Clipped Voronoi Meshing: Deterministic Grids for Industrial-Scale LES

For most teams running scale-resolving simulation, the solver is not the constraint. WMLES on a 100M to 1B+ cell grid is a known quantity, resolving separation, vortex shedding, mixing, and acoustic source behavior that no RANS closure will produce.

The constraint is upstream. Getting a grid that an LES will tolerate, on real geometry with tight gaps and intersecting passages and thin walls, is where the schedule disappears. A senior engineer spends two weeks on inflation layer tuning and cleanup, nobody else on the team can reproduce the result exactly, and by the time it runs, the design study that justified it has moved on. That cost is labor, not compute. More nodes will not fix it.

Figure 1: Full-scale Honda Fit meshed with clipped Voronoi diagrams in Fidelity Stitch. Polyhedral cells throughout, no prism stack anywhere on the vehicle.

Topology Stops Being a Negotiation

A Voronoi diagram partitions space by Euclidean distance to a set of generating points. Each cell is the region closer to its own point than to any other, and the faces are perpendicular bisectors between neighbors. Clip that diagram against the CAD surface and you get a body-fitted polyhedral mesh: exterior cells cut by the geometry, interior cells defined purely by point spacing.

Figure 2: (a) Generating points define cells whose faces are perpendicular bisectors between neighbors. (b) The bounding surface clips the exterior cells, leaving interior cells defined by point spacing alone. Topology never depends on surface topology or domain decomposition. (Brès et al., 2023c)

Mesh topology, therefore, depends on the point cloud alone. Not on surface topology, and not on how the domain was partitioned across ranks during parallel generation. Two engineers on two machines, given the same spacing rules, produce the same mesh. Design studies become directly comparable, certification evidence becomes defensible, and you stop paying the quiet tax of a multi-site program where the Detroit mesh and the Stuttgart mesh disagree, and nobody can say why.

You specify resolution intent instead of topology. Point placement alone then yields Cartesian-like regions, highly anisotropic cells appropriate for WMLES, and deliberately coarse zones where the physics permits.

The Inflation Layer Goes Away

This is the largest labor line item removed. Near-wall resolution comes from tightening point spacing toward the surface. No prism stack to grow, no first-layer-height against growth-rate negotiation, no collapsed layers or tangled prisms to diagnose at 11 PM.

For conjugate heat transfer, it is structural rather than ergonomic. Clipping produces fluid and solid cells meeting on a shared, perfectly aligned interface, and both domains mesh in one pass. The PAW-05 dual-bypass nozzle work predicted wall heat flux, shock structure, and plume behavior with WMLES plus CHT on automatically generated grids, a case class that historically consumed a meshing specialist for a month.

Because volumetric resolution is decoupled from fine surface features, quality holds where body-fitted meshers usually break: turbomachinery tip gaps, automotive underbody and cooling packages, effusion cooling holes, intersecting ducts. Motion works for the same reason. Within an ALE framework with a sliding interface, the per-timestep rebuild updates Voronoi faces on the moving-stationary boundary only, preserving a single conformal grid and a conservative discretization at every step.

Figure 3: Near-wall resolution on a rotor blade set by point spacing alone: 0.125 mm wall-normal, 0.5 mm tangential, aspect ratio 4, 5 layers over the surface. No inflation layer was grown to produce this.

The Full Methodology and Validation Record

The white paper Deterministic Voronoi Meshing for Complex, Multiphysics Geometries covers the clipped Voronoi construction, the NASA validation history, and the propulsion, automotive, turbomachinery, and CHT application cases.

Read the white paper.

The Solver Has to Deserve the Mesh

The Fidelity Charles Solver uses a finite volume discretization built on a generalization of the discrete entropy framework for unstructured meshes, with KEEP schemes. The result is a stable, homogeneous flux discretization without shock sensors, upwinding hybridization, or hand-tuned stability coefficients. You are not spending a week hunting the dissipation setting that stops vortices smearing before they reach the FW-H surface.

Coverage runs subsonic through hypersonic, plus a low-Mach Helmholtz formulation whose pressure field carries both hydrodynamic and acoustic components, so FW-H data and vibro-acoustic input come out of one solve. Sub-grid stresses use the Vreman model. Post-processing includes FW-H propagation from permeable surfaces and modal decomposition via POD and DMD.

A Production Case, Not a Benchmark Case

Toyota Motor Europe ran this stack on the Cadence Millennium M1 platform for HVAC vent noise, across two full-scale duct geometries at 0 and 32 degree blade angles. The Voronoi mesh came to roughly 30 million cells with sub-0.2 mm resolution at blades and outlets, generated in 4 minutes on 96 CPU cores. On-GPU streaming mode computed the acoustic signals during runtime for about 25% additional throughput.

Figure 4a: Toyota vent exhaust mesh: Roughly 30 million cells with sub-0.2 mm resolution at the blades and outlets, generated in 4 minutes on 96 CPU cores.

Against the facility’s own microphone array the simulation held within 3 dBA from 1 to 5 kHz, the band where HVAC content becomes audible once there is no engine to mask it, and it captured the difference between blade angles in both trend and magnitude. Under 6 hours on 8 GPUs on Millennium M1, against 60-plus hours on 512 CPUs conventionally. That is the difference between comparing vent designs inside a sprint and inside a quarter.

Toyota Motor Europe’s full case study, Toyota Cuts HVAC Noise Simulation Time by 90% with GPU-Accelerated CFD, covers the mesh setup, FW-H configuration, and the band-by-band agreement with their rig data.

Read the case study

Figure 4b: Predicted against measured SPL at microphone 1, vent blades at 0 and 32 degrees. Agreement within 3 dBA from 1 to 5 kHz, including the difference between the two blade angles.

What It Costs to Run

Mesh generation at the top end: 11.4 billion cells on the NASA HL-CRM in 22 minutes on 43,200 cores, from the NASA-validated Stitch generator developed at Cascade Technologies, now part of Cadence.

Solver turnaround as published in the Fidelity Charles Solver technical brief, two Millennium nodes each: DrivAer 144M cells in 4.6 hours, NASA SDT turbofan 142M in 6.7, GE E3 combustor 180M in 7.8, JSM airframe 185M in 13.9.

Scaling holds well enough to buy your way out of a deadline. On a 118 Mcv full-scale sedan the low-Mach solver stayed above 90% scalability at 32,768 CPU cores and scaled near-ideally to 32 NVIDIA V100 GPUs at 3.7 Mcv per GPU: 16,000 CPU-hours on 2,560 cores reduced to 50 GPU-hours for identical acoustic spectra. The solver is GPU-resident on both NVIDIA and AMD architectures, with the Honda full-scale eVTOL case run on Mi210.

Where This Is Not the Answer

RANS is not displaced. For attached-flow parametric sweeps at high Reynolds number, where SST, GEKO, or EARSM closures are calibrated against your own test data and a case turns around in minutes, WMLES is the wrong tool and a Voronoi grid is overkill. The rotor work cited here is wall-modeled, at y+ around 30 with 50 to 100 cv per chord. Wall-resolved LES on complex geometry remains expensive.

Judgment does not disappear either, it relocates. Instead of debugging prism stacks you decide where resolution belongs, and a bad spacing specification produces a fast, clean, wrong mesh. The difference is that you find out in minutes rather than a fortnight.

See It on Your Own Geometry

Benchmark cases prove a method works. They do not tell you what it does to your schedule, or whether it reproduces the one result your team already argues about.

Fidelity CFD Software is available as a 30-day trial on your own geometry at your own operating conditions, with a Cadence CFD engineer helping get it running on your setup. The useful test is not a tutorial case. Bring something where you already know the answer: a rig you have measured, a configuration your current RANS setup gets wrong, a geometry whose meshing has cost you a fortnight before. Then compare cell count, turnaround time, and agreement with your own data.