""" extrude3d.py -- extrude the 2D x-y cross-section (section2d) into the 3D semi-structured mesh for the rotating-cube case. 3D shape subtlety (see CLAUDE.md): The cube is finite in z: it occupies |z| < c/2 only. In that mid z-band the x-y section has the diamond "hole" (cube is solid); above and below it the section is FULL (fluid), and the cube top/bottom faces (z = +/- c/2) are walls. Strategy: Mesh the full section ONCE -- including the diamond interior -- and extrude it in THREE z-bands so node-planes land exactly on z = +/- c/2. Every band extrudes the *identical* surface set, so the mesh is automatically conformal. Only the mid-band diamond volume is tagged as a separate "cube" cellZone; a later subsetMesh removes it, exposing the cube walls. This avoids any fragile per-band surface bookkeeping. Output (variant a, single connected mesh for the static-cube validation): section3d.msh -- physical volumes: fluid, cube ; physical surfaces: inlet, outlet, sides, zMin, zMax. (interface circle + cube walls stay internal here; the AMI split is variant b, later.) """ import os, math, gmsh # ---- in-plane parameters (identical to section2d.py) ----------------------- c = 1.0 a = c / math.sqrt(2.0) R = 1.0 * c x_in, x_out = -2.5*c, 5.0*c y_lo, y_hi = -1.5*c, 1.5*c n_tang = 26 n_rad = 18 prog = 1.14 # ---- z parameters ---------------------------------------------------------- zc = c / 2.0 # cube half-height: cube spans [-zc, +zc] z_far = 3.5 * c # outer z extent (extends beyond paper's +/-2.5c) nz_mid = 16 # uniform layers across the cube band [-zc, +zc] nz_band = 26 # graded layers in each outer band (fine near cube) z_ratio = 1.12 # geometric growth of z-layers away from the cube gmsh.initialize() gmsh.option.setNumber("General.Terminal", 1) geo = gmsh.model.geo def P(x, y, z=0.0): return geo.addPoint(x, y, z) # base section is built at z = -z_far, then extruded upward through the bands z0 = -z_far O = P(0, 0, z0) DE, DN, DW, DS = P(a,0,z0), P(0,a,z0), P(-a,0,z0), P(0,-a,z0) # diamond / cube wall CE, CN, CW, CS = P(R,0,z0), P(0,R,z0), P(-R,0,z0), P(0,-R,z0) # interface circle B1, B2, B3, B4 = P(x_in,y_lo,z0), P(x_out,y_lo,z0), P(x_out,y_hi,z0), P(x_in,y_hi,z0) # diamond edges (cube surface), circle arcs (interface), radial connectors dEN, dNW, dWS, dSE = (geo.addLine(DE,DN), geo.addLine(DN,DW), geo.addLine(DW,DS), geo.addLine(DS,DE)) aEN = geo.addCircleArc(CE, O, CN); aNW = geo.addCircleArc(CN, O, CW) aWS = geo.addCircleArc(CW, O, CS); aSE = geo.addCircleArc(CS, O, CE) rE, rN = geo.addLine(DE,CE), geo.addLine(DN,CN) rW, rS = geo.addLine(DW,CW), geo.addLine(DS,CS) oB, oR = geo.addLine(B1,B2), geo.addLine(B2,B3) oT, oL = geo.addLine(B3,B4), geo.addLine(B4,B1) # ---- diamond interior: one transfinite quad block (cube footprint) --------- dia_loop = geo.addCurveLoop([dEN, dNW, dWS, dSE]) sDia = geo.addPlaneSurface([dia_loop]) # ---- O-grid annulus: 4 transfinite quad blocks ----------------------------- def block(d, r2, arc, r1): cl = geo.addCurveLoop([d, r2, -arc, -r1]) return geo.addPlaneSurface([cl]) sEN = block(dEN, rN, aEN, rE) sNW = block(dNW, rW, aNW, rN) sWS = block(dWS, rS, aWS, rW) sSE = block(dSE, rE, aSE, rS) 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) geo.mesh.setTransfiniteSurface(sDia, "Left", [DE, DN, DW, DS]) 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) for s in (sDia, sEN, sNW, sWS, sSE): 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() # ---- in-plane size field (same intent as section2d) ------------------------ 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") 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) gmsh.option.setNumber("Mesh.RecombinationAlgorithm",1) # ---- z-banded extrusion ---------------------------------------------------- # base surface set, diamond FIRST so it is volume index 0 in every band. base = [(2, s) for s in (sDia, sEN, sNW, sWS, sSE, sOuter)] def graded(n, ratio, fine_at_end): """Return (numElements, cumHeights) for n single-element layers whose thickness grows geometrically; fine_at_end clusters thin layers near 1.0.""" th = [ratio**i for i in range(n)] if fine_at_end: th = th[::-1] tot = sum(th); cum, acc = [], 0.0 for t in th: acc += t/tot; cum.append(acc) cum[-1] = 1.0 return [1]*n, cum def extrude_band(surfs, dz, nE, hs): out = geo.extrude(surfs, 0, 0, dz, numElements=nE, heights=hs, recombine=True) vols, tops = [], [] for i, (d, t) in enumerate(out): if d == 3: # extrude block = [top(2), vol(3), sides...] vols.append(t); tops.append(out[i-1][1]) return vols, [(2, t) for t in tops] # band 1: bottom, [-z_far, -zc], fine near top (the cube) nE, hs = graded(nz_band, z_ratio, fine_at_end=True) v1, top1 = extrude_band(base, (-zc) - (-z_far), nE, hs) # band 2: middle, [-zc, +zc], uniform v2, top2 = extrude_band(top1, 2*zc, [nz_mid], [1.0]) # band 3: top, [+zc, +z_far], fine near bottom (the cube) nE, hs = graded(nz_band, z_ratio, fine_at_end=False) v3, top3 = extrude_band(top2, z_far - zc, nE, hs) geo.synchronize() # ---- physical groups ------------------------------------------------------- # cube = mid-band diamond volume only (v2[0]); fluid = everything else. cube_vol = v2[0] fluid_vol = [t for t in (v1 + v2 + v3) if t != cube_vol] gmsh.model.addPhysicalGroup(3, fluid_vol, name="fluid") gmsh.model.addPhysicalGroup(3, [cube_vol], name="cube") # exterior box faces, classified by their (planar) bounding box after meshing def classify_boundary(): tol = 1e-6 groups = {"inlet": [], "outlet": [], "sides": [], "zMin": [], "zMax": []} for (d, t) in gmsh.model.getEntities(2): x0,y0,zz0,x1,y1,zz1 = gmsh.model.getBoundingBox(2, t) if abs(x1-x0) < tol and abs(x0-x_in) < tol: groups["inlet"].append(t) elif abs(x1-x0) < tol and abs(x0-x_out) < tol: groups["outlet"].append(t) elif abs(y1-y0) < tol and (abs(y0-y_lo) < tol or abs(y0-y_hi) < tol): groups["sides"].append(t) elif abs(zz1-zz0) < tol and abs(zz0-(-z_far)) < tol: groups["zMin"].append(t) elif abs(zz1-zz0) < tol and abs(zz0-( z_far)) < tol: groups["zMax"].append(t) return groups groups = classify_boundary() for name, tags in groups.items(): if tags: gmsh.model.addPhysicalGroup(2, tags, name=name) gmsh.model.mesh.generate(3) # ---- report ---------------------------------------------------------------- OUT = os.path.dirname(os.path.abspath(__file__)) types, etags, _ = gmsh.model.mesh.getElements(3) import numpy as np counts = {4:"tets",5:"hexes",6:"prisms",7:"pyramids"} tot = 0 print("--- 3D element counts ---") for et, ets in zip(types, etags): n = len(ets); tot += n print(f" {counts.get(et,et):8s}: {n}") print(f" TOTAL 3D cells (incl. cube block to be removed): {tot}") print(f" boundary faces: " + ", ".join(f"{k}={len(v)}" for k,v in groups.items())) print(f" z bands: [-{z_far},-{zc}] x{nz_band} | [-{zc},{zc}] x{nz_mid} | [{zc},{z_far}] x{nz_band}") gmsh.write(os.path.join(OUT, "section3d.msh")) print("wrote section3d.msh") gmsh.finalize()