Honorary Argyris Lecture: Per-Olof Persson

We are happy to welcoming you on site for the public Honorary Argyris Lecture of Per-Olof Persson.

Once a year, we award an Argyris Visiting Professorship to a leading personality in the field of simulation technology. With this award, we honor internationally renowned scientists from Germany and abroad, who are outstanding representatives of their disciplines in the field of simulation technology.

High-Order Methods on Unstructured Meshes for Fluid and Solid Mechanics

Numerical simulations have become indispensable tools for advancing engineering and scientific research. High-order accurate methods, such as the discontinuous Galerkin (DG) method, have attracted significant attention for their potential to outperform traditional low-order methods, particularly in complex applications such as turbulent flows, multiphysics simulations, and wave propagation. However, high computational costs and sensitivity to under-resolved features, such as shocks, remain challenges for their widespread adoption in real-world applications. This talk will present a series of recent advancements in numerical schemes and solvers designed to address these challenges, with applications to practical problems such as Wall-Resolved Large Eddy Simulation of turbulent flows.

I will begin by introducing the need for unstructured curved meshes, discussing both the DistMesh algorithm and our recent work applying Deep Reinforcement Learning for multiblock mesh generation. I will then focus on new discretization schemes, including the naturally sparse Line-DG and half-closed DG methods, which offer significant improvements in computational scaling at higher polynomial degrees. These schemes allow for efficient solution of the resulting systems of equations using parallel solvers based on a new static condensation technique and optimally ordered incomplete factorizations.

Next, I will discuss extensions of these methods to applications with deforming domains, moving meshes, and fully discrete adjoint calculations, which support high-order discretizations for coupled multiphysics problems, such as fluid-structure interaction. These problems are integrated using partitioned methods based on Implicit-Explicit (IMEX) schemes. The adjoint methods further enable gradient-based optimization, demonstrated in our work on optimal designs for flapping flight.

Finally, I will present a numerical approach for accurate shock tracking using curved elements, formulated as an optimization problem over both the flow solution and element geometry. This High-Order Implicit Shock Tracking (HOIST) method integrates our work on curved moving meshes, adjoints, and optimization, achieving accurate solutions with significantly fewer elements than traditional adaptive shock-capturing methods.

[Picture: University of Berkeley]