A fast dynamic smooth adaptive meshing scheme with applications to compressible flow

We develop a fast-running smooth adaptive meshing (SAM) algorithm for dynamic curvilinear mesh generation, which is based on fast solution strategy of the time-dependent Monge-Ampère (MA) equation, det⁡∇ψ(x,t)=G∘ψ(x,t). The novelty our approach new so-called perturbation formulation MA, constructs map ψ via composition sequence near-identity deformations reference mesh. Then, we formulate version deformation method [21] that results in simple, fast, and high-order accurate numerical scheme SAM optimal complexity when applied to generation solutions hyperbolic systems such as Euler equations gas dynamics. perform series challenging 2D 3D experiments grids with large deformations, demonstrate able produce meshes comparable state-of-the-art solvers [22], [18], while running approximately 200 times faster. then coupled simple Arbitrary Lagrangian Eulerian (ALE) Specifically, implement C-method [64], [65] ALE interface tracking contact discontinuities. both Noh implosion problem well classical Rayleigh-Taylor instability problem. Results confirm low-resolution simulations using SAM-ALE compare favorably high-resolution uniform runs.