Solution Algorithm

Abstract

This chapter describes in detail the finite element solution algorithm for the Euler equations. The application of the finite element method to the spatial discretization is described, and section 4.3 introduces the Galerkin finite element, “cell-vertex” finite element and “central difference” finite element methods. The implementation of boundary conditions is discussed in section 4.4. All of these methods require added damping for stability, and this is discussed in section 4.5. Section 4.6 describes the pseudo-time marching method. Finally, section 4.7 describes the conditions on the test and trial functions needed to obtain consistency and conservation.