64th NIA CFD Seminar: Topic: Third-Order Edge-Based Scheme and New Hyperbolic Navier-Stokes System

Speaker: Hiro Nishikawa Speaker Bio: 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. He then worked as a postdoctoral fellow at the University of Michigan 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 hyperbolic methods for robust, efficient, highly accurate viscous discretization schemes. Abstract: This talk will discuss a special third-order edge-based scheme and new hyperbolic Navier-Stokes formulations, HNS17 and HNS20. The edge-based scheme achieves third-order accuracy on simplex elements by linear flux extrapolation and with straight-edge grids. The scheme is highly efficient in that the residual is computed over a loop over edges with a single flux evaluation per edge. This efficient scheme, originally discovered for hyperbolic conservation laws by Katz and Sankaran, is made immediately applicable to viscous terms by a hyperbolic viscous formulation. A versatile hyperbolic formulation, HNS20, is introduced to enable accurate computations of the gradients of all primitive variables. It allows us to construct not only superior Navier-Stokes discretizations but also a third-order inviscid and second-order viscous discretization by second-order algorithms. New techniques, artificial hyperbolic diffusion and dissipation, which are essential to the new formulations, are also introduced to raise the order of accuracy of the velocity and density gradients by one order. 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