Local preconditioning in a stagnation point

Local preconditioning yields desirable effects such as convergence acceleration and preservation of accuracy in the incompressible limit, but these come at the expense of robustness. Current research focuses on making the various preconditioned Euler discretizations that have been developed more reliable near flow singularities such as sonic and stagnation points. In this report we discuss the loss of stability in computing stagnating flow with the symmetric Van Leer-Lee-Roe preconditioning, and do an exhaustive search for modifications of the matrix (for low Mach numbers) by which the instability can be avoided. Some numerical support regarding the effectiveness of these modifications is presented.