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FEATool Multiphysics
v1.17.2
Finite Element Analysis Toolbox
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FEATool Multiphysics
v1.17.2
Finite Element Analysis Toolbox
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EX_FLUIDSTRUCTURE2 Fluid-structure interaction for an elastic beam.
[ FEA, OUT ] = EX_FLUIDSTRUCTURE2( VARARGIN ) Example for fluid- structure interaction flow around an elastic beam at Re = 100.
[1] Hron J. A monolithic FEM/multigrid solver for ALE formulation of fluid structure interaction with application in biomechanics. In H.-J. Bungartz and M. Schäfer, editors, Fluid-Structure Interaction: Modelling, Simulation, Optimisation, LLNCSE. Springer, 2006.
Accepts the following property/value pairs.
Input Value/{Default} Description
-----------------------------------------------------------------------------------
sf_u string {sflag1} Shape function for velocity
sf_p string {sflag1} Shape function for pressure
iplot scalar 0/{1} Plot solution (=1)
.
Output Value/(Size) Description
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fea struct Problem definition struct
out struct Output struct
cOptDef = { 'sf_u', 'sflag1';
'sf_p', 'sflag1';
'iplot', 1;
'tmax', 15;
'tol', [0.1 0.1 0.1];
'fid', 1 };
[got,opt] = parseopt(cOptDef,varargin{:});
fid = opt.fid;
rho = 1e3;
miu = 1;
umean = 1;
diam = 0.1;
% Geometry.
fea.sdim = { 'x', 'y' };
gobj1 = gobj_rectangle( 0, 2.5, 0, 0.41, 'R1' );
gobj2 = gobj_circle( [0.2 0.2], 0.05, 'C1' );
gobj3 = gobj_rectangle( [0.2], [0.6], [0.2-0.01], [0.2+0.01], 'R2' );
fea.geom.objects = { gobj1 gobj2 gobj3 };
fea.geom = copy_geometry_object( 'C1', fea.geom );
fea.geom = copy_geometry_object( 'R2', fea.geom );
fea.geom = geom_apply_formula( fea.geom, 'R1-C1-R2' );
fea.geom = geom_apply_formula( fea.geom, 'R3-C2' );
% Grid generation.
hmaxb = [ 0.025*ones(1,4) 0.01*ones(1,4) 0.005*ones(1,5) ]*1;
fea.grid = gridgen( fea, 'hmaxb', hmaxb, 'gridgen', 'gridgen2d', 'fid', opt.fid );
p_A = [0.6;0.2];
[~,i_A] = min(sum((fea.grid.p'-repmat(p_A',size(fea.grid.p,2),1)).^2,2));
fea.grid.p(:,i_A) = p_A;
% Equation settings.
fea = addphys( fea, @fluidstructure );
fea.phys.fsi.sfun = { opt.sf_u, opt.sf_u, opt.sf_p, opt.sf_u, opt.sf_u };
fea.phys.fsi.eqn.coef{1,end} = { rho, 1e4 }; % Density.
fea.phys.fsi.eqn.coef{2,end} = { miu, 0 }; % Viscosity.
fea.phys.fsi.eqn.coef{3,end} = { 0, 0.4 }; % Poisson's ratio.
fea.phys.fsi.eqn.coef{4,end} = { 0, 1.4e6 }; % Modulus of elasticity.
fea.phys.fsi.prop.active = [ 1, 0; 1, 0; 1, 0; 0, 1; 0, 1 ];
% Boundary settings.
fea.phys.fsi.bdr.sel = [ 1 3 1 2 1 1 1 1 6 6 -2 -2 -2 ];
fea.phys.fsi.bdr.coef{2,end}{1,4} = ...
[num2str(1.5*umean*4/0.1608),'*y*(0.41-y)*(0.5*(1-cos(pi/2*t))*(t<2)+(t>=2))']; % Inflow velocity.
% Solver.
fea = parsephys(fea);
fea = parseprob(fea);
[fea.sol.u,fea.sol.t,fea.sol.grid.p] = ...
fsisolve( fea, 'tstep', 0.01, 'tmax', opt.tmax, 'fid', opt.fid );
% Calculate benchmark quantities (line integration method).
s_tfx = ['nx*p+',num2str(miu),'*(-2*nx*ux-ny*(uy+vx))'];
s_tfy = ['ny*p+',num2str(miu),'*(-nx*(vx+uy)-2*ny*vy)'];
i_int = [5:8,11:13]; % Integration boundaries.
i_cub = 10;
i1 = find(fea.sol.t>=fea.sol.t(end)-1); i1 = i1(1);
i2 = length(fea.sol.t);
i_cnt = 0;
for i=i1:i2
i_cnt = i_cnt + 1;
p_Ai = fea.sol.grid.p(:,i_A,i);
ux_A(i_cnt) = evalexpr( 'dx', p_Ai, fea, i );
uy_A(i_cnt) = evalexpr( 'dy', p_Ai, fea, i );
F_d(i_cnt) = intbdr( s_tfx, fea, i_int, i_cub, i, 1 );
F_l(i_cnt) = intbdr( s_tfy, fea, i_int, i_cub, i, 1 );
end
% Postprocessing.
if( opt.iplot>0 )
postplot(fea,'surfexpr','p')
figure
subplot(2,2,1)
plot( fea.sol.t(i1:i2), ux_A )
xlabel('time')
ylabel('x-displacement')
subplot(2,2,2)
plot( fea.sol.t(i1:i2), uy_A )
xlabel('time')
ylabel('y-displacement')
subplot(2,2,3)
plot( fea.sol.t(i1:i2), F_l )
xlabel('time')
ylabel('lift force')
subplot(2,2,4)
plot( fea.sol.t(i1:i2), F_d )
xlabel('time')
ylabel('drag force')
end
% Error checking.
out.t = fea.sol.t(i1:i2);
out.ux_A = ux_A;
out.uy_A = uy_A;
out.F_d = F_d;
out.F_l = F_l;
out.vals = [ min(ux_A), max(ux_A) ;
min(uy_A), max(uy_A) ;
min(F_d), max(F_d) ;
min(F_l), max(F_l) ];
out.ref = [ -14.58e-3-12.44e-3, -14.58e-3+12.44e-3 ;
1.23e-3-80.6e-3, 1.23e-3+80.6e-3 ;
208.83-73.75, 208.83+73.75 ;
0.88-234.2, 0.88+234.2 ];
out.err = abs(out.vals-out.ref)./abs(out.ref);
out.pass = all(out.err(:) < 0.1 | (out.err(:)>=0.1 & out.err(:)<0.5));
if( nargout==0 )
clear fea out
end