Improved ALE mesh velocities for complex flows

Abstract

Summary A key choice in the development of arbitrary Lagrangian‐Eulerian solution algorithms is how to move the computational mesh. The most common approaches are smoothing and relaxation techniques, or to compute a mesh velocity field that produces smooth mesh displacements. We present a method in which the mesh velocity is specified by the irrotational component of the fluid velocity as computed from a Helmholtz decomposition, and excess compression of mesh cells is treated through a noniterative, local spring‐force model. This approach allows distinct and separate control over rotational and translational modes. The utility of the new mesh motion algorithm is demonstrated on a number of 3D test problems, including problems that involve both shocks and significant amounts of vorticity.

Simulation-Driven Optimization of High-Order Meshes in ALE Hydrodynamics

“…They only require information about the local Jacobians, and thus can be applied to meshes of any order (including linear meshes), element type, and dimension. The proposed methods can be applied to both monolithic ALE methods [19,20,21] to define their mesh velocity, and ALE methods that split the Lagrangian, mesh optimization and remap phases. They can also be applied to diffused interface methods, where ALE errors are decreased by shrinking the transition region of the volume fraction functions, or exact interface representation methods [22], where ALE errors can be decreased by obtaining better mesh resolution in the interface regions.…”