method (GFEM); in fact, the resulting scheme is probably better described as a hybrid method (FEM/FDM). Many aspects of these short-cuts have been described and/or are discussed in more detail elsewhere. Here, attention is focused on the effects of using 1-poing quadrature to approximate the resulting Galerkin integrals. (ERA citation 07:051963)