code/section2d.py

import math, gmsh

# ---- parameters (non-dimensional, c = 1) -----------------------------------
c      = 1.0
a      = c / math.sqrt(2.0)     # diamond half-diagonal (cube corner radius)
R      = 1.0 * c               # co-rotating interface (cylinder) radius
x_in, x_out = -2.5*c, 5.0*c    # domain in x  (inflow side at x_in)
y_lo, y_hi  = -1.5*c, 1.5*c    # domain in y

n_tang = 26    # nodes per diamond edge / per circle quarter-arc
n_rad  = 18    # radial nodes across the co-rotating annulus
prog   = 1.14  # radial grading: >1 clusters cells near the cube wall

gmsh.initialize()
gmsh.option.setNumber("General.Terminal", 0)
geo = gmsh.model.geo

def P(x, y): return geo.addPoint(x, y, 0.0)

O  = P(0, 0)
DE, DN, DW, DS = P(a,0), P(0,a), P(-a,0), P(0,-a)        # diamond (cube wall)
CE, CN, CW, CS = P(R,0), P(0,R), P(-R,0), P(0,-R)        # interface circle
B1, B2, B3, B4 = P(x_in,y_lo), P(x_out,y_lo), P(x_out,y_hi), P(x_in,y_hi)

# diamond edges (cube surface)
dEN, dNW, dWS, dSE = (geo.addLine(DE,DN), geo.addLine(DN,DW),
                      geo.addLine(DW,DS), geo.addLine(DS,DE))
# circle arcs (interface)
aEN = geo.addCircleArc(CE, O, CN); aNW = geo.addCircleArc(CN, O, CW)
aWS = geo.addCircleArc(CW, O, CS); aSE = geo.addCircleArc(CS, O, CE)
# radial connectors (wall -> interface)
rE, rN = geo.addLine(DE,CE), geo.addLine(DN,CN)
rW, rS = geo.addLine(DW,CW), geo.addLine(DS,CS)
# outer rectangle
oB, oR = geo.addLine(B1,B2), geo.addLine(B2,B3)
oT, oL = geo.addLine(B3,B4), geo.addLine(B4,B1)

# ---- O-grid annulus: 4 transfinite quad blocks -----------------------------
def block(d, r2, arc, r1):  # diamond edge, outer radial, arc(rev), inner radial(rev)
    cl = geo.addCurveLoop([d, r2, -arc, -r1])
    s  = geo.addPlaneSurface([cl]); return s

sEN = block(dEN, rN, aEN, rE)
sNW = block(dNW, rW, aNW, rN)
sWS = block(dWS, rS, aWS, rW)
sSE = block(dSE, rE, aSE, rS)
annulus = [sEN, sNW, sWS, sSE]

for ln in (dEN,dNW,dWS,dSE, aEN,aNW,aWS,aSE):
    geo.mesh.setTransfiniteCurve(ln, n_tang)
for ln in (rE,rN,rW,rS):
    geo.mesh.setTransfiniteCurve(ln, n_rad, "Progression", prog)
for s, corners in ((sEN,[DE,DN,CN,CE]),(sNW,[DN,DW,CW,CN]),
                   (sWS,[DW,DS,CS,CW]),(sSE,[DS,DE,CE,CS])):
    geo.mesh.setTransfiniteSurface(s, "Left", corners)
    geo.mesh.setRecombine(2, s)

# ---- outer (static) region: rectangle with circular hole, recombined -------
outer_loop = geo.addCurveLoop([oB, oR, oT, oL])
hole_loop  = geo.addCurveLoop([aEN, aNW, aWS, aSE])
sOuter     = geo.addPlaneSurface([outer_loop, hole_loop])
geo.mesh.setRecombine(2, sOuter)
geo.synchronize()

# size field: fine near body+wake, coarse far
fd = gmsh.model.mesh.field
f_dist = fd.add("Distance"); fd.setNumbers(f_dist, "CurvesList", [aEN,aNW,aWS,aSE])
f_thr  = fd.add("Threshold")
fd.setNumber(f_thr,"InField",f_dist); fd.setNumber(f_thr,"SizeMin",0.030)
fd.setNumber(f_thr,"SizeMax",0.28); fd.setNumber(f_thr,"DistMin",0.05); fd.setNumber(f_thr,"DistMax",2.2)
f_box  = fd.add("Box")            # wake refinement downstream
fd.setNumber(f_box,"VIn",0.06); fd.setNumber(f_box,"VOut",0.4)
fd.setNumber(f_box,"XMin",0.4); fd.setNumber(f_box,"XMax",x_out)
fd.setNumber(f_box,"YMin",-1.0); fd.setNumber(f_box,"YMax",1.0); fd.setNumber(f_box,"Thickness",0.4)
f_min = fd.add("Min"); fd.setNumbers(f_min,"FieldsList",[f_thr,f_box]); fd.setAsBackgroundMesh(f_min)

gmsh.option.setNumber("Mesh.MeshSizeExtendFromBoundary",0)
gmsh.option.setNumber("Mesh.MeshSizeFromCurvature",0)
gmsh.option.setNumber("Mesh.Algorithm",8)              # Frontal-Delaunay for quads
gmsh.option.setNumber("Mesh.RecombinationAlgorithm",1) # blossom

# physical groups (named so patches survive the .msh export)
def pg(dim, tags, name): gmsh.model.addPhysicalGroup(dim, tags, name=name)
pg(1,[dEN,dNW,dWS,dSE],"cube"); pg(1,[aEN,aNW,aWS,aSE],"interface")
pg(1,[oL],"inlet"); pg(1,[oR],"outlet"); pg(1,[oB,oT],"sides")
pg(2,annulus,"corotating"); pg(2,[sOuter],"static")

gmsh.model.mesh.generate(2)

# ---- report + preview -------------------------------------------------------
ntype, ntags = {}, gmsh.model.mesh.getElements(2)
types, etags, enodes = ntags
import numpy as np
node_tags, coords, _ = gmsh.model.mesh.getNodes()
xyz = {int(t): coords[3*i:3*i+2] for i,t in enumerate(node_tags)}
nq = nt = 0
import matplotlib; matplotlib.use("Agg")
import matplotlib.pyplot as plt
from matplotlib.collections import PolyCollection
polys=[]
for et, ets, ens in zip(types, etags, enodes):
    npe = {2:3,3:4}.get(et)
    if not npe: continue
    ens = ens.reshape(-1,npe)
    for row in ens:
        polys.append([xyz[int(n)] for n in row])
    if et==3: nq+=len(ets)
    if et==2: nt+=len(ets)
print(f"2D cells: {nq+nt}  (quads={nq}, tris={nt}, quad fraction={nq/(nq+nt):.3f})")

fig, axs = plt.subplots(1,2,figsize=(14,4.2))
for ax,(xl,yl,ttl) in zip(axs,[((x_in,x_out),(y_lo,y_hi),"full section"),
                               ((-1.6,1.6),(-1.6,1.6),"near-cube O-grid")]):
    pc=PolyCollection(polys, facecolors="none", edgecolors="#1f4e79", linewidths=0.25)
    ax.add_collection(pc); ax.set_xlim(*xl); ax.set_ylim(*yl); ax.set_aspect("equal")
    ax.set_title(ttl,fontsize=10)
    th=np.linspace(0,2*np.pi,200)
    ax.plot(R*np.cos(th),R*np.sin(th),"--",color="#c00000",lw=1.0)  # interface
import os
OUT = os.path.dirname(os.path.abspath(__file__))
plt.tight_layout(); plt.savefig(os.path.join(OUT,"section2d.png"),dpi=130)
print("saved preview")
gmsh.write(os.path.join(OUT,"section2d.msh"))
gmsh.finalize()