Description

EX_NAVIERSTOKES17 2D Example for incompressible turbulent flow in a channel.

[ FEA, OUT ] = EX_NAVIERSTOKES17( VARARGIN ) Sets up and solves stationary turbulent flow at Re = 42800 in a between two flat parallel plates. The inflow profile is constant and the outflow should assume a fully developed turbulent profile (Ref. Laufer, J. 1950). Accepts the following property/value pairs.

Input       Value/{Default}        Description
-----------------------------------------------------------------------------------
igrid       scalar {3}             Grid refinement level
                                   (>0=quadrilaterals, <0=triangles)
sf_u        string {sflag1}        Shape function for velocity
sf_p        string {sflag1}        Shape function for pressure
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 = { ...
             'igrid',    3;
             'solver',   '';
             'sf_u',     'sflag1';
             'sf_p',     'sflag1';
             'iplot',    1;
             'fid',      1 };
 [got,opt] = parseopt(cOptDef,varargin{:});
 fid       = opt.fid;


% Model parameters.
 Re        = 42800;
 rho       = 1;           % Density.
 miu       = 1/Re;        % Molecular/dynamic viscosity.
 uin       = 1;
% Geometry and grid parameters.
 h         = 1;           % Height of rectangular domain.
 l         = 5;           % Length of rectangular domain.
% Discretization parameters.
 sf_u      = opt.sf_u;    % FEM shape function type for velocity.
 sf_p      = opt.sf_p;    % FEM shape function type for pressure.


% Geometry definition.
 gobj = gobj_rectangle( 0, l, -h/2, h/2 );
 fea.geom.objects = { gobj };
 fea.sdim = { 'x', 'y' };   % Coordinate names.


% Grid generation.
 fea.grid = rectgrid( linspace(0,5,20), [-0.5 -0.45 -0.35 -0.2 0 0.2 0.35 0.45 0.5] );
 for i=1:abs(opt.igrid)-1
   fea.grid = gridrefine( fea.grid, fid );
 end
 if( opt.igrid<0 )
   fea.grid = quad2tri( fea.grid );
 end


% Problem definition.
 fea = addphys( fea, @navierstokes );
 fea.phys.ns.eqn.coef{1,end} = { rho };
 fea.phys.ns.eqn.coef{2,end} = { miu };
 fea.phys.ns.eqn.coef{5,end} = { uin };
 if( strcmp(opt.solver,'openfoam') )
   fea.phys.ns.sfun = { 'sflag1', 'sflag1', 'sflag1' };
 else
   fea.phys.ns.sfun = { sf_u sf_u sf_p };           % Set shape functions.
 end

% Boundary conditions.
 i_inflow  = 4;
 i_outflow = 2;
 fea.phys.ns.bdr.sel(i_inflow)  = 2;
 fea.phys.ns.bdr.sel(i_outflow) = 3;
 fea.phys.ns.bdr.coef{2,end}{1,i_inflow} = uin;     % Set inflow velocity.

 fea.phys.ns.prop.turb.model = 'algebraic';
 if( strcmp(opt.solver,'openfoam') )
   fea.phys.ns.prop.turb.model = 'SpalartAllmaras';
 end
 fea = parsephys(fea);   % Check and parse physics modes.


% Parse and solve problem.
 fea = parseprob(fea);             % Check and parse problem struct.
 if( strcmp(opt.solver,'openfoam') )
   logfid = fid; if( ~got.fid ), fid = []; end
   fea.sol.u = openfoam( fea, 'fid', fid, 'logfid', logfid );
   fid = logfid;
 else
   mxnit = 25;
   nlrlx = 0.5;
   told  = 1e-3;
   tolc  = 1e-4;
   fea.sol.u = solvestat( fea, 'fid', fid, 'maxnit', mxnit, 'nlrlx', nlrlx, 'tolchg', tolc, 'toldef', told );
 end


% Postprocessing.
 y_ref = [0,0.09830508474576277,0.2101694915254238,0.31186440677966104,0.3661016949152544,0.4508474576271188,0.5491525423728814,0.6271186440677967,0.7016949152542376,0.7864406779661017,0.8440677966101697,0.898305084745763,0.9593220338983053,0.9796610169491529,0.9864406779661019,1]/2;
 u_ref = [0.9972834919897843,0.9886928256326912,0.9780357557464595,0.9674135128859997,0.9487346180636177,0.9278964476433715,0.9029022521476668,0.8718133271418624,0.8469003947062924,0.7972951009983751,0.7457278848386352,0.6962270722080338,0.5357441374506622,0.32608544230322756,0.19455537497097786,0]';
 n = length(y_ref);
 x = 0.96*l*ones(1,n);
 u = evalexpr( 'u', [x;y_ref], fea );
 if( opt.iplot>0 )
   figure
   subplot(2,1,1)
   postplot( fea, 'surfexpr', 'sqrt(u^2+v^2)', 'isoexpr', 'sqrt(u^2+v^2)' )
   title('Velocity field')
   subplot(2,1,2)
   postplot( fea, 'surfexpr', 'p' )
   title('Pressure')

   figure
   plot( u/max(u), y_ref, 'b.-' )
   hold on
   plot( u_ref, y_ref, 'ro--' )
   ylabel('y')
   xlabel('u/u_{max}')
   grid on
   legend('Computed','Laufer (1950)','location','southwest')
 end


% Error checking.
 err = sqrt(sum((u-u_ref).^2)/sum(u_ref.^2));

 if( ~isempty(fid) )
   fprintf(fid,'\nL2 Error: %f\n',err)
   fprintf(fid,'\n\n')
 end


 out.err  = err;
 out.pass = err<0.26;
 if ( nargout==0 )
   clear fea out
 end