Polyhedral, Tetrahedral, and Hexahedral Mesh Comparison
Are you wondering how a polyhedral (dual) mesh compares to the equivalent tetrahedral and hexahedral meshes? Then you're in the right place. This study compares the volume element count, convergence, accuracy, and runtimes of the three different types of meshes for a simple duct.
This study focuses on a 3D backward facing step within a duct. The duct geometry was decomposed into 6-faced blocks so it could support a hexahedral mesh as well as the more general tetrahedral and polyhedral meshes.
Slices through the meshes revealing volume elements are shown below.
The polyhedral mesh is derived directly from the tetrahedral mesh by forming polygons around each node in the tetrahedral mesh.
The pressure residual for each mesh type is show below.
The solution on the polyhedral mesh produced the lowest absolute residual value.
The number of iterations for each mesh type to reach the same level of convergence (1x10-4) for the pressure residual are shown below.
Accuracy (Pressure Drop)
The pressure drop for each mesh type is shown below.
While there are minor differences in the converged pressure drop the simulations are in broad agreement on the overall value.
The number of iterations for each mesh type to reach a steady state value for the pressure drop are shown below.
Assuming our goal is to reach the steady state pressure drop for each simulation, then the runtimes (scaled against the slowest simulation) are shown below.
Cleary this study shows that polyhedral cells hold great promise in producing equivalent accuracy results compared to other mesh types with the added benefits of:
- Faster converge with fewer iterations
- Robust convergence to lower residual values
- Faster solution runtimes