# Mesh Morphing

### Key Takeaways

• Mesh morphing is the process of making modifications to the initial mesh so that it can better represent changes in the flow domain.

• Mesh morphing can be done using either of two approaches: the mesh-based method or the meshless method.

• For well-defined or complex problems, mesh morphing ensures accuracy in flow behavior prediction and facilitates design optimization. The fundamental of simulation in computational fluid dynamics (CFD) is high-quality mesh generation. The meshing process discretizes the domain of interest into a finite number of small geometric elements where the applied governing equations are solved for fluid motion analysis. In many cases, accurately capturing the geometry and its features can be a challenge. Through mesh morphing, it is possible to make modifications to the mesh to allow for improved accuracy of the CFD simulation.

Different mesh morphing techniques are used in CFD for modification of the mesh so it can better represent the geometry of the problem and ensure efficiency simulation. This article will provide a general overview of the mesh morphing process and its various techniques.

## Defining Mesh Morphing

Mesh morphing is the process of implementing modifications to the mesh without affecting the underlying geometry of the fluid flow domain. In CFD, modification may be required when the initial domain is not representative of the problem at hand. For instance, when fluid forces cause deformation in the structure, mesh morphing may be required to analyze this change. Similarly, in optimization studies, mesh morphing may be required to explore different design changes.

For mesh morphing, the nodes and vertices in the mesh are moved. This is done in a controlled manner so the connectivity of the mesh is not compromised. This process of mesh morphing provides the following advantages in CFD analysis:

1. Mesh quality enhancement: Mesh morphing refines the initial coarse mesh to improve the resolution and quality of the mesh.

2. Adaptation to geometric changes: Through mesh morphing, mesh adjustments can be made to accommodate changes in geometry due to deformation or motion.

3. Accuracy improvement: By modifying the mesh to better define the flow pattern, boundary conditions, etc., it is possible to improve the accuracy of the solution.

4. Optimization: Mesh morphing enables the optimization of structural design so as to achieve the optimal geometry. This is useful in aerodynamic studies to minimize drag and maximize lift by making optimal changes to the design.

The above importance of mesh morphing can be used in CFD using different types of mesh morphing techniques, which we will discuss further.

## The Different Mesh Morphing Techniques

The mesh morphing approach can be differentiated into two categories — a traditional mesh-based method and a meshless method.

1. Mesh-Based Method

The mesh-based morphing technique takes into account the role of fixed mesh and relies on the controlled movement of the vertices or nodes of the mesh to account for deformation or other geometrical changes. The mesh-based approach can be further classified into the following techniques:

 Deformation-based Mesh is deformed by the controlled movement of the nodes and vertices. For example, the free-form deformation technique. Grid-based Mesh is discretized into a grid of cells to represent the fluid domain. Each cell is independently deformed to capture the fluid-structure interaction in detail. Level-set-based Uses a level-set function where a value is assigned to each point in the mesh, which indicates the distance to the fluid interface. The mesh deformation is then done by moving the points to simulate fluid-structure interaction. Optimization-based Mesh deformation is based on the cost function, which measures the mesh quality. The coordinates of the nodes are adjusted to the optimal points to improve simulation accuracy.
1. Meshless Method

The meshless method does not rely on the fixed mesh structure. Instead, it represents the domain using a set of nodes. Accounting for the deformation can be done by repositioning these nodes in a controlled way. The meshless method may include the following approach:

 Radial basis function (RBF) interpolation Discrete set of control points and radial basis functions are used for interpolation.  This is done by evaluating the RBF and weighing them by the displacement values at the associated control points. Moving least squares (MLS) interpolation Polynomial function is used to interpolate the displacement values at each node.  The polynomial function minimizes the least-square error between the data points and the polynomial function. Smoothed particle hydrodynamics (SPH) The fluid is represented by a set of discrete moving particles and a kernel approximation is made to interpolate the particle properties at any given point. Element-free Galerkin (EFG) The domain is discretized by a set of nodes and a weighted combination of basis functions is used to compute the solution at any specific node.

## Modified Mesh for CFD Simulation Accuracy

Mesh morphing is the solution to accurately implement modifications to the problem in the flow domain without incurring issues like distortion. Due to its flexibility and efficiency, mesh morphing is widely performed by engineers and system designers to improve the quality of CFD simulation. CFD tools can use mesh-based or meshless methods of mesh morphing depending on the requirements. In general, the mesh-based method is used for a well-defined geometry while the meshless method is used for complex problems with changing boundaries.

Using tools such as Cadence’s CFD solver, it is possible to efficiently perform mesh discretization, deformation, interpolation, and modification to account for changes in flow and boundary conditions. Through a better representation of the flow problem, accurate prediction of flow behavior and deformations can be made for efficient simulation and design optimization.