Why mesh topology is the secret to accurate wave physics.
In Computational Fluid Dynamics, we often focus on cell count as the primary metric for accuracy. However, when simulating time-accurate phenomena like wave propagation, the topology of the mesh, how those cells are connected, becomes the deciding factor between a physical result and a numerical artifact.
Let's look at two meshes. The first is based on the Ennova polyhedral mesh and the second is a more conventional Cartesian mesh.
What you should pay attention to is the transition of the mesh element size from one element to the next. In the polyhedral mesh, there are no obvious large jumps from one cell to another. In contrast, the Cartesian mesh shows rows and columns of elements of one size transitioning across a single face to elements with twice the length and width. In 3D, this will cause the element volume to change by a factor of eight from one cell to the next.
Below we show the results of a pulse of high-pressure air being driven down an open-ended pipe. When the pulse of air hits the end of the pipe there is a shock wave that propagates out into the open cavity. That is the real physical effect that we want to simulate.
In the case of the Cartesian mesh, the sound wave appears to bounce or reflect off empty space. The high-pressure area is not quite circular and seems to propagate more quickly vertically and horizontally than diagonally.
As time progresses, the rearward reflected waves become much larger in amplitude for the Cartesian mesh, and the main blue pressure wave is very clearly not circular.
Many automated meshers rely on Cartesian or octree-based refinement. While fast to generate, these grids often create hanging nodes where a single large cell face meets several smaller ones.
By using a Dualizer approach, converting a tetrahedral base into a honeycomb-like polyhedral structure, Ennova achieves a conformal transition. Because polyhedral cells have a high number of neighbors, the mesh is naturally isotropic, so the wave sees the same resistance in every direction.
| Feature | Smooth Polyhedral (Dual) | Cartesian (Octree) |
|---|---|---|
| Wave Shape | Perfectly spherical | Distorted / squared |
| Connectivity | Conformal (shared faces) | Non-conformal (hanging nodes) |
| Energy Loss | High energy preservation | High numerical diffusion |
An additional benefit of moving to an Ennova polyhedral mesh is a significant reduction in total cell count compared to octree-based Cartesian grids. In a Cartesian mesh, refining the free surface or a complex hull requires a power-of-two cell splitting, creating a massive number of redundant cells in the volume just to get the required resolution at the interface.
The choice of mesh is not just a matter of aesthetics; it is the foundation of high-fidelity physics. Whether resolving marine waves around a hull, shock waves in hypersonics, or sound propagation in aeroacoustics, a smooth polyhedral mesh ensures that the physics, not the grid, dictates the result.
The full video of this study can be found here.
Ennova Marine is the first dedicated marine application to recognize that accurate surface waves require a conformal mesh.
