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@conference{zahr2025psu, abstract = {Shock-dominated flows are notoriously challenging to simulate accurately and efficiently using modern numerical methods. Strong propagating features such as shock waves and contact discontinuities often require delicate stabilization, small time steps, tight grid spacing, and sometimes additional requirements on the mesh (e.g., well-conditioned quad/hex elements aligned with shocks). In this talk, I will present recent advances to implicit shock tracking, a class of numerical methods that aim to overcome these challenges by deforming the mesh such that element faces align with flow features. This ensures discontinuous features (contacts and inviscid shocks) are represented perfectly by inter-element jumps in the solution basis without the need for stabilization. Viscous features (viscous shocks and boundary layers) are accurately represented without stabilization by compressing elements into the thickness of the feature and locally increasing the polynomial degree. Unlike traditional shock fitting methods, the optimal grid is computed as the solution of a PDE-constrained optimization problem. Numerical demonstrations of the method for supersonic and hypersonic flows show implicit shock tracking delivers accurate solutions on traditionally coarse grids.}, address = {Portland, Oregon}, author = {Zahr, Matthew J.}, booktitle = {Mathematics Department Seminar, Portland State University (Host: Will Pazner)}, conftype = {seminar}, date-added = {2025-01-31 18:57:14 -0500}, date-modified = {2025-01-31 18:58:27 -0500}, organization = {Portland State University}, pres = {content/slides/zahr2025psu.pdf}, presenter = {Zahr, Matthew J.}, project = {shktrk}, status = {invited}, title = {High-order implicit shock tracking for shock-dominated flows}, year = {3/14/2025} }
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