H-grid topology

An H-grid is a structured grid topology for internal flow in a duct: the mesh fills the duct interior, with the streamwise direction running through the inlet and outlet faces and the cross-section faces meshing the duct walls. No body wraps the inside — the H-grid is empty inside, by design.

The name comes from the cross-section view of an H-grid wrapping a body in a channel (the wraps for the body and the channel walls, viewed end-on, look like the letter H). This page covers the body-less H-grid baseline: a duct without an internal body. When a body in a channel is needed, the standard CFD pattern is to compose an H-grid (filling the channel) with an O-grid or C-grid (wrapping the body), via SHORE's existing Chimera assembly pipeline.

Variants

shore.primitive exposes two analytic H-grid primitives:

Variant	CLI	Cross-section	Block layout	Use case
Rectangular	shore primitive h-grid-rect	rectangle	1 hex block, no singular axis	prismatic rectangular ducts; channels
Circular	shore primitive h-grid-tube	circle	1 hex block, j-periodic, polar singular axis at the centerline	straight cylindrical ducts; simple SRM chambers

A third variant — STL-driven H-grid — for variable-cross-section or non-circular ducts is on the roadmap (shore mesh --topology hgrid). The user supplies an inner-surface STL of the duct walls; the slicer extracts cross-section polylines per streamwise station and fits a structured 2D mesh to each. Star-shaped cross-sections from the centroid are the planned scope.

Conventions (both variants)

• Block axes: i is streamwise, j and k are the two cross-section directions.
• World alignment: streamwise_axis ("x", "y", or "z") selects which world axis the duct length runs along. Default x.
• Default face BCs: streamwise faces (i_lo, i_hi) are FREE (inflow / outflow); cross-section faces are WALL.
• The j_lo / j_hi faces are SHARED by periodic_j = True on the circular tube (closed circumferential direction); on the rectangular duct they are independent WALL faces.

Rectangular duct

shore primitive h-grid-rect \
    --length 1.0 --width 0.1 --height 0.2 \
    --ni 80 --nj 20 --nk 24 \
    --streamwise-axis x \
    --j-spacing tanh2 --j-beta 4.0 \
    --k-spacing tanh2 --k-beta 4.0 \
    -o duct
# → duct.geo

Single hex block of shape (ni, nj, nk, 3). length / width / height set the three Cartesian extents (length along the streamwise axis, width along block j, height along block k). Tanh / tanh2 spacing on the cross-section axes clusters nodes near the duct walls — the natural choice for boundary-layer resolution.

Face boundary conditions

Face	BC	Meaning
i_lo	FREE	Streamwise inflow
i_hi	FREE	Streamwise outflow
j_lo / j_hi	WALL	Two of the four duct walls
k_lo / k_hi	WALL	The other two duct walls

For a chimera assembly the streamwise FREE faces become inflow / outflow BCs in cc.par.

Circular tube

shore primitive h-grid-tube \
    --length 0.5 --radius 0.05 \
    --n-axial 60 --n-circ 32 --n-radial 10 \
    --streamwise-axis x \
    --k-spacing tanh --k-beta 3.0 \
    -o tube
# → tube.geo

Single hex block of shape (n_axial, n_circ, n_radial, 3) with a polar 2D cross-section:

• j = circumferential angle (0 → 2π), periodic by construction (block.periodic_j = True).
• k = radial coordinate from the centerline (k=0) to the outer wall (k=n_radial-1).
• i = streamwise.

Polar singular axis

The k = 0 row at the duct centerline is a polar singular axis: all n_circ angular nodes collapse to a single point at the centerline of the duct. Formally, the cells at k=0 are degenerate (zero-volume on the singular axis); finite-volume CFD codes that expect singular-axis handling (Xall's sphere-grid path is one) deal with this transparently. Codes that don't can be fed an h-grid-rect instead.

Face boundary conditions

Face	BC	Meaning
i_lo	FREE	Streamwise inflow
i_hi	FREE	Streamwise outflow
j_lo / j_hi	SHARED (periodic)	Circumferential periodicity
k_lo	WALL	Centerline singular axis (degenerate)
k_hi	WALL	Outer wall (real wall)

Python API

from shore.primitive import HGridRectMesh, HGridTubeMesh

# Rectangular duct.
duct = HGridRectMesh.build(
    length=1.0, width=0.1, height=0.2,
    ni=80, nj=20, nk=24,
    streamwise_axis="x",
    j_law="tanh2", j_beta=4.0,
    k_law="tanh2", k_beta=4.0,
)
duct.write_geo("duct.geo")
duct.write_vtk("duct.vtm")

# Circular tube.
tube = HGridTubeMesh.build(
    length=0.5, radius=0.05,
    n_axial=60, n_circ=32, n_radial=10,
    streamwise_axis="x",
    k_law="tanh", k_beta=3.0,
)
tube.write_geo("tube.geo")
tube.write_vtk("tube.vtm")

Both primitives follow the same PrimitiveMesh contract as BoxMesh / AnnularCylinderMesh / FlatCapsCylinder: self.blocks is a one-element list of HexBlock with the BCs already set.

Examples

End-to-end:

• examples/07-h-grid/visualize_h_grid.py — Python script generating both variants with optional PyVista viewer.
• examples/07-h-grid/visualize_h_grid.sh — bash equivalent, shore primitive h-grid-rect + h-grid-tube + shore export.

See also

• Topology catalogue — pick the right topology for your case.
• shore primitive — full CLI reference for all primitives.
• Chimera assembly walkthrough — how to compose an H-grid background with body-fitted near-mesh blocks.