Application of two-step integration procedures for hyperbolic equations

It is pointed out that many physical flow processes are governed by nonlinear hyperbolic equations of a certain form, involving a conserved quantity G, a velocity field V, and a specified function of V and G. Very accurate finite-difference techniques have been developed for the solution of the considered equation. Considerable promise for a numerical solution of fluid flow problems shows the finite element method (FEM). Its main drawback is related to the lack of a broad experience base. The present investigation has the objective to study a group of two-step time integration procedures for the integration of the shock wave equations. Thus, a contribution is to be made towards the creation of a broader experience base with respect to the use of the finite element method for the solution of fluid flow problems. Attention is given to the use of linear and parabolic elements in the spatial discretization.