Near-Wall Resolution

Near-Wall Resolution#

Accurate prediction of wall-bounded flows — drag, heat transfer, separation — depends on resolving the thin region of rapidly-changing velocity near solid surfaces. In Gradient Dynamics, near-wall resolution is achieved through AMR block refinement near geometry surfaces, without the need for traditional prismatic boundary layer extrusion.

How It Works#

The structured Cartesian cut-cell approach resolves near-wall flow by recursively refining blocks in the AMR hierarchy near geometry surfaces. The cut-cells at the geometry boundary form the wall-adjacent layer, and the resolution of those cells is set by the AMR level applied near the surface.

This is different from traditional unstructured meshing approaches, which grow prismatic “prism layers” from wall surfaces. With block AMR:

  • Near-wall resolution is controlled by the surface refinement level setting

  • The wall-adjacent cell size is base_cell_size / 2^(AMR_levels_near_wall)

  • Resolution increases geometrically approaching the surface — similar in effect to growth-rate prism layers, but achieved through the block hierarchy

  • No separate configuration of layer count, first-layer height, or growth rate is needed

Wall Cell Size and y+#

The y+ value of the first wall cell determines which wall treatment your turbulence model uses. You control y+ through the near-wall AMR level setting (in the Mesh Settings tab → Surface Refinement → Near-Wall Levels).

Estimating Wall Cell Size#

For a given near-wall AMR level n and base cell size h:

wall_cell_size ≈ h / 2^n

Use the y+ calculator in the Mesh Settings tab to compute the expected y+ for your flow speed and geometry scale.

y+ Guidelines by Turbulence Model#

Turbulence Model

Target y+

Near-Wall AMR

Wall Treatment

k-ω SST

~30 (wall function)

Medium (default)

Spalding or Reichardt

k-ω SST

~1 (resolved)

Fine or Very Fine

None (resolved)

k-ε

30 – 300

Medium

Spalding or Reichardt

Spalart-Allmaras

~1 or ~30

Medium to Fine

Spalding or Linelets

RSM

~30 or ~1

Medium to Fine

Spalding or Reichardt

LES (any SGS model)

~1

Very Fine

None (resolved)

DES / DDES

~1 – 30

Fine

Spalding (RANS region)

Tip

For most RANS simulations, the default Medium surface refinement with y+ ≈ 30 and Spalding wall function gives good results. Use Fine or Very Fine only when wall-resolved treatment is needed (LES, detailed heat transfer, or sensitive separation prediction). The linelet wall treatment offers a middle ground — wall-resolved accuracy at wall-function mesh resolution — and is particularly effective on Cartesian cut-cell meshes. See Solver Settings for details on wall treatment options.

Configuring Near-Wall Resolution#

  1. Navigate to the Mesh Settings tab

  2. Under Surface Refinement, set the Near-Wall Levels slider

  3. Use the y+ Calculator to verify the resulting wall cell size for your flow speed

  4. Generate the mesh and check the reported y+ distribution in the Mesh Quality panel

Anisotropic Near-Wall Refinement#

For high-Reynolds-number flows where extreme wall resolution would be costly in all directions, enable anisotropic near-wall refinement. Instead of splitting blocks into 8 equal children (2×2×2), anisotropic refinement can split in selected directions only — for example, 2×1×1 in the wall-normal direction. This produces cells that are fine in the wall-normal direction but coarser in the wall-parallel directions, dramatically reducing cell count while maintaining the y+ target at the wall.

How it works:

  • Blocks adjacent to geometry surfaces are tagged for directional refinement based on the local wall-normal direction

  • The refinement direction is determined automatically from the geometry surface orientation

  • 2:1 balance is still enforced between neighboring blocks to ensure smooth transitions

  • The solver handles the resulting anisotropic cells natively — no special treatment required

When to use anisotropic refinement:

  • High-Reynolds-number external aerodynamics where y+ ≈ 1 would otherwise produce excessive cell counts

  • Cases where near-wall resolution is critical but far-field cell count must be controlled

  • LES or DES simulations where wall-parallel resolution requirements are less stringent than wall-normal

Note

Anisotropic near-wall refinement is available on Pro tier and above.

Mesh Quality Near Walls#

The wall-adjacent cut-cells are the only cells that deviate from perfect Cartesian quality. The mesher automatically:

  • Merges very small cut-cell slivers (volume fraction < 0.1) with neighboring cells

  • Reports the minimum cut-cell volume fraction in the quality report

  • Flags problematic cut-cells for inspection in the 3D viewer

High aspect-ratio cells in the near-wall region are expected and desirable — these are flagged informatively, not as errors.

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