À¶Ý®ÊÓƵ

Per-Olof Persson, Department of Mathematics, University of California, Berkeley

High-order accurate methods, such as the discontinuous Galerkin (DG) method, offer significant advantages over traditional low-order methods in applications like turbulent flows, multiphysics simulations, and wave propagation. However, their high computational cost and sensitivity to under-resolved features, such as shocks, remain major challenges. This talk presents recent advances in numerical schemes and solvers aimed at addressing these issues, with applications to Wall-Resolved Large Eddy Simulation of turbulence.

I will first discuss the importance of unstructured curved meshes, highlighting both the DistMesh algorithm and our recent work using Deep Reinforcement Learning for multiblock mesh generation. I will then introduce new discretization schemes, including the naturally sparse Line-DG and half-closed DG methods, which achieve better computational scaling at high polynomial degrees. These methods are coupled with efficient parallel solvers based on a new static condensation technique and optimally ordered incomplete factorizations. I will also discuss the use of adjoint methods for gradient-based optimization, demonstrated in our work on optimal designs for flapping flight, and how these techniques extend to high-order implicit shock tracking (HOIST).