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mikolchon August 16, 2014 16:50

Issue with arbitrary Lagrangian-Eulerian method and mesh optimization
 
I hope someone can help me with this. I implemented a mesh optimizer following an Ansys paper "An Approach to Combined Laplacian and Optimization-Based Smoothing for Triangular, Quadrilateral, and Quad-Dominant Meshes (1998)" by Scott Canann, Joseph Tristano & Matt Staten. The optimizer works really well to correct any mesh. What I did next is to try to use it to correct the triangle deformations caused by the big displacements that happen in a moving body simulation with ALE method.

First of all, I'm new to CFD and I'm not sure if the optimizer is suitable for this task. From the paper it seems that it is meant to be used after mesh generation/remeshing only. But anyways, the implementation was done and it has an issue concerning the mesh velocity & displacement discontinuity that resulted from the optimizer corrections.

Given a displacement of the boundary points of the moving object, we propagate this displacement to the rest of the mesh points via spring analogy. This would naturally result in a smooth displacement field of the mesh, ranging from the displacements on the moving boundary to zero on the mesh fixed boundaries; and hence a smooth mesh velocity too. But when a triangle drops below a given quality tolerance, the optimizer is called and corrects the triangle (and maybe the neighboring triangles as well), messing up the smoothness of the mesh displacement & velocity field. Also, the correction displacements made by the optimizer are often too big compared to the average displacements (x10e5 ~ x10e7), which is good in terms of optimizing the mesh alone (it optimizes in few steps), but results in nodes with extremely high mesh velocities. One idea in mind is to adjust the step size so that the correction displacement has to be near the same size of the original displacement, but even though I'm not sure if this is the correct tool for the job. Any opinions are welcome. Thanks!


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