A fast dynamic smooth adaptive meshing scheme with applications to compressible flow
A fast dynamic smooth adaptive meshing scheme with applications to compressible flow
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DOI：
10.1016/j.jcp.2023.112280
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发表时间：
2022-05
期刊：
影响因子：
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通讯作者：
Raaghav Ramani;S. Shkoller
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文献类型：
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作者：
Raaghav Ramani;S. Shkoller
基于时变Monge-Ampère(MA)方程det∇ψ(x，t)=G∘ψ(x，t)的快速求解策略，提出了一种快速光滑自适应网格生成算法。该方法的创新之处在于提出了一种新的MA摄动公式，它通过组合参考网格的一系列近似恒等式的变形来构造解映射ψ。然后，我们提出了一种新的形变方法[21]，它产生了一种简单、快速、高精度的数值格式和一种动态SAM算法，当应用于求解双曲型方程组(如气体动力学的Euler方程)时，动态SAM算法具有最佳的复杂性。我们对具有大变形的网格进行了一系列具有挑战性的2D和3D网格生成实验，并证明了SAM能够生成与最先进的求解器[22]、[18]相当的平滑网格，同时运行速度大约快200倍。然后将SAM算法耦合到二维气体动力学的简单任意拉格朗日欧拉(ALE)格式。具体地说，我们实现了C方法[]，[65]，并开发了一种新的接触不连续的ALE界面跟踪算法。我们对Noh内爆问题和经典的Rayleigh-Taylor不稳定性问题进行了数值实验。结果证实，使用我们的SAM-ALE算法进行的低分辨率模拟优于高分辨率的均匀网格运行。
We develop a fast-running smooth adaptive meshing (SAM) algorithm for dynamic curvilinear mesh generation, which is based on a fast solution strategy of the time-dependent Monge-Ampère (MA) equation, det∇ ψ (x, t)= G∘ ψ (x, t). The novelty of our approach is a new so-called perturbation formulation of MA, which constructs the solution map ψ via composition of a sequence of near-identity deformations of a reference mesh. Then, we formulate a new version of the deformation method [21] that results in a simple, fast, and high-order accurate numerical scheme and a dynamic SAM algorithm that is of optimal complexity when applied to time-dependent mesh generation for solutions to hyperbolic systems such as the Euler equations of gas dynamics. We perform a series of challenging 2D and 3D mesh generation experiments for grids with large deformations, and demonstrate that SAM is able to produce smooth meshes comparable to state-of-the-art solvers [22],[18], while running approximately 200 times faster. The SAM algorithm is then coupled to a simple Arbitrary Lagrangian Eulerian (ALE) scheme for 2D gas dynamics. Specifically, we implement the C-method [64],[65] and develop a new ALE interface tracking algorithm for contact discontinuities. We perform numerical experiments for both the Noh implosion problem as well as a classical Rayleigh-Taylor instability problem. Results confirm that low-resolution simulations using our SAM-ALE algorithm compare favorably with high-resolution uniform mesh runs.