CSE Community Seminar
October 11, 2024, 12-1PM
Conference Room 45-432 in Building 45
Adaptive reduced-order models for high-speed flow via optimally transported meshes
Robert Loek Van Heyningen
PhD student, Department of Aeronautics and Astronautics, MIT
Abstract:
The simulation of high-speed flow problems with parametrically varying shocks poses challenges for high-fidelity discretization methods and surrogate model construction. We use an r-adaptive mesh adaptation method to aid in the accurate resolution of flows with strong shocks and the development of reduced-order models of these same flows. Using high-order solutions of the Monge-AmpeĢre equation for optimal transport, grid nodes of a fixed reference mesh are redistributed towards features that require more resolution. When applied to parametrized PDEs, each solution snapshot consists of a solution field and a corresponding grid deformation. The mapping defining the grid movement can be used to pull the solution back onto the reference mesh. Here, sharp and local features will be smoothed out and made more globally distributed over the domain, making them more suitable for linear basis model reduction methods like the proper orthogonal decomposition. Reduced order models can then efficiently be built on the reference mesh for the solution field and grid mappings.
This presentation will detail previous results and explore extensions to viscous flows and problems with multiple parameters. For some problems, nonintrusive interpolation ROMs are sufficient for both the mesh deformation and solution fields. To reach greater accuracy levels for sparse training sets, we use an intrusive projection-based ROM for the solution fields. This requires the development of novel projection strategies for hybridized discontinuous Galerkin discretizations.
October 11, 2024, CSE Community Seminar
Robert Loek Van Heyningen
PhD student, Department of Aeronautics and Astronautics, MIT