130th NIA CFD Seminar, "U-MUSCL and FSR Schemes" by Hiroaki Nishikawa, (03-26-2024)

Here's the link to the presentation file (pdf):
https://www.researchgate.net/publicat...

Title: U-MUSCL and FSR Schemes: Designing Unstructured-Grid Schemes for Smooth Hexahedral Grids
Speaker: Hiroaki Nishikawa, National Institute of Aerospace
Date: Tuesday, March 26, 2024
Time: 11am-12pm (EDT)
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/soda/pastries, meet other CFD researchers, and support NIA CFD Seminars!

Abstract:
In this talk, I will discuss unstructured-grid schemes designed to achieve high-order accuracy when the grid is smooth and hexahedral. Starting with the clarification of some confusion over Burg’s U-MUSCL scheme, I will show that it can be made genuinely third-order accurate for smooth hexahedral grids by adding flux reconstruction. The resulting scheme is a third-order flux-solution-reconstruction (FSR) scheme, which can be extended to fourth- and fifth-order accuracy. However, these schemes, FSR3, FSR4, and FSR5, require the computation and storage of first and second derivatives of fluxes, which can be very expensive in 3D. To develop more efficient schemes, I will discuss the use of the chain rule and a quadratic flux polynomial, leading to CFSR3/CFSR4/CFSR5 and QFSR3/QFSR4/QFSR5 schemes. I will show a few numerical results to highlight their capabilities, and end the talk with conclusions and current status.

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 improved discretization methods for practical unstructured-grid CFD solvers.