Appropriate mesh generation is essential for an accurate solution, faster convergence, and reduction of numerical diffusion. Poorly formed meshes introduce numerical error, increasing the computational cost of convergence. For especially poor elements, the numerical order may be locally reduced to promote convergence and stability or, even worse, the solution may fail to converge entirely.
1. Structured grids are identified by regular connectivity (ordered type by indices such as i, j, and k and the topology is easily associated to the next indices). The possible element choices are quadrilateral in 2D and hexahedra in 3D. The regularity of the connectivity lets you conserve space because neighborhood relationships are defined by the storage arrangement.
1. Unstructured grids have no such ordering. Therefore, a node is associated to a single integer index and the topology is known by associating connections of the node with the neighboring nodes. Compared to structured meshes, the storage requirements for an unstructured mesh can be substantially larger because the neighborhood connectivity must be explicitly stored.
2. Grids can be Cartesian or Curvilinear (usually body-fitted). In the Cartesian grid, grid lines are always parallel to the coordinate axes. In the Curvilinear grid, coordinate surfaces are curved to fit boundaries. There is an alternative division into orthogonal and non-orthogonal grids. In orthogonal grids (for example, Cartesian or polar meshes), all grid lines cross at 90º. Some flows can be treated as axisymmetric, and in these cases, the flow equations can be expressed in terms of polar coordinates (r, θ), rather than Cartesian coordinates (x, y), with slight modifications.
2. Grids can be triangular (tetrahedral), quadrilateral (hexahedral), polygon (polyhedral), and hybrid. Unstructured grids can accommodate completely arbitrary geometries. Grid generators for such meshes are also very complex.
3. Advantages of structured girds are better convergence, a high degree of quality and control, less memory and time resolution (does not need the storage of any connectivity table because the mesh is defined according to a specified pattern).
3. Advantages of unstructured grids are the ability to handle complex geometries and the possibility to generate anisotropic meshes in the far field without cell clustering and propagation, ideal for marine applications, for example, to capture the free surface and keep the lower cell count.
4. Structured meshes can be generated using a variety of well-defined mathematical techniques, ranging from algebraic to conformal mapping to the solution of partial differential equations.
4. Algorithms used to generate unstructured meshes are generally based on the Delaunay algorithm or an advancing front technique.
Unstructured meshes are generated using Fidelity Hexpress and Fidelity Pointwise.
Two different generation approaches are available in Fidelity Hexpress and can serve different purposes based on the inputs and needs of the user:
Volume-to-surface approach: Generation of the mesh starts from the domain volume, and it is successively adapted to the geometry. This approach is particularly convenient for complex geometries and unclean geometry inputs (for example, non-watertight geometries, non-conformal triangulations).
Surface-to-volume approach: Generation of the mesh starts from surfaces of the geometry and is successively propagated to the domain volume. This approach can produce very high-quality unstructured meshes with very tidy cell patterns on the surfaces. It requires conformal geometries.
Fidelity Autogrid technology automates the laborious geometry preparation process without losing any detail of the geometry and delivers quality meshes ready for CFD simulations in real real-time and is used for turbo machinery configuration.
Figure 1: Unstructured mesh generation done by Fidelity Hexpress
Figure 2: Structured mesh generation done by Fidelity Autogrid
Fidelity Pointwise can generate structured multi-block, unstructured, hybrid, and overset meshes for viscous simulations with precise control over point placement and clustering to get the desired resolution. At the same time, Pointwise’s core meshing methods produce cells of high quality to ensure convergence and accuracy in your CFD solution.
Figure 3: Unstructured mesh generation done by Fidelity Pointwise
Cadence Design Systems