2014-12-16, You Already Have it: Accuracy-Preserving Boundary Quadrature for EB Finite-Volume Scheme

Описание: 56th NIA CFD Seminar:

Accuracy-Preserving Boundary Quadrature for Edge-Based Finite-Volume Scheme: Third-order accuracy without curved elements by Hiroaki Nishikawa

Paper:
JCP2015: "Accuracy-Preserving Boundary Flux Quadrature for Finite-Volume Discretization on Unstructured Grids" PDF at https://www.researchgate.net/publicat...

Abstract:
This talk will discuss a third-order edge-based finite-volume scheme on unstructured grids. It will be shown why the edge-based scheme can be third-order and also why it cannot be third-order if the numerical flux is exact for quadratic fluxes. A general boundary flux quadrature formula is presented that preserves third-order accuracy at boundary nodes with linear elements. Numerical results show that the general formula as well as acccurate boundary normals are essential to achieve third-order accuracy for a curved boundary problem with linear elements.

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.