Least-Squares Spectral Element Method for 2D Hyperbolic Systems of Equations

The least-squares spectral element method (LSSEM) is a relatively new state of the art numerical method which is capable of solving complex problems with high accuracy. Very promising results for hyperbolic equations using a spacetime formulation have recently been obtained. In this report steady state solutions for 2D hyperbolic systems of equations are investigated. Especially, the solutions which contain discontinuities are a point of interest. The shallow water equations (SWE) and Euler equations are used for this purpose. By defining test cases for which the exact solutions are known the accuracy of the LSSEM is determined and more importantly it was observed that the shock position found by the LSSEM matched the analytical shock positions. However, this was only the case when conserved quantities were used. The use of primitive variables does not lead to correct shock positions. The results for the 2D channel flow with a circular bump are in agreement with known results for all (subsonic, transonic and supersonic) cases. However, applying and weighing the slip flow boundary condition is tricky and will influence the solution. Nonetheless, the LSSEM is capable of finding solutions for this type of problems which are in agreement with other numerical methods.Aerospace Engineerin