What are the advantages and disadvantages of using structured vs unstructured meshes?

1 Structured meshes

A structured mesh is composed of regular and uniform elements, such as hexahedra, quadrilaterals, or prisms, that are arranged in a logical pattern. Structured meshes are easier to generate and store, as they require less data and can be mapped by simple indices. They also offer higher accuracy and lower numerical errors, as they conform well to the boundary conditions and have smooth transitions between elements. However, structured meshes have some limitations, such as difficulty in handling complex geometries, curved boundaries, or irregular regions. They may also require more elements to capture fine details or local variations, which can increase the computational cost and memory usage.

2 Unstructured meshes

An unstructured mesh is composed of irregular and non-uniform elements, such as tetrahedra, triangles, or pyramids, that are randomly distributed and connected. Unstructured meshes are more flexible and adaptable, as they can handle any geometry and topology, including holes, cracks, or curved surfaces. They can also use adaptive mesh refinement techniques, which allow for local adjustments of the element size and shape according to the solution features or error estimates. However, unstructured meshes have some drawbacks, such as higher complexity and overhead, as they require more data and connectivity information. They also tend to have lower accuracy and higher numerical errors, as they may not fit well to the boundary conditions and have abrupt changes between elements.

3 Hybrid meshes

A hybrid mesh is a combination of structured and unstructured meshes, which aims to exploit the strengths and overcome the weaknesses of each type. Hybrid meshes can use structured elements in regions where the geometry is simple and the solution is smooth, and unstructured elements in regions where the geometry is complex and the solution is sharp or discontinuous. Hybrid meshes can also use different types of elements, such as hexahedra, tetrahedra, or polyhedra, to optimize the mesh quality and efficiency. However, hybrid meshes have some challenges, such as maintaining the compatibility and continuity between different types of elements, and ensuring the balance and robustness of the mesh generation algorithm.

4 Mesh quality metrics

Regardless of the type of mesh, it is important to evaluate the quality of the mesh before performing the simulation. Mesh quality metrics are numerical indicators that measure how well the mesh represents the geometry and the physics of the problem. Some common mesh quality metrics are aspect ratio, skewness, orthogonality, smoothness, and distortion. These metrics reflect the shape, size, alignment, and variation of the elements, and how they affect the accuracy, stability, and convergence of the solution. Ideally, a good mesh should have low values of these metrics, meaning that the elements are close to equilateral, orthogonal, smooth, and undistorted.

5 Mesh quality improvement

If the mesh quality metrics indicate that the mesh is poor or inadequate for the simulation, you may need to improve the mesh by modifying the elements or the nodes. Mesh improvement techniques are methods that aim to enhance the mesh quality by changing the shape, size, or position of the elements or the nodes, while preserving the topology and the boundary of the mesh. Some common mesh improvement techniques are smoothing, swapping, refinement, coarsening, and optimization. These techniques can be applied globally or locally, manually or automatically, depending on the type and degree of the mesh quality issue.

6 Mesh quality trade-offs

While improving the mesh quality is desirable and beneficial for the simulation, it may also entail some trade-offs or compromises. For example, increasing the number of elements or reducing the element size may improve the accuracy and resolution of the solution, but it may also increase the computational time and memory usage. Similarly, using more complex or irregular elements may improve the flexibility and adaptability of the mesh, but it may also increase the numerical errors and instability of the solution. Therefore, you need to consider the objectives and constraints of your design problem, and find the optimal balance between mesh quality and performance.

7 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?