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Package hex (in hex.i) - 3D transport equation solver

Index of documented functions or symbols:

DOCUMENT nlist = bi_dir(tracker, mesh, rays, slimits, c, s) Perform hexX_track and track_reduce on a ray that enters the problem at the given point on the ray. This requires tracking the ray in both directions from the given point, hence this function name indicating bi-directional tracking. This is unnecessary when the entry point search was over the problem boundary, or when the SLIMITS for the rays always lie in one direction relative to the starting point. TRACKER is the function used to track the rays, normally one of hex5_track, hex_24f_track, or hex24b_track. MESH is the problem mesh returned by hex_mesh or hydra_mesh; it should be generated using the entry option that finds the cell containing the given point on the ray. RAYS is the 3-by-nrays-by-2 array of rays, as for hex5_track SLIMITS is nil or the ray tracking limits as for track_reduce C, S, together with NLIST are the output arrays, as for track_reduce

SEE ALSO: track_reduce, hex5_track, hex24f_track, hex24b_track, track_combine

DOCUMENT conv3_rays(rays) convert [p,q] representation to or from best_rays representation. If the first dimension of RAYS is 3, returns 5-by-raydims array of best_rays; if first dimension of RAYS is 5, returns 3-by-raydims- by-2 [p,q] for use with hex5_track.

SEE ALSO: hex5_track, pic3_rays, best_rays

DOCUMENT nlist= cs_adjust(nlist, c, s, ireg) adjust NLIST, C, S returned from track_reduce to remove transits of cells for which IREG == 0. Can be called before or after c_adjust, depending on layout of IREG.

SEE ALSO: c_adjust

DOCUMENT c_adjust, c, mesh or c_adjust, c, mesh, 1 or c= c_adjust(c, mesh, how) adjust the cell number array C returned by track_reduce to allow for a different layout of cell arrays than the one assumed by the tracking routines. Two HOW values are currently supported: 0 (or nil) if the cell arrays are the same shape as the nodal arrays, but the non-existent cell is at the end of each row rather than at the beginning. And 1 if the cell arrays are smaller by one along each dimension than the nodal arrays. If you call c_adjust as a subroutine, the input C array is modified; if you call it as a function, the input C is unchanged and the new values returned.

SEE ALSO: track_reduce, hex5_track, cs_adjust

SEE: hex5_track

SEE: hex5_track

DOCUMENT c= hex5_track(mesh, rays, s) c= hex24f_track(mesh, rays, s) c= hex24b_track(mesh, rays, s) track 3 x Nrays x 2 RAYS through the 3D MESH. RAYS(,,1) are points on the rays, while RAYS(,,2) are normalized ray directions. The c return value and the S parameter are a long and double array respectively, with number of elements equal to the total number of intersections of all the RAYS with faces of the MESH, plus one for any RAY which misses MESH entirely. The values of c are: [#hits,cell1,cell2,cell3,..., #hits,cell1,cell2,cell3,..., ...] where each #hits is followed by the list of cell indices (assuming i=1, j=1, and k=1 are present but meaningless in cell arrays -- that is, assuming zone centered arrays have the same dimensions as XYZ rather than one less in each direction). Rays which miss the mesh entirely have #hits=1, all others have #hits>=2 since they must exit. #hits<0 means a ray reentered the mesh for abs(#hits) more face crossings, but this currently cannot happen. The values of S correspond to c: [s0,s1,s2,s3,..., s0,s1,s2,s3,..., ...] which are the distances along the ray measured from RAYS(,,1) in the direction of RAYS(,,2) where the ray pierces a cell face. For rays which miss the mesh, the value of s0 is a diagnostic telling why they missed (see compiled code). Function hex5_track uses the 5-tet decomposition for hexes, which is not unique when the quad faces are non-planar. You may be able to get an idea of this effect by setting hex_triang the opposite way and redoing the trace. Functions hex24f_track and hex24b_track use the face and body centered 24-tet decompositions for hexes. These are unique; however, hex_triang may in rare cases change the trace slightly, since the entry search algorithm still involves triangulating the surface quads.

SEE ALSO: hydra_mesh, hex_triang, reg_track, track_reduce, c_adjust, pic3_rays, conv3_rays

DOCUMENT mesh= hex_mesh(xyz, bound, nbnds, &mbnds, nblk, &blks, start) create a 3D mesh object from the multiblock mesh parameters XYZ is NBLK 3 x Ni x Nj x Nk coordinate arrays packed together BOUND is NBLK 3 x Ni x Nj x Nk face boundary markers packed NBNDS is length of MBNDS MBNDS is HX_blkbnd describing each internal block boundary face NBLK is number of blocks BLKS is NBLK HX_block objects describing the block structure START is 0-origin 6*cell+face index of first boundary face/cell or -1-cell to trace from centroid of that cell to point p on ray to begin tracking

SEE ALSO: hex5_track, hydra_mesh, hex_startflag

DOCUMENT mesh= hex_mesh2(xyz, bounds) old interface for hex_mesh create a 3D mesh object from the 3 x Ni x Nj x Nk coordinate array XYZ and the list of 6 BOUNDS: BOUNDS(1), BOUNDS(2) for the i=1,Ni boundaries BOUNDS(3), BOUNDS(4) for the j=1,Nj boundaries BOUNDS(5), BOUNDS(6) for the k=1,Nk boundaries The BOUNDS values are: 1 if this is a problem boundary 2 if this is a reflecting boundary 3 if this is a periodic boundary

SEE ALSO: hydra_mesh

DOCUMENT start= hex_query(mesh, xyz, bound, mbnds, blks) query a mesh created by hex_mesh, returning the arrays passed to that function (these are not copies -- be careful not to clobber them) function return value is the start index

SEE ALSO: hex5_track, hydra_mesh

DOCUMENT mesh= hydra_mesh(f) or mesh= hydra_mesh(f, ublk, i0, j0, k0, face) or mesh= hydra_mesh(f, ublk, i0, j0, k0) read a 3D mesh object from the hydra PDB/Silo file F. Note that the boundary arrays are adjusted to the hex convention that cells with i=1, j=1, k=1 are missing, rather than the hydra convention that i=imax, j=jmax, k=kmax are missing. In the first form, the ray entry search will start on the first open boundary face in the mesh. If the actual problem boundary is not convex, you need to identify a surface of constant i, j, or k in the problem which is convex, and which all the rays you intend to trace intersect. UBLK is the user block number (starting from 0), I0, J0, K0 are the (1-origin) logical coordinates of a hydra *cell*. Note that unlike hex cells, the hydra cell bounded by nodes (1,1,1) and (2,2,2) is numbered (1,1,1). (Hex numbers it (2,2,2).) FACE is the face number on cell (I0,J0,K0) which you want a ray to enter. 0 means the -I face, 1 the +I face, 2 the -J face, 3 the +J face, 4 the -K face, and 5 the +K face. As you step from this cell to its neighbors, then to their neighbors, and so on, this face must trace out a convex surface for the ray entry search. Rays not intersecting this surface will not enter the problem; the ray trace will begin at this surface, not at -infinity. If FACE==-1 or is omitted (as in the third form), then the given points on the rays are assumed to lie inside the mesh, and a pseudo ray from the centroid of cell (I0, J0, K0) will be tracked to the given point on each ray; the ray will be launched into the cell containing that point.

SEE ALSO: hex_query, hex5_track, h_data, h_openb

DOCUMENT hydra_start, mesh, start change the starting cell of the hydra MESH (returned by hydra_mesh) to START. If called as a function, returns old start value.

SEE ALSO: hydra_mesh, h_data

DOCUMENT make_sphere(radius, [imax,jmax,kmax], [phi1, phi2], [theta1, theta2]) return a mesh (see hex_mesh) representing the given section of the sphere of given RADIUS. IMAX, JMAX, and KMAX are the number of nodes (cells+1) in the radial, longitude (phi), and colatitude (theta) directions, respectively. Note that for a right handed coordinate system, phi1theta2.

SEE ALSO: hex_mesh

DOCUMENT rays= pic3_rays(xpict, ypict, ray) or rays= pic3_rays(xpict, ypict, ray, q_up) Like picture_rays, but returns rays in the [p,q] representation appropriate for hex5_track. (XPICT,YPICT) are 2D arrays of pixel corners in the image plane; RAY is the central ray (0,0) in (XPICT,YPICT) coordinates, given in [p,q] representation (i.e. RAY is a 3-by-2 array). The optional Q_UP is a 3-vector specifying the orientation of the y-axis in the picture plane (see theta_up, phi_up in picture_rays for a description of default orientation). Q_UP must not be parallel to RAY(,2).

SEE ALSO: hex5_track, conv3_rays, picture_rays

DOCUMENT c= reg_track(x, y, z, rays, s) track RAYS through regular mesh defined by the 1D coordinate arrays X, Y, and Z. Return values S and C are as for hex5_track, where the mesh is numberof(X) by numberof(Y) by numberof(Z).

SEE ALSO: hex5_track, track_reduce

DOCUMENT nlist = track_combine(nm,cm,sm, np,cp,sp, c, s) combine two track_reduce results NM,CM,SM, and NP,CP,SP, which represent the first and second halves of a set of rays. See bi_dir for a typical application. The returned NLIST is NM+NP, or NM+NP-1 for those rays where the final CM is identical to the initial CP. C, S, together with NLIST are the output arrays, as for track_reduce.

SEE ALSO: track_reduce, bi_dir

DOCUMENT result= track_integ(nlist, transp, selfem, last) integrates a transport equation by doing the sums: transparency(i) = transparency(i-1) * TRANSP(i) emissivity(i) = emissivity(i-1) * TRANSP(i) + SELFEM(i) returning only the final values transparency(n) and emissivity(n). The NLIST is a list of n values, so that many transport integrals can be performed simultaneously; sum(NLIST) = numberof(TRANSP) = numberof(SELFEM). The result is 2-by-dimsof(NLIST). If TRANSP is nil, result is dimsof(NLIST) sums of SELFEM. If SELFEM is nil, result is dimsof(NLIST) products of TRANSP. TRANSP and SELFEM may by 2D to do multigroup integrations simultaneously. By default, the group dimension is first, but if LAST is non-nil and non-zero, the group dimension is second. In either case, the result will be ngroup-by-2-by-dimsof(NLIST). track_solve is the higher-level interface.

SEE ALSO: track_reduce, track_solve, track_solve

DOCUMENT nlist= track_reduce(c, s) or nlist= track_reduce(c, s, rays, slimits) compresses the C and S returns from the tracking routines (see hex5_track) to the following form: [cell1,cell2,cell3,..., cell1,cell2,cell3,..., ...] [s1-s0,s2-s1,s3-s2,..., s1-s0,s2-s1,s3-s2,..., ...] returning nlist as [#hits, #hits, ...] In this form, any negative #hits are combined with the preceding positive values, and #hits=1 (indicating a miss) appear as #hits=0 in nlist. Hence, nlist always has exactly Nrays elements. If RAYS is supplied, it is used to force the dimensions of the returned nlist to match the dimensions of RAYS (the value of RAYS is never used). The RAYS argument need not have the trailing 2 dimension, so if you specified RAYS as [P,Q] if the call to hex5_track, you can use just P or Q as the RAYS argument to track_reduce. If SLIMITS is supplied, it should be [smin,smax] or [smin,smax]- by-dimsof(nlist) in order to reject input S values outside the specified limits. The C list will be culled appropriately, and the first and last returned ds values adjusted. With a non-zero flip= keyword, the order of the elements of C and S within each group of #hits is reversed, so that a subsequent track_solve will track the ray backwards. If you use this, both the ray direction input to the tracking routine and any SLIMITS argument here should refer to the reverse of the ray you intend to track.

SEE ALSO: hex5_track, c_adjust, track_solve, track_integ, bi_dir, track_combine

DOCUMENT result= track_solve(nlist, c, s, akap, ekap, last) integrates a transport equation for NLIST, C, and S returned by track_reduce (and optionally c_adjust). The RAYS argument is used only to set the dimensions of the result. AKAP and EKAP are mesh-sized arrays of opacity and emissivity, respectively. They may have an additional group dimension, as well. The units of AKAP are 1/length (where length is the unit of S), while EKAP is (spectral) power per unit area (length^2), where the power is what ever units you want the result in. The emission per unit volume of material is EKAP*AKAP; an optically thick block of material emits EKAP per unit surface. The NLIST is a list of n values, so that many transport integrals can be performed simultaneously; sum(NLIST) = numberof(AKAP) = numberof(EKAP). The result is 2-by-dimsof(NLIST), where the first element of the first index is the transmission fraction through the entire ray path, and the second element of the result is the self-emission along the ray, which has the same units as EKAP. If EKAP is nil, result is dimsof(NLIST) -- exactly the same as the transparency (1st element of result) when both EKAP and AKAP are specified. If AKAP is nil, result is dimsof(NLIST). In this case, EKAP must have units of emission per unit volume instead of per unit area; the result will be the sum of EKAP*S along each ray. AKAP and EKAP may by 2D to do multigroup integrations simultaneously. By default, the group dimension is first, but if LAST is non-nil and non-zero, the group dimension is last. In either case, the result will be ngroup-by-2-by-dimsof(NLIST). To use in conjuction with hex5_track, one might do this: c= hex5_track(mesh, rays, s); nlist= track_reduce(c, s, rays); c_adjust, c, mesh; // if necessary result= track_solve(nlist, c, s, akap, ekap);

SEE ALSO: track_reduce, hex5_track