Скачать или смотреть 139th NIA CFD Seminar: .. 3rd-Derivative-Free 4th-Order Shock-Capturing Scheme for Tetrahedral Grids

[ 25 minutes for the talk, 24 minutes for Q&A ] Here's the link to the paper (pdf): https://www.researchgate.net/publicat...

Title: Towards a Third-Derivative-Free Fourth-Order Accurate Shock-Capturing Scheme for Arbitrary Tetrahedral Grids

Speaker: Hiro Nishikawa, National Institute of Aerospace
Date: Tuesday, February 03, 2025
Time: 11am-12pm (EST)
Location: NIA Room 317 (3rd floor), Large Conference Room, 1100 Exploration Way, Hampton, VA 23666 Please come in person if you are local, to enjoy coffee/pastries, meet other CFD researchers, and support NIA CFD Seminars!

Abstract:
In this talk, I will present an economical fourth-order accurate cell-centered scheme for the Euler equations on arbitrary tetrahedral grids. In this method, numerical solutions are stored at cell centers as point values, and gradients and second derivatives are explicitly computed from the cell-center solutions by a cubic least-squares fit at nodes (not cell centers). Having gradients and second derivatives at nodes, we can have third derivatives as Green-Gauss gradients of second derivatives over a tetrahedral cell, leading to a very efficient fourth-order scheme that requires only a single solution array to store second derivatives. I will explain the core idea of the economical fourth-order scheme without third derivatives and show some preliminary results.

Bio: Hiroaki Nishikawa is Research Fellow at National Institute of Aerospace (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, semi-coarsening multigrid methods, rotated-hybrid Riemann solvers, and high-order upwind and viscous schemes. In 2007, he joined NIA and has since been working on the algorithm development for CFD, focusing on the hyperbolic method for diffusion/viscous terms and economical high-order discretizations for practical unstructured-grid CFD solvers.