/usr/share/octave/packages/bim-1.1.5/bim2a_axisymmetric_advection_upwind.m is in octave-bim 1.1.5-4.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 | ## Copyright (C) 2006-2014 Carlo de Falco, Massimiliano Culpo
##
## This file is part of:
## BIM - Diffusion Advection Reaction PDE Solver
##
## BIM is free software; you can redistribute it and/or modify
## it under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 2 of the License, or
## (at your option) any later version.
##
## BIM is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
## GNU General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with BIM; If not, see <http://www.gnu.org/licenses/>.
##
## author: Carlo de Falco <cdf _AT_ users.sourceforge.net>
## author: Massimiliano Culpo <culpo _AT_ users.sourceforge.net>
## author: Matteo porro <meoo85 _AT_ users.sourceforge.net>
## author: Emanuela Abbate <emanuela.abbate _AT_ mail.polimi.it>
## -*- texinfo -*-
##
## @deftypefn {Function File} @
## {[@var{A}]} = @
## bim2a_axisymmetric_advection_upwind (@var{mesh}, @var{beta})
##
## Build the Upwind stabilized stiffness matrix for an advection problem
## in cylindrical coordinates with axisymmetric configuration.
##
## The equation taken into account is:
##
## 1/r * d/dr (r * @var{beta}_r u) + d/dz (@var{beta}_z u) = f
##
## where @var{beta} is an element-wise constant vector function.
##
## Instead of passing the vector field @var{beta} directly one can pass
## a piecewise linear conforming scalar function @var{phi} as the last
## input. In such case @var{beta} = grad @var{phi} is assumed.
##
## If @var{phi} is a single scalar value @var{beta} is assumed to be 0
## in the whole domain.
##
## @seealso{bim2a_axisymmetric_rhs, bim2a_axisymmetric_reaction,
## bim2a_axisymmetric_advection_diffusion, bim2c_mesh_properties}
## @end deftypefn
function A = bim2a_axisymmetric_advection_upwind (mesh, beta)
## Check input
if nargin != 2
error("bim2a_axisymmetric_advection_upwind: wrong number of input parameters.");
elseif !(isstruct(mesh) && isfield(mesh,"p") &&
isfield (mesh,"t") && isfield(mesh,"e"))
error("bim2a_axisymmetric_advection_upwind: first input is not a valid mesh structure.");
elseif !(all(mesh.p(1,:) >= 0) || all(mesh.p(1,:) <= 0))
error("bim2a_axisymmetric_advection_upwind: the input mesh cannot intersect the rotation axis r=0.");
endif
nnodes = columns(mesh.p);
nelem = columns(mesh.t);
x = abs (mesh.p(1,:));
x = x(mesh.t(1:3,:));
y = mesh.p(2,:);
y = y(mesh.t(1:3,:));
alphaareak = reshape (mesh.area, 1, 1, nelem);
shg = mesh.shg(:,:,:);
## Build local Laplacian matrix
Lloc = zeros(3,3,nelem);
for inode = 1:3
for jnode = 1:3
ginode(inode,jnode,:) = mesh.t(inode,:);
gjnode(inode,jnode,:) = mesh.t(jnode,:);
Lloc(inode,jnode,:) = sum( shg(:,inode,:) .* shg(:,jnode,:),1) .* alphaareak;
endfor
endfor
if all(size(beta)==1)
v12 = 0;
v23 = 0;
v31 = 0;
elseif all(size(beta)==[2,nelem])
v12 = beta(1,:) .* (x(2,:)-x(1,:)) + beta(2,:) .* (y(2,:)-y(1,:));
v23 = beta(1,:) .* (x(3,:)-x(2,:)) + beta(2,:) .* (y(3,:)-y(2,:));
v31 = beta(1,:) .* (x(1,:)-x(3,:)) + beta(2,:) .* (y(1,:)-y(3,:));
elseif all(size(beta)==[nnodes,1])
betaloc = beta(mesh.t(1:3,:));
v12 = betaloc(2,:)-betaloc(1,:);
v23 = betaloc(3,:)-betaloc(2,:);
v31 = betaloc(1,:)-betaloc(3,:);
else
error("bim2a_axisymmetric_advection_upwind: coefficient beta has wrong dimensions.");
endif
[bp12, bm12] = deal (- (v12 - abs (v12))/2, (v12 + abs (v12))/2);
[bp23, bm23] = deal (- (v23 - abs (v23))/2, (v23 + abs (v23))/2);
[bp31, bm31] = deal (- (v31 - abs (v31))/2, (v31 + abs (v31))/2);
r12 = (x(2,:) + x(1,:)) / 2;
r23 = (x(3,:) + x(2,:)) / 2;
r31 = (x(1,:) + x(3,:)) / 2;
bp12 = reshape(r12 .* bp12,1,1,nelem).*Lloc(1,2,:);
bm12 = reshape(r12 .* bm12,1,1,nelem).*Lloc(1,2,:);
bp23 = reshape(r23 .* bp23,1,1,nelem).*Lloc(2,3,:);
bm23 = reshape(r23 .* bm23,1,1,nelem).*Lloc(2,3,:);
bp31 = reshape(r31 .* bp31,1,1,nelem).*Lloc(3,1,:);
bm31 = reshape(r31 .* bm31,1,1,nelem).*Lloc(3,1,:);
Sloc(1,1,:) = (-bm12-bp31);
Sloc(1,2,:) = bp12;
Sloc(1,3,:) = bm31;
Sloc(2,1,:) = bm12;
Sloc(2,2,:) = (-bp12-bm23);
Sloc(2,3,:) = bp23;
Sloc(3,1,:) = bp31;
Sloc(3,2,:) = bm23;
Sloc(3,3,:) = (-bm31-bp23);
A = sparse(ginode(:), gjnode(:), Sloc(:));
endfunction
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