When mesh boundaries move in a simulation because of the motion of a target object such as translation, rotation, and oscillation, the mesh should be regenerated to the points it will obey the locations of its new boundaries. Because recreating new mesh from the beginning is a time-consuming task, new mesh is usually created by deforming an initial mesh, which is called the mesh moving method (or mesh deformation method). In this paper, we present a new mesh moving method that produces a higher quality deformed mesh than the current mesh moving methods. In the proposed method, the deformation of mesh is evaluated by two energy quantities that are related to (i) the distortion of mesh that is invariant to translation, rotation, and size changes of the elements of the mesh and (ii) the deformation of mesh calculated using elements’ size based on stiffened-linear elasticity equations. The total deformation energy of mesh is defined as a weighted sum of these two quantities. Because there is no need to pre-fix the locations of the outer boundary points for most mesh moving problems, we use new constraints, allowing the outer boundary points to move along tangential directions in the proposed method. The deformed mesh is computed by calculating the positions of the mesh points where the total deformation energy of the mesh is minimized. For test purposes, the proposed method is applied to 2D triangular meshes and a 3D tetrahedral mesh, where the meshes are deformed by the motions of the target objects such as translation, rotation, and deformation. When the quality of the deformed meshes computed with the proposed method are compared with the ones computed with current mesh moving methods, the meshes from the proposed method are shown to be better than the other meshes.
Derivation of Mean Value Coordinates Using Interior Distance and Their Application on Mesh Deformation
