发表机构
Lawrence Livermore National Laboratory; Portland State University; Dortmund Technical University; Divergent 3D（劳伦斯利弗莫尔国家实验室; 波特兰州立大学; 多特蒙德工业大学; Divergent 3D）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
我们提出一种高阶有限元ALE方法，在解析弯曲域上通过弱边界条件、TMOP网格优化及守恒映射实现滑移壁边界，数值实验验证了其边界保真与解特征。
AI 中文摘要
我们提出了一种高阶有限元任意拉格朗日-欧拉（ALE）方法，用于在解析弯曲域上处理具有滑移壁边界条件的流体动力学问题。该方法结合了不同的拉格朗日、网格重构和映射阶段，同时保留弯曲边界的几何特征并允许边界节点的切向运动。在拉格朗日阶段，我们采用弱边界条件施加方式来强制执行滑移壁条件，而不冻结切向运动。在网格优化阶段，我们将TMOP（目标矩阵优化范式）适应于解析壁面，通过将选定的边界坐标自由度替换为曲线或曲面参数来实现。随后，牛顿求解使边界节点相对于指定几何形状进行切向移动，同时携带拉格朗日阶段引入的漂移。在映射阶段，我们通过基于守恒平流的映射在伪时间上将解从旧网格传递到优化网格。我们展示了二维和三维的数值结果，证明了该方法在高阶弯曲网格上的有效性，并表明它在保持边界保真度的同时产生了预期的流体动力学解特征。
英文摘要
We present a high-order finite element arbitrary Lagrangian-Eulerian (ALE) method for hydrodynamics with slip-wall boundary conditions on analytically curved domains. The method combines distinct Lagrangian, remesh, and remap phases while preserving the geometric features of curved boundaries and allowing tangential motion of boundary nodes. In the Lagrangian phase, we use weak boundary condition enforcement to impose the slip-wall condition without freezing tangential motion. In the mesh optimization phase, we adapt TMOP (target-matrix optimization paradigm) to analytic walls by replacing selected boundary coordinate degrees of freedom with curve or surface parameters. The Newton solve then moves boundary nodes tangentially with respect to the prescribed geometry while carrying the drift introduced by the Lagrangian phase. In the remap phase, we transfer the solution from the old mesh to the optimized mesh by a conservative advection-based remap over pseudo-time. We present numerical results in two and three dimensions demonstrating the method on high-order curved meshes and showing that it preserves boundary fidelity while producing the expected hydrodynamic solution features.
Comments17 pages, 9 figures
