FEATool  v1.9
Finite Element Analysis Toolbox
ex_compressibleeuler2.m File Reference

Description

EX_COMPRESSIBLEEULER2 2D Steady oblique shock wave.

[ FEA, OUT ] = EX_COMPRESSIBLEEULER2( VARARGIN ) Sets up and solves a steady 2D compressible Euler equation for a Ma=2 10 degree oblique shock wave and compares with the analytical solution.

Ref. H. W. Liepmann, A. Roshko, Elements of Gas Dynamics, Courier Corporation, 2013.

Accepts the following property/value pairs.

Input       Value/{Default}        Description
-----------------------------------------------------------------------------------
hmax        scalar {0.05}          Max grid cell size
sfun        string {sflag1}        Shape function
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 = { 'hmax',     0.05;
             'sfun',     'sflag1';
             'solver',   '';
             'iplot',    1;
             'tol',      0.05;
             'fid',      1 };
 [got,opt] = parseopt(cOptDef,varargin{:});
 fid       = opt.fid;


 fea.sdim = { 'x', 'y' };
 fea.geom.objects = { gobj_rectangle() };
 fea.grid = rectgrid(ceil(1/opt.hmax));

 gamma = 7/5;

 al  = pi/18;   % 10 degrees indicence angle.
 Min = 2;
 Ma  = @(th) sqrt( 2/( sin(th+al)*cos(th+al)*( (gamma+1)*tan(th) - (gamma-1)*tan(th+al) ) ) ) - Min;
 th  = fzero(Ma,atan(29.3/180*pi));   % Shock angle.

 rin = 1;
 uin =  cos(al);
 vin = -sin(al);
 pin = (sqrt(uin^2+vin^2)/Min)^2*rin/gamma;

 Mout = 1/sin(th) * sqrt( (1+(gamma-1)/2*Min^2*sin(th+al)^2) / ...
                          (gamma*Min^2*sin(th+al)^2-(gamma-1)/2) );
 rout = (gamma+1)*Min^2*sin(th+al)^2/( (gamma-1)*Min^2*sin(th+al)^2 + 2 );
 pout = pin*(1 + 2*gamma/(gamma + 1)*( Min^2*sin(th+al)^2 - 1 ));
 uout = Mout*sqrt(gamma*pout/rout);

 rref = sprintf( '%g+(y<x*%g)*(%g-%g)', rin, atan(th), rout, rin );
 uref = sprintf( '%g+(y<x*%g)*(%g-%g)', uin, atan(th), uout, uin );
 vref = sprintf( '%g+(y<x*%g)*(%g-%g)', vin, atan(th), 0,    vin );
 pref = sprintf( '%g+(y<x*%g)*(%g-%g)', pin, atan(th), pout, pin );

 fea = addphys(fea,@compressibleeuler);
 fea.phys.ee.prop.artstab.id_coef = 2*fea.phys.ee.prop.artstab.id_coef;
 fea.phys.ee.prop.artstab.sd_coef = 2*fea.phys.ee.prop.artstab.sd_coef;

 init0 = { rin, uin, vin, pin };
 fea.phys.ee.eqn.coef{5,end}{1} = rin;
 fea.phys.ee.eqn.coef{6,end}{1} = uin;
 fea.phys.ee.eqn.coef{7,end}{1} = vin;
 fea.phys.ee.eqn.coef{8,end}{1} = pin;

 fea.phys.ee.bdr.sel(2)   = 2;
 fea.phys.ee.bdr.sel(3:4) = 1;
 fea.phys.ee.bdr.coef{1,end}{1,3} = rin;
 fea.phys.ee.bdr.coef{1,end}{2,3} = uin;
 fea.phys.ee.bdr.coef{1,end}{3,3} = vin;
 fea.phys.ee.bdr.coef{1,end}{4,3} = pin;
 fea.phys.ee.bdr.coef{1,end}{1,4} = rin;
 fea.phys.ee.bdr.coef{1,end}{2,4} = uin;
 fea.phys.ee.bdr.coef{1,end}{3,4} = vin;
 fea.phys.ee.bdr.coef{1,end}{4,4} = pin;

 fea = parsephys(fea);
 fea = parseprob(fea);


 if( strcmp(opt.solver,'openfoam') )
   logfid = fid; if( ~got.fid ), fid = []; end
   fea.sol.u = openfoam( fea, 'deltaT', 0.01, 'endTime', 10, 'fid', fid, 'logfid', logfid );
   fid = logfid;
 else
   fea.sol.u = solvestat( fea, 'init', init0, 'fid', fid );
 end


% Postprocessing.
 s_Ma = fea.phys.ee.eqn.vars{end-1,2};
 if( opt.iplot>0 )
   postplot( fea, 'surfexpr', s_Ma )
   title(fea.phys.ee.eqn.vars{end-1,1})
 end


% Error checking.
 r = evalexprp( fea.dvar{1}, fea );
 u = evalexprp( fea.dvar{2}, fea );
 v = evalexprp( fea.dvar{3}, fea );
 p = evalexprp( fea.dvar{4}, fea );
 r_ref = evalexprp( rref, fea );
 u_ref = evalexprp( uref, fea );
 v_ref = evalexprp( vref, fea );
 p_ref = evalexprp( pref, fea );
 out.err = [ sum(abs(r_ref-r))/size(fea.grid.p,2), ...
             sum(abs(u_ref-u))/size(fea.grid.p,2), ...
             sum(abs(v_ref-v))/size(fea.grid.p,2), ...
             sum(abs(p_ref-p))/size(fea.grid.p,2) ];
 out.pass = all(out.err<opt.tol);


 if( nargout==0 )
   clear fea out
 end