Description

EX_NAVIERSTOKES12 3D Example flow over a backwards facing step.

[ FEA, OUT ] = EX_NAVIERSTOKES12( VARARGIN ) Sets up and solves stationary and laminar 3D flow over a backwards facing step. Accepts the following property/value pairs.

Input       Value/{Default}        Description
-----------------------------------------------------------------------------------
rho         scalar {1}             Density
miu         scalar {2/3/389}       Molecular/dynamic viscosity
uin         scalar {1}             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 <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',      2/3/389;
   'uin',      1;
   'igrid',    1;
   'sf_u',     'sf_hex_Q1nc';
   'sf_p',     'sf_disc0';
   'tol',      0.2;
   'solver',   'openfoam';
   'iplot',    1;
   'fid',      1 };
 [got,opt] = parseopt(cOptDef,varargin{:});
 fid       = opt.fid;


% Geometry.
 fea.sdim = { 'x', 'y', 'z' };
 gobj1 = gobj_block( -1.9802, 7.9208, 0, 1, 0, 1, 'B1' );
 gobj2 = gobj_block( -1.9802, 0, 0, 1, 0, 0.4851, 'B2' );
 fea.geom.objects = { gobj1 gobj2 };
 fea = geom_apply_formula( fea, 'B1-B2' );


% Grid generation.
 if( opt.igrid==1 )
   n = 4;
   fea.grid = rectgrid(10*n,n,[-1.9802, 7.9208;0 1]);
   fea.grid = delcells( fea.grid, selcells(fea.grid,'(y<=0.5).*(x<=0)') );
   ix = find( abs(fea.grid.p(2,:)-0.5)<=sqrt(eps) );
   fea.grid.p(2,ix) = 0.4851;
   fea.grid = gridextrude( fea.grid, n, 1, -2 );
   fea.grid.p(2,:) = fea.grid.p(2,:) + 1;
   fea.grid = assign_bdr( fea.grid, fea.geom, [] );
   [~,ix] = findbdr( fea , 'z>=1-sqrt(eps)', 0 );
   fea.grid.b(3,ix) = 6;
 else
   fea.grid = gridgen( fea, 'hmax', 0.4, 'fid', [] );
   fea.grid = gridsmooth( tet2hex( fea.grid ), 5 );
 end


% 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 };


% Boundary conditions.
 fea.phys.ns.bdr.sel(5) = 2;
 fea.phys.ns.bdr.sel(3) = 4;
 if( strcmp(opt.solver,'openfoam') )
   fea.phys.ns.bdr.coef{2,end}{1,5} = 3/2*opt.uin;
 else
   fea.phys.ns.bdr.coef{2,end}{1,5} = ['4*',num2str(opt.uin),'*(z-0.4851)*(1-z)/(1-0.4851)^2'];
 end


% Parse and solve problem.
 fea  = parsephys( fea );
 fea  = parseprob( fea );
 if( strcmp(opt.solver,'openfoam') )
   fea = openfoam( fea );
 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.
 [~,slen] = minmaxsubd( '(u<-eps)*x/0.4851*(z<0.4851)*(z>0)*(y<0.51)*(y>0.49)', fea );
 out.err  = abs( slen - 3 )/3;
 out.pass = out.err < opt.tol;


 if ( nargout==0 )
   clear fea out
 end