FEATool Multiphysics
v1.17.0
Finite Element Analysis Toolbox
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EX_COMPRESSIBLEEULER6 2D Compressible inviscid flow past a wedge.
[ FEA, OUT ] = EX_COMPRESSIBLEEULER6( VARARGIN ) This verification test case studies steady inviscid compressible flow past a wedge at an incident angle of 15 degrees. As the supersonic flow (Ma = 2.5) hits the wedge a sharp oblique shock wave is formed, resulting in a reduced downstream flow velocity. The simulation uses the inviscid compressible Euler equations to model the flow, adaptively refining the mesh, and using FEM-TVD upwinding to stabilize the solution and resolve shock discontinuities.
The angle of the shock wave and downstream Mach number can be determined using oblique shock theory, Ma = 1.873526 at an angle of 36.9449 degrees, and also comparing to results from the NASA/NPARC CFD Verification and Validation Database and from the Wind-US CFD code [1].
[1] NPARC Alliance, Computational Fluid Dynamics (CFD) Verification and Validation Web Site https://www.grc.nasa.gov/WWW/wind/valid/wedge/wedge.html
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 openfoam/su2/{} Use OpenFOAM, SU2, 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
cOptDef = { 'hmax', 0.05; 'sfun', 'sflag1'; 'solver', ''; 'endTime', 2; 'iplot', 1; 'tol', 0.03; 'fid', 1 }; [got,opt] = parseopt(cOptDef,varargin{:}); fid = opt.fid; fea.sdim = { 'x', 'y' }; fea.geom.objects = { gobj_rectangle( 0, 2, 0, 1, 'R1' ) }; fea = geom_split_object( fea, { 'R1' }, [1 0], [1 atan(pi*15/180)] ); fea = geom_split_object( fea, { 'SP1' }, [1 0], [1 atan(pi*(15+36.9449)/180)] ); fea.geom.objects(3) = []; hmaxb = opt.hmax * ones(1,7); hmaxb(3) = opt.hmax / 50; fea.grid = gridgen( fea, 'gridgen', 'default', 'hmax', opt.hmax, 'hmaxb', hmaxb, 'fid', opt.fid ); fea = addphys(fea,@compressibleeuler); Ma = 2.5; rho0 = 1; p0 = 1; u0 = Ma*sqrt(1.4*p0/rho0); v0 = 0; init0 = {rho0, u0, v0, p0}; [fea.phys.ee.eqn.coef{5,end}{:}] = deal(rho0); [fea.phys.ee.eqn.coef{6,end}{:}] = deal(u0); [fea.phys.ee.eqn.coef{7,end}{:}] = deal(v0); [fea.phys.ee.eqn.coef{8,end}{:}] = deal(p0); i_in = findbdr( fea, 'x<=sqrt(eps)' ); i_out = findbdr( fea, 'x>=2-sqrt(eps)' ); fea.phys.ee.bdr.sel(i_in) = 1; fea.phys.ee.bdr.sel(i_out) = 2; fea.phys.ee.bdr.coef{1,end}{1,i_in} = rho0; fea.phys.ee.bdr.coef{1,end}{2,i_in} = u0; fea.phys.ee.bdr.coef{1,end}{3,i_in} = v0; fea.phys.ee.bdr.coef{1,end}{4,i_in} = p0; fea.phys.ee.prop.artstab.id = 0; fea.phys.ee.prop.artstab.sd = 0; fea.phys.ee.prop.artstab.iupw = 1; fea = parsephys(fea); fea = parseprob(fea); if( strcmp(opt.solver,'openfoam') ) logfid = fid; if( ~got.fid ), fid = []; end fea.sol.u = openfoam( fea, 'deltaT', 0.005, 'endTime', opt.endTime, 'maxCo', 0.5, 'fid', fid, 'logfid', logfid, 'nproc', 1 ); fid = logfid; elseif( strcmp(opt.solver,'su2') ) logfid = fid; if( ~got.fid ), fid = []; end fea.sol.u = su2( fea, 'upwind', 'jst', 'fid', fid, 'logfid', logfid, 'nproc', 1 ); fid = logfid; else fea.sol.u = solvestat( fea, 'init', init0, 'maxnit', 50, 'nlrlx', 0.9, 'fid', fid ); end % Postprocessing. s_Ma = fea.phys.ee.eqn.vars{end-1,2}; if( opt.iplot>0 ) postplot( fea, 'surfexpr', s_Ma, 'isoexpr', s_Ma ) title(fea.phys.ee.eqn.vars{end-1,1}) end % Error checking. out.err = abs(evalexpr('sqrt(u^2+v^2)/sqrt(ga_ee*p/rho)',[1.9;0.4],fea) - 1.873526) / 1.873526; out.pass = all(out.err<opt.tol); if( nargout==0 ) clear fea out end