FEATool  v1.9
Finite Element Analysis Toolbox
ex_navierstokes10.m File Reference

Description

EX_NAVIERSTOKES10 3D Example for stationary flow in a pipe.

[ FEA, OUT ] = EX_NAVIERSTOKES10( VARARGIN ) Sets up and solves stationary and laminar 3D flow in a circular pipe. The inflow profile is constant and the outflow should assume an offset parabolic profile. Accepts the following property/value pairs.

Input       Value/{Default}        Description
-----------------------------------------------------------------------------------
rho         scalar {1}             Density
miu         scalar {0.01}          Molecular/dynamic viscosity
uin         scalar {0.3}           Magnitude of inlet velocity
R           scalar {0.5}           Channel radius
sf_u        string {sf_hex_Q1nc}   Shape function for velocity
sf_p        string {sf_disc0}      Shape function for pressure
solver      string <tt>openfoam</tt>/{'} Use OpenFOAM or default solver
iplot       scalar 0/{1}           Plot solution and error (=1)
                                                                                  .
Output      Value/(Size)           Description
-----------------------------------------------------------------------------------
fea         struct                 Problem definition struct
out         struct                 Output struct

Code listing

 cOptDef = {   ...
   'rho',      1;
   'miu',      1e-2;
   'uin',      0.3;
   'R',        0.5;
   'sf_u',     'sf_hex_Q1nc';
   'sf_p',     'sf_disc0';
   'tol',      0.2;
   'solver',   '';
   'iplot',    1;
   'fid',      1 };
 [got,opt] = parseopt(cOptDef,varargin{:});
 fid       = opt.fid;


% Geometry and grid generation.
 fea.sdim = { 'x', 'y', 'z' };
 fea.geom.objects = { gobj_cylinder([0 0 0],opt.R,3,1) };
 fea.grid = cylgrid(4,4,20,opt.R,3,[0;0;0],1);


% Problem definition.
 fea = addphys( fea, @navierstokes );
 fea.phys.ns.eqn.coef{1,end} = { opt.rho };
 fea.phys.ns.eqn.coef{2,end} = { opt.miu };
 fea.phys.ns.sfun            = { opt.sf_u opt.sf_u opt.sf_u opt.sf_p };
 if( strcmp(opt.solver,'openfoam') )
   [fea.phys.ns.sfun{:}] = deal('sflag1');
 end


% Boundary conditions.
 fea.phys.ns.bdr.sel(5) = 2;
 fea.phys.ns.bdr.sel(6) = 4;
 fea.phys.ns.bdr.coef{2,end}{1,5} = opt.uin;
 fea.phys.ns.prop.artstab.iupw = 4;


% Parse and solve problem.
 fea = parsephys( fea );
 fea = parseprob( fea );
 if( strcmp(opt.solver,'openfoam') )
   logfid = fid; if( ~got.fid ), fid = []; end
   fea.sol.u = openfoam( fea, 'fid', fid, 'logfid', logfid );
   fid = logfid;
 else
   fea.sol.u = solvestat( fea, 'fid', fid );
 end


% Postprocessing.
 if( opt.iplot>0 )
   postplot( fea, 'sliceexpr', 'sqrt(u^2+v^2+w^2)' )
 end


% Error checking.
 n = 15;
 y = linspace(0.05,0.95,n)' - 0.5;
 p = repmat([3 0 0]',1,n);
 p(2,:) = y;
 u = evalexpr( 'u', p, fea );
 u_ref = 2*opt.uin*(1-(y/opt.R).^2);
 out.err  = mean(abs(u-u_ref)./u_ref);
 out.pass = out.err < opt.tol;


 if ( nargout==0 )
   clear fea out
 end