Reformulated Osher-Type Riemann Solver [chapter]

Eleuterio F. Toro, Michael Dumbser
2011 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
more » ... tational 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.
doi:10.1007/978-3-642-17884-9_14 fatcat:jshzzwvgs5ekbbz5sr6xpptvgy