51st NIA CFD Seminar: First-, Second-, and Third-Order Hyperbolic Navier-Stokes Solver

Speaker: Hiro Nishikawa Abstract: Is it possible that a third-order CFD solver is less expensive on a given grid than a conventional second-order solver? No, it is impossible because a higher-order scheme requires more work on the same grid. However, as history demonstrates, it only takes a radical idea to turn the impossible into the possible. This talk will investigate whether the hyperbolization of the viscous terms is radical enough to make it happen. The Navier-Stokes equations are made hyperbolic, discretized by first, second, and third-order finite-volume schemes with upwind fluxes, and solved by a fully implicit solver: Newton’s method for the first-order scheme, and a defect correction method for others. The developed solver will be compared with a conventional second-order solver for some simple but realistic viscous flow problems, focusing on computation time and accuracy especially in the viscous stresses and heat fluxes on fully unstructured viscous grids. Biography Dr. Hiro Nishikawa is Associate Research Fellow, NIA. He earned Ph.D. in Aerospace Engineering and Scientific Computing at the University of Michigan in 2001, worked as a postdoctoral fellow on adaptive grid methods, local preconditioning methods, multigrid methods, rotated-hybrid Riemann solvers, high-order upwind and viscous schemes, etc., and joined NIA in 2007. His area of expertise is the algorithm development for CFD, focusing on multigrid methods and hyperbolic methods for robust, efficient, highly accurate viscous discretization schemes. Additional information, including the webcast link, can be found at the NIA CFD Seminar website, which is temporarily located at http://www.hiroakinishikawa.com/niacfds/index.html