We present an adaptive moving mesh method for unstructured meshes which is a three-dimensional extension of the previous works of Ceniceros et al. [10], Tang et al. [40] and Chen et al. [11]. The iterative solution of a variable diffusion Laplacian model on the reference domain is used to adapt the mesh to moving sharp solution fronts while imposing slip conditions for the displacements on curved boundary surfaces. To this aim, we present an approach to project the nodes on a given curved geometry, as well as an a-posteriori limiter for the nodal displacements developed to guarantee the validity of the adapted mesh also over non-convex curved boundaries with singularities.

We validate the method on analytical test cases, and we show its application to two and three-dimensional unsteady compressible flows by coupling it to a second order conservative Arbitrary Lagrangian-Eulerian flow solver.

我们提出了一种针对非结构化网格的自适应移动网格方法，它是Ceniceros等人先前工作的三维扩展。[10]，Tang等。[40]和Chen等。[11]。参考域上的可变扩散拉普拉斯模型的迭代解用于使网格适应移动的锋利解前沿，同时为弯曲边界面上的位移施加滑动条件。为此，我们提出了一种将节点投影到给定弯曲几何结构上的方法，以及对节点位移的后向限制器，以确保在具有奇异性的非凸弯曲边界上也能适应网格的有效性。

我们在分析测试用例上验证了该方法，并通过将其与二阶保守的任意Lagrangian-Eulerian流动解算器耦合将其应用于二维和三维非定常可压缩流。