P-Version Finite Element Method for the Compressible Navier-Stokes Equations with and without Body Force

This proposal is concerned with the accurate computer simulation of compressible transonic and supersonic flows. It explores the feasibility of developing a Computational Fluid Dynamics (CFD) code based on the p-version of the finite element method, which alleviates some of the inherent limitations and difficulties of established finite difference/finite volume methods for such flows. Numerical difficulties related to unphysical oscillations or nonconvergence that are usually corrected by "upwind" schemes will be specially addressed and are expected to be more efficiently suppressed by the higher order approximation of the p-FEM using a non-iterative predictor corrector approach that also eliminates the false diffusion inaccuracy caused by the upwind formulation used in conventional finite difference/finite volume and h-version finite element methods. An existing research version of a p-FEM code developed by Alabama A&M University for NASP will be modified to implement a p-FEM CFD formulation for incompressible flow. The dominant factors that control the efficiency of the p-FEM model in eliminating the limitations of finite volume/h-FEM models will be identified through sensitivity analysis of the p-FEM model on benchmark problems.