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Center for Nonlinear Studies |
Accurate and robust simulation of compressible flows in a Lagrangian frame presents significant numerical challenges, particularly in the presence of shocks, material interfaces, and high impact problems. These difficulties necessitate the development of numerical schemes that not only achieve high-order accuracy but also preserve key physical invariants of the governing equations. This talk will focus on the development of a novel high-order invariant-domain preserving method for Lagrangian cell-centered hydrodynamics and show how our robust low-order robust method can be used to stabilize existing high-order schemes. Particular attention will be given to ensuring robustness, local mass conservation, positivity of density, minimum principle on the specific internal energy, and compatibility with arbitrary equations of state. Beyond traditional fluid dynamics, we have extended this framework to model nonlinear elasticity with both isotropic and anisotropic equations of state, enabling us to capture material response in ways that, to our knowledge, have not been explored before.
Host: Eric Tovar (T-5)