FEATool  v1.9
Finite Element Analysis Toolbox
ex_brinkman1.m File Reference

Description

EX_BRINKMAN1 Coupled Navier-Stokes and Brinkman equations model.

[ FEA, OUT ] = EX_BRINKMAN1( VARARGIN ) Example using the Navier-Stokes equations coupled with the Brinkman equations for porous media flow.

Accepts the following property/value pairs.

Input       Value/{Default}        Description
-----------------------------------------------------------------------------------
hmax        scalar {2e-4}          Grid size
sfun        string {sflag2}        Shape function for pressure
iplot       scalar 0/{1}           Plot solution (=1)
                                                                                  .
Output      Value/(Size)           Description
-----------------------------------------------------------------------------------
fea         struct                 Problem definition struct
out         struct                 Output struct

Code listing

 cOptDef = { 'hmax',     4e-4;
             'iplot',    1;
             'tol',      0.25;
             'fid',      1 };
 [got,opt] = parseopt(cOptDef,varargin{:});
 fid       = opt.fid;


% Model constants.
 rho = 1.23;     % Density.
 eta = 2.1e-4;   % Viscosity.
 kap = 3.2e-7;   % Permeability.


% Geometry and grid generation.
 fea.sdim = { 'x' 'y' };
 fea.geom.objects = { gobj_rectangle(-2e-3,0,-8e-3,8e-3,'R1') ...
                      gobj_polygon([0 -6e-3;2e-3 -5e-3;2e-3 4e-3;0 6e-3],'P1') ...
                                     };
 fea.grid = gridgen( fea, 'hmax', opt.hmax, 'fid', opt.fid );
 fea.grid = gridbdrx( fea.grid );   %  Reconstruct internal boundaries.


% Problem definition.

% Navier-Stokes equations.
 fea = addphys( fea, @navierstokes );   % Add Navier-Stokes equations physics mode.

 fea.phys.ns.eqn.coef{1,end} = rho;
 fea.phys.ns.eqn.coef{2,end} = eta;

 fea.phys.ns.bdr.sel(1) = 2;
 fea.phys.ns.bdr.coef{2,end}{2,1} = 2e-2;   % Set inflow velocity.
 fea.phys.ns.bdr.sel(4) = 4;
 fea.phys.ns.bdr.sel(9) = 2;
 fea.phys.ns.bdr.coef{2,end}{1,9} = 'u2';   % Brinkman velocity from shared boundary.
 fea.phys.ns.bdr.coef{2,end}{2,9} = 'v2';

% Brinkman equations.
 fea = addphys( fea, @brinkmaneqns );   % Add Brinkman equations physics mode.

 fea.phys.br.eqn.coef{1,end} = rho;
 fea.phys.br.eqn.coef{2,end} = eta;
 fea.phys.br.eqn.coef{3,end} = kap;

 fea.phys.br.bdr.sel(9) = 2;
 fea.phys.br.bdr.coef{2,end}{1,9} = 'u';   % NS velocity from shared boundary.
 fea.phys.br.bdr.coef{2,end}{2,9} = 'v';


% Parse and solve problem.
 fea = parsephys( fea );
 fea = parseprob( fea );
 fea.sol.u = solvestat( fea, 'solcomp', {{1 0} {1 0} {1 0} {0 1} {0 1} {0 1} }, 'fid', opt.fid );


% Postprocessing.
 x = linspace( -1e-3, 1e-3, 100 );
 y = zeros(size(x));
 u_ns = evalexpr( 'sqrt(u^2+v^2)', [x;y], fea );
 u_br = evalexpr( 'sqrt(u2^2+v2^2)', [x;y], fea );
 if( opt.iplot )
   subplot(1,2,1)
   postplot( fea, 'surfexpr', 'sqrt(u^2+v^2)', 'arrowexpr', {'u' 'v'} )
   postplot( fea, 'surfexpr', 'sqrt(u2^2+v2^2)', 'arrowexpr', {'u2' 'v2'} )

   subplot(1,2,2)
   plot( x, u_ns ), hold on
   plot( x, u_br ), hold on
 end


% Error checking.
 out.err = [ abs(max( u_ns ) - 0.0175)/0.0175, ...
             abs(mean( u_br(~isnan(u_br)) ) - 9e-3)/9e-3];
 out.pass = all( out.err < opt.tol );


 if ( nargout==0 )
   clear fea out
 end