Mesh generation is one of the most critical aspects of solving problems through computational fluid dynamics (CFD). As highlighted in a Pointwise article back in 2013, one could be forgiven for thinking structured grids are almost entirely redundant in today's unstructured or hybrid meshing world. However, the article rightly pointed out a number of reasons why things may not be quite as they seem, and that both grid types warrant careful consideration. In this article, we highlight the key advantages of the structured mesh over an unstructured mesh.
Advantages Of Structured Meshing Over Unstructured Meshing
Quick Background: The partial differential equations that govern fluid flow and heat transfer are not usually amenable to analytical solutions, except for very simple cases. Therefore, in order to analyze fluid flows, the geometric space is divided into finite elements or volumes, across which first or second order numerics can be applied. The elements generated are typically either triangles or quadrilaterals in 2D and volumes are generally tetrahedral or hexahedral in 3D. An appropriate mesh is necessary for an accurate solution, faster convergence, and reduction of numerical diffusion.
Mesh generation could be classified in mainly three categories-structured, unstructured or hybrid (combination of structured and unstructured). In a structured mesh, a repeated pattern is followed where every node is uniquely defined according to a specified algorithm; while in an unstructured grid all nodes are typically arbitrarily defined automatically and no regular pattern is followed. In a structured grid, a node or vertex is surrounded by an equal number of nodes or vertices across space while there is no such requirement in unstructured grids.
Some of the advantages offered by structured mesh are:
1. Requirement of less computational memory and cost
Unstructured grids require large computational memory for storing elements, nodes, and a connectivity table to link them. The structured mesh, on the other hand, does not need the storage of any connectivity table as the mesh is defined according to a specified pattern.
2. Data Locality
Related to memory layout is data locality. In structured meshes, data for elements which are close geometrically is also close in memory by design. This results in less cache misses which means better usage of memory bandwidth. This is a critical concern for CFD on massively parallel GPU architectures where often memory bandwidth, not computation power, is the limitation.
3. Available solution algorithms
Structured data allows the use of solution algorithms which are not possible to implement on unstructured data. An example is a sweeping TDMA routine, which can be very beneficial to convergence in certain scenarios.
4. High degree of control
This is arguably the best reason that structured grids are not going anywhere. Structured meshing typically allows the user better control of interior node locations and sizes as interior node placement is directly linked to the user-defined exterior nodes. On the other hand, interior nodes for unstructured grids are generated automatically, losing the control over precise number cells or refinement in mesh you need locally.
5. Alignment leading to better convergence
Structured grids are typically aligned in the flow direction leading to more accurate results and a better convergence in CFD solvers. Unstructured grids have no such defined alignment towards flow contours. This is critically important at boundary walls where even in unstructured meshing, structured oriented elements are placed along the walls to better resolve the boundary layer.
Structured Mesh: A Great Choice
Traditionally, structured meshes were the norm but currently unstructured meshes have become commonplace due to their advantages in faster grid generation, ability to handle complex geometry and not much need of grid generation experience. Nevertheless, the efficacy of structured grids still make them a great choice for the reasons mentioned in this article.
Pointwise mesh example
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