FEATool Multiphysics  v1.13 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
sf_u        string {sf_hex_Q1nc}   Shape function for velocity
sf_p        string {sf_disc0}      Shape function for pressure
solver      string openfoam/su2/{} Use OpenFOAM, SU2 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',      0.25;
'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( any(strcmp(opt.solver,{'openfoam','su2'})) )
[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;
elseif( strcmp(opt.solver,'su2') )
logfid = fid; if( ~got.fid ), fid = []; end
fea.sol.u = su2( 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