DIRECTIONALLY ADAPTIVE LEAST SQUARES FINITE ELEMENT METHOD FOR THE COMPRESSIBLE EULER EQUATIONS

Abstract

The least-squares finite element method is used to solve the compressible Euler equations in both 2-D Cartesian and axisymmetric forms. Since the method is naturally diffusive, no explicit artificial viscosity is added to the for­ mulation. The inherent artificial viscosity, however, is usually large and hence does not allow sharp resolution of discontinuities unless extremely fine grids are used. To remedy this problem, while retaining the advantages of the least squares method, a moving-node grid adaptation technique is used. The out­ standing feature of the adaptive method is its sensitivity to directional •features like shock waves, leading to the automatic construction of adapted grids where the element edge(s) are strongly aligned with such flow phenomena.

Using well-known transonic and supersonic test cases, it is demonstrated that by coupling the least squares method with a robust adaptive method, shocks can be captured with high resolution despite using relatively coarse grids.

A paper extracted from the thesis was accepted to be presented at the lASTED international conference on modeling and simulation (MS 2006), which will be held May 24 to May 26, 2006, at Montreal, Canada. Paper title

"Enhanced Adaptive Finite Element Method for The Cartesian and Axi­

symmetric lnviscid Compressible Flows"