# Annotation of /trunk/finley/test/python/FCT_test2.py

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Thu Feb 7 04:24:00 2008 UTC (11 years, 7 months ago) by gross
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```a new version of the algebric upwinding a. flux limiter
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 1 gross 1400 # 2 # upwinding test moving a Gaussian hill around 3 # 4 # we solve U_,t - E *u_,ii + v_i u_,i =0 (E is small) 5 # 6 # the solution is given as u(x,t)=1/(4*pi*E*t)^{dim/2} * exp ( - |x-x_0(t)|^2/(4*E*t) ) 7 # 8 # where x_0(t) = [ cos(OMEGA0*T0)*0.5,-sin(OMEGA0*T0)*0.5 ] and v=[-y,x]*OMEGA0 for dim=2 and 9 # 10 # x_0(t) = [ cos(OMEGA0*T0)*0.5,-sin(OMEGA0*T0)*0.5 ] and v=[-y,x]*OMEGA0 for dim=3 11 # 12 # the solution is started from some time T0>0. 13 # 14 # We are using five quality messurements for u_h 15 # 16 # - inf(u_h) > 0 17 # - sup(u_h)/sup(u(x,t)) = sup(u_h)*(4*pi*E*t)^{dim/2} ~ 1 18 # - integrate(u_h) ~ 1 19 # - | x_0h-x_0 | ~ 0 where x_0h = integrate(x*u_h) 20 # - sigma_h/4*E*t ~ 1 where sigma_h=sqrt(integrate(length(x-x0h)**2 * u_h) * (DIM==3 ? sqrt(2./3.) :1 ) 21 # 22 # 23 gross 1410 from esys.escript import * 24 from esys.escript.linearPDEs import LinearSinglePDE, TransportPDE 25 from esys.finley import Rectangle, Brick 26 gross 1400 from math import pi, ceil 27 gross 1410 NE=128 28 gross 1400 DIM=2 29 THETA=0.5 30 OMEGA0=1. 31 ALPHA=pi/4 32 T0=0.5*pi 33 gross 1410 T_END=2.5*pi 34 dt=1e-3*10 35 E=1.e-3 36 TEST_SUPG=False # or True 37 gross 1400 38 gross 1410 39 gross 1400 def getCenter(t): 40 if DIM==2: 41 x0=[cos(OMEGA0*t)*0.5,-sin(OMEGA0*t)*0.5] 42 gross 1410 x0=[-sin(OMEGA0*t)*0.5,cos(OMEGA0*t)*0.5] 43 gross 1400 else: 44 x0=[cos(ALPHA)*cos(OMEGA0*t)*0.5,-sin(OMEGA0*t)*0.5,-sin(ALPHA)*cos(OMEGA0*t)*0.5] 45 return x0 46 def QUALITY(t,u_h): 47 dom=u_h.getDomain() 48 x=dom.getX() 49 a=inf(u_h) 50 b=sup(u_h)*(4*pi*E*t)**(DIM/2.)-1. 51 c=integrate(u_h,Function(dom))-1. 52 x0=getCenter(t) 53 x0h=integrate(x*u_h,Function(dom)) 54 d=length(x0-x0h) 55 sigma_h2=sqrt(integrate(length(x-x0h)**2 * u_h, Function(dom))) 56 if DIM == 3: sigma_h2*=sqrt(2./3.) 57 e=sigma_h2/sqrt(4*E*t)-1 58 gross 1410 # return a,b,c,e,1./(4*pi*E*t)**(DIM/2.) 59 return b, d 60 # return a,b,c,d,e 61 gross 1400 62 63 gross 1368 64 65 gross 1400 if DIM==2: 66 dom=Rectangle(NE,NE) 67 else: 68 dom=Brick(NE,NE,NE) 69 dom.setX(2*dom.getX()-1) 70 71 # set initial value 72 gross 1370 x=dom.getX() 73 gross 1400 u0=1/(4.*pi*E*T0)**(DIM/2.)*exp(-length(dom.getX()-getCenter(T0))**2/(4.*E*T0)) 74 gross 1371 75 gross 1400 print "QUALITY ",QUALITY(T0,u0) 76 77 x=Function(dom).getX() 78 if DIM == 2: 79 gross 1410 V=OMEGA0*(x[0]*[0,-1]+x[1]*[1,0]) 80 gross 1400 else: 81 V=OMEGA0*(x[0]*[0,cos(ALPHA),0]+x[1]*[-cos(ALPHA),0,sin(ALPHA)]+x[2]*[0.,-sin(ALPHA),0.]) 82 #=================== 83 fc=TransportPDE(dom,num_equations=1,theta=THETA) 84 x=Function(dom).getX() 85 fc.setValue(M=Scalar(1.,Function(dom)),C=V,A=-Scalar(E,Function(dom))*kronecker(dom)) 86 #============== 87 if TEST_SUPG: 88 supg=LinearSinglePDE(dom) 89 supg.setValue(D=1.) 90 supg.setSolverMethod(supg.LUMPING) 91 dt_supg=1./(1./inf(dom.getSize()/length(V))+1./inf(dom.getSize()**2/E))*0.3 92 u_supg=u0*1. 93 94 gross 1370 c=0 95 gross 1400 saveVTK("u.%s.xml"%c,u=u0) 96 fc.setInitialSolution(u0) 97 t=T0 98 gross 1410 while t