The Finite Element Method (FEM) which is mainly used in the fields of structural mechanics is applied to the branch of fluid mechanics, especially Euler equation, and various techniques for solving transonic and supersonic flow problems are studied. First, to enhance its discontinuity-capturing ability introduce Flux-Corrected-Transport (FCT) technique. Second, to reduce computer CPU time and memory requirements adaptive remeshing is applied with unstructured grid generation using three data structures, heap tree, quad tree, linked list, to provide O(Nlog(N)) searching algorithm. And finally first and new unstructured multi grid convergence acceleration technique is suggested by author and achieve remarkable computer time reduction in solving steady-state problems.
Numerical examples are comparison with Taylor-Galerkin FEM and FEM-FCT on the 10% thickness circular arc bump in channel exposed by supersonic inlet mach number and show enhanced solution in spite of smaller node numbers and element numbers with adaptive mesh on the NACA-0012 airfoil. Finally new multi grid convergence acceleration technique is assured by transonic flow computation on the 10% thickness circular arc bump in channel and NACA-0012 airfoil.
