Development of Time-Accurate Finite Element Techniques for First-Order Hyperbolic Systems with Particular Emphasis on the Compressible Euler Equations

摘要

A Petrov-Galerkin finite element formulation for first-order hyperbolic systems is developed generalizing the streamline approach which has been successfully applied previously to convection-diffusion and incompressible Navier-Stokes equations. The formulation is shown to possess desirable stability and accuracy properties. The algorithm is applied to the Euler equations in conservation-law form and is shown to be effective in all cases studied, including ones with discontinuous solutions. Accurate and crisp representation of shock fronts in transonic problems is achieved.