Finite element solution of the Euler equations in two and three dimensions

The paper presents a finite element procedure for solving the equations of compressible flow over bodies of arbitrary geometry. The numerical solution algorithm employed is an explicit two-step version of a second order Taylor-Galerkin scheme. The discretization of the computational domain into unstructured meshes of triangles in two dimensions and tetrahedra in three dimensions is performed by an automatic mesh generator. In the approach, the mesh generator is coupled to the finite element solver to produce an adaptive remeshing procedure.