A 3D adaptive mesh moving scheme

This paper presents an adaptive mesh moving technique for three-dimensional (3D) fluid flow problems that involve moving fluid boundaries and fluid-solid interfaces. Such mesh moving techniques are an essential ingredient of fluid-structure interaction methods that typically employ arbitrary Lagrangian-Eulerian (ALE) frameworks. In the ALE frame, the velocity field representing motion of the underlying continuum is integrated in the fluid flow equations. In the discretized setting, the velocity field of the underlying continuum gives rise to the mesh displacement field that needs to be solved for in addition to the flow equations and the structural equations. Emphasis in the present work is on the motion and deformation of 3D grids that are composed of linear tetrahedral and hexahedral elements in structured and unstructured configurations. The proposed method can easily be extended to higher-order elements in 3D. A variety of moving mesh problems from different fields of engineering are presented that show the range of applicability of the proposed method and the class of problems that can be addressed with it.