An implicit finite element method for high speed flows

A fast algorithm is presented for constructing continuous lines, consisting of element sides, on general unstructured two-dimensional triangular meshes. The lines must pass through each node of the mesh once and only once. The discussion focuses on the use of these lines in a relaxation method for the solution of the equation system arising from an implicit algorithm for the solution of two-dimensional Euler and Navier-Stokes equations on general unstructured grids. It is also shown that the method can be used for solving three-dimensional Navier-Stokes equations on a grid composed of both structured and unstructured regions.