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High-order implicit shock tracking (fitting) is a class of high-order,optimization-based numerical methods to approximate solutions of conservationlaws with non-smooth features by aligning elements of the computational meshwith non-smooth features. This ensures the non-smooth features are perfectlyrepresented by inter-element jumps and high-order basis functions approximatesmooth regions of the solution without nonlinear stabilization, which leads toaccurate approximations on traditionally coarse meshes. In this work, weintroduce a robust implicit shock tracking framework specialized for problemswith parameter-dependent lead shocks (i.e., shocks separating a farfieldcondition from the downstream flow), which commonly arise in high-speedaerodynamics and astrophysics applications. After a shock-aligned mesh isproduced at one parameter configuration, all elements upstream of the leadshock are removed and the nodes on the lead shock are positioned for newparameter configurations using the implicit shock tracking solver. The proposedframework can be used for most many-query applications involving parametrizedlead shocks such as optimization, uncertainty quantification, parameter sweeps,"what-if" scenarios, or parameter-based continuation. We demonstrate therobustness and flexibility of the framework using a one-dimensional space-timeRiemann problem, and two- and three-dimensional supersonic and hypersonicbenchmark problems.

High-order implicit shock tracking boundary conditions for flows with parametrized shocks