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view extra/bim/inst/bim2a_axisymmetric_advection_upwind.m @ 12628:4cacfa5f9470 octave-forge
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author | cdf |
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date | Mon, 08 Jun 2015 08:51:06 +0000 |
parents | afa2a6681ec6 |
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## 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