Reformulated Osher-Type Riemann Solver
Computational Fluid Dynamics 2010
We reformulate the Osher Riemann solver by, first, adopting the canonical path in phase space, and then performing numerical integration of a matrix. We compare the reformulated scheme of this paper with the original Osher scheme on a series of test problems for the one-dimensional Euler equations for ideal gases, concluding that the present solver is simpler, more robust, more accurate and can be applied to any hyperbolic system. Abstract. A method for enhancing the robustness of implicit
... ss of implicit computational algorithms without adversely impacting their efficiency is investigated. The method requires control over two key issues: obtaining a reliable estimate of the magnitude of the solution change and defining a realistic limit for its allowable variation. The magnitude of the solution change is estimated from the calculated residual in a manner that requires negligible computational time. An upper limit on the local solution change is attained by a proper nondimensionalization of variables in different flow regimes within a single problem or across different problems. The method precludes unphysical excursions in Newton-like iterations in highly non-linear regions where Jacobians are changing rapidly as well as non-physical results during the computation. The method is tested against a series of problems to identify its characteristics and to verify the approach. The results reveal a substantial improvement in the robustness of implicit CFD applications that enables computations starting from simple initial conditions without user intervention.