Abstract
This survey reviews the recent development of mesh deformation methods. During the past two decades a vast number of researches have been concerned with developing an efficient and robust mesh deformation technique. This has been achieved either by proposing a novel approach, improving an existing one, or by combining two existing approaches together resulting in a new hybrid approach. It is important to keep track of the most up to date developments in the field of mesh deformation, in order to allow the researchers to adopt the most efficient and application compatible scheme as well as to propose new methods of improvements. In this survey the mesh deformation techniques have been classified into two main categories, 1) physical analogy based techniques and 2) interpolation based techniques. The most significant techniques under these two classes are reviewed and the aspects of strength and weaknesses are highlighted.
Highlights
The numerical simulation of dynamically updated threedimensional (3D) meshes arises in many engineering applications, such as moving boundary problems [1], bio-fluid mechanics problems [2,3] free surface flows, and Fluid–Structure Interaction (FSI) problems [4]
FSI are of great importance in many real-life applications, such as industrial processes, aero-elasticity, and bio-mechanics
The results reported a reduction of computational costs for IDW mesh deformation with respect to the radial basis function (RBF) method of a factor 20
Summary
The numerical simulation of dynamically updated threedimensional (3D) meshes arises in many engineering applications, such as moving boundary problems [1], bio-fluid mechanics problems [2,3] free surface flows, and Fluid–Structure Interaction (FSI) problems [4]. Most structured grid regeneration and deformation techniques are based on transfinite interpolation (TFI) [37] In this method, an interior fluid node motion is assumed to be equal to the motion of the moving boundary times a scale factor. RBF can be used as an interpolation function to transfer the displacements known at the boundaries of the structural mesh to the fluid mesh This scheme produces high-quality meshes with reasonable orthogonality preservation near deforming boundaries. By deforming the Delaunay graph, which the displacements are already known for, the interior nodes new locations are interpolated [50] This method includes the following four steps: 1. This method includes the following four steps: 1. Generating the Delaunay graph
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