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Assistant Professor Matthew Zahr, Aerospace and Mechanical Engineering, College of Engineering, University of Notre Dame
Simulation of shock-dominated flows using high-order implicit shock tracking
High-order implicit shock tracking (fitting) is a new class of numerical methods to approximate solutions of conservation laws with non-smooth features, e.g., contact lines, shock waves, and rarefactions. These methods align elements of the computational mesh with non-smooth features to represent them perfectly, allowing high-order basis functions to approximate smooth regions of the solution without the need for nonlinear stabilization, which leads to accurate approximations on traditionally coarse meshes. The hallmark of these methods is the underlying optimization formulation whose solution is a feature-aligned mesh and the corresponding high-order approximation to the flow, which circumvents the geometric complexity of traditional shock fitting approaches. In this talk, I will introduce the High-Order Implicit Shock Tracking method and its application to several shock-dominated flows.