A parallel and adaptive interface tracking approach for evolving geometry problems

Abstract

Numerical simulations employing an interface tracking approach are desired in many evolving-geometry applications, particularly those involving fluid-structure and/or multiphase interactions with moving boundaries/interfaces. For example, a projectile fired from a cannon or a solid combusting into gases. In these problems, interface tracking can be crucial to accurately model and capture the interface physics, for example, a shear layer or discontinuous variables (such as density or normal velocity) at the interface. A necessary capability in an interface tracking approach is the evolution of the computational domain and mesh while maintaining a desired level of accuracy. This thesis presents a parallel and adaptive interface tracking approach for evolving geometry problems. In the current approach, the computational domain is defined using a geometric model which is updated and maintained as dictated by the analysis and the mesh is updated to be consistent with the geometric model at every step. At the interface, a frame that moves at the interface velocity is employed, while an arbitrary Lagrangian-Eulerian (ALE) frame is used elsewhere with arbitrary mesh motion. A combination of mesh motion and mesh modification is employed to update the mesh. Mesh motion is applied until mesh deformation leads to undesirable elements, at which point local mesh modification/adaptation is used. A mesh size field, which describes the desired mesh resolution over the domain, is used to drive mesh adaptation. In addition, the mesh size field is determined at every time step using a VMS-based explicit error estimator when discretization error control is applied. Further, during adaptation the local structure of the highly anisotropic layered elements in the mesh is maintained. All steps are performed on partitioned meshes on distributed-memory parallel computers. We demonstrate the effectiveness of the current approach for problems with large motion or deformation in the geometry, where changes in the location and/or size of the geometric features are significant (i.e., of the same order as the characteristic length), for example, a projectile moving from one end of the cannon to the other or phase change resulting in a significant volume reduction of a phase.