gravity_waves_tsrk.py 10.2 KB
 zhang committed Feb 09, 2013 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 ``````from extrude import * from dgpy import * from math import * import time, os, sys import gmshPartition #from matplotlib import pyplot as plt #### Physical constants ### gamma=1.4 Rd=287 p0=1.0e5 g=9.80616 Cv=Rd/(gamma-1) Cp=Rd*(1+1/(gamma-1)) ########################### #### Begin and end time ### Ti=0 Tf=30.0 ########################### order=3 dimension=2 model = GModel() name='line' if Msg.GetCommSize()>1: partStr='_part_%i' % Msg.GetCommSize() else: partStr='' model.load(name + partStr + '_2d_XY.msh') #model.load('gravity_waves.msh') #######Perform multiple runs to get convergence plot### #components for sol #rhop = sol(i,0) #rhou = sol(i,1) #rhov = sol(i,2) #rhothetap = sol(i,3) errp=[] erru=[] errv=[] errthetap=[] errall=[] stepsizes=[] dt = 0.4 #if (Msg.GetCommRank()==0): # plt.ion() # fig = plt.figure() # pltP,=plt.plot(stepsizes,errp,label="rhop") # pltU,=plt.plot(stepsizes,erru,label="rhou") # pltV,=plt.plot(stepsizes,errv,label="rhov") # pltThetap,=plt.plot(stepsizes,errthetap,label="rhothetap") # pltAll,=plt.plot(stepsizes,errall,label="all") # plt.legend(loc='upper right') # axes=plt.gca() # axes.set_ylim(0,1) groups = dgGroupCollection(model, dimension, order) groups.splitGroupsByPhysicalTag(); groupsH = dgGroupCollection.newByTag(model, dimension-1, order, ["bottom_domain"]) extrusion = dgExtrusion(groups, groupsH, ["bottom_domain"]) groups.splitFaceGroupsByOrientation(extrusion, ["bottom_domain", "top_domain"]) claw = dgEulerAtmLaw(dimension) ####Load reference solution from file### reloaded =dgDofContainer(groups,claw.getNbFields()) `````` Jonathan Lambrechts committed Oct 19, 2016 67 ``````reloaded.importIdx("refSolERK/refSolERK.idx") `````` zhang committed Feb 09, 2013 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 `````` solution = dgDofContainer(groups, claw.getNbFields()) XYZ = groups.getFunctionCoordinates() def hydrostaticState(z) : N=1.e-2 theta0=300 thetaHs=theta0*exp(N**2*z/g) exnerHs=1+ g**2/(Cp*theta0*N**2) * (exp(-N**2*z/g)-1) rhoHs=p0/(Rd*thetaHs)*exnerHs**(Cv/Rd) return rhoHs,exnerHs,thetaHs def initialCondition(FCT, XYZ) : a=5000 dtheta0=1.0e-2 H=10000 xc=-50000 U=20.0 for i in range (0,XYZ.size1()) : x=XYZ(i,0) z=XYZ(i,1) rhoHs,exnerHs,thetaHs = hydrostaticState(z) thetaPert=thetaHs+dtheta0*(sin(pi*z/H)/(1+(x-xc)**2/a**2)) rhoPert=p0/(Rd*thetaPert)*exnerHs**(Cv/Rd) FCT.set(i,0,rhoPert-rhoHs) FCT.set(i,1,U*rhoPert) FCT.set(i,2,0.0) FCT.set(i,3,rhoPert*thetaPert-rhoHs*thetaHs) def rhoHydrostatic(FCT, XYZ) : for i in range (0,XYZ.size1()) : z=XYZ(i,1) rhoHs,exnerHs,thetaHs = hydrostaticState(z) FCT.set(i,0,rhoHs) def rhoThetaHydrostatic(FCT, XYZ) : for i in range (0,XYZ.size1()) : z=XYZ(i,1) rhoHs,exnerHs,thetaHs = hydrostaticState(z) FCT.set(i,0,rhoHs*thetaHs) def getVelocity(FCT, sol, XYZ) : for i in range (0,sol.size1()) : z=XYZ(i,1) rhoHs,exnerHs,thetaHs = hydrostaticState(z) rho=rhoHs+sol(i,0) FCT.set(i,0,sol(i,1)/rho) FCT.set(i,1,sol(i,2)/rho) FCT.set(i,2,0) def getRhop(FCT, sol) : for i in range (0,sol.size1()) : FCT.set(i,0,sol(i,0)) def getpp(FCT, sol, XYZ) : for i in range (0,sol.size1()) : z=XYZ(i,1) rhoHs,exnerHs,thetaHs = hydrostaticState(z) rho=rhoHs+sol(i,0) rhoTheta = rhoHs*thetaHs+sol(i,3) pHs=p0*(rhoHs*thetaHs*Rd/p0)**gamma p=p0*(rhoTheta*Rd/p0)**gamma FCT.set(i,0,p-pHs) def getpHs(FCT, sol, XYZ) : for i in range (0,sol.size1()) : z=XYZ(i,1) rhoHs,exnerHs,thetaHs = hydrostaticState(z) pHs=p0*(rhoHs*thetaHs*Rd/p0)**gamma FCT.set(i,0,pHs) def getp(FCT, sol, XYZ) : for i in range (0,sol.size1()) : z=XYZ(i,1) rhoHs,exnerHs,thetaHs = hydrostaticState(z) rhoTheta = rhoHs*thetaHs+sol(i,3) p=p0*(rhoTheta*Rd/p0)**gamma FCT.set(i,0,p) def getThetap(FCT, sol, XYZ) : for i in range (0,sol.size1()) : z=XYZ(i,1) rhoHs,exnerHs,thetaHs = hydrostaticState(z) rho=rhoHs+sol(i,0) FCT.set(i,0,(sol(i,3)+(rhoHs*thetaHs))/rho-thetaHs) uv=functionPython(3, getVelocity, [solution.getFunction(), XYZ]) rhop=functionPython(1, getRhop, [solution.getFunction()]) pHs=functionPython(1, getpHs, [solution.getFunction(), XYZ]) p=functionPython(1, getp, [solution.getFunction(), XYZ]) pp=functionPython(1, getpp, [solution.getFunction(), XYZ]) thetap=functionPython(1, getThetap, [solution.getFunction(), XYZ]) initF=functionPython(4, initialCondition, [XYZ]) solution.interpolate(initF) rhoHs = dgDofContainer(groups, 1) rhoHs.interpolate(functionPython(1, rhoHydrostatic, [XYZ])) rhoThetaHs = dgDofContainer(groups, 1) rhoThetaHs.interpolate(functionPython(1, rhoThetaHydrostatic, [XYZ])) claw.setHydrostaticState(rhoHs,rhoThetaHs) claw.setPhysicalConstants(gamma,Rd,p0,g) boundaryWall = claw.newBoundaryWall() claw.addBoundaryCondition('bottom_domain', boundaryWall) claw.addBoundaryCondition('top_domain', boundaryWall) #We need to use a dof container to restrict the initial condition # (=boundary condition) to the discretization space initDof = dgDofContainer(groups, 4) initDof.interpolate(initF) outsideBoundary = claw.newOutsideValueBoundary("",initDof.getFunction()) claw.addBoundaryCondition('left', outsideBoundary) claw.addBoundaryCondition('right', outsideBoundary) #zero=claw.new0FluxBoundary() #claw.addBoundaryCondition('bottom', zero) #claw.addBoundaryCondition('top', zero) #claw.addBoundaryCondition('left', zero) #claw.addBoundaryCondition('right', zero) ###settings for implicit or imex integrators### claw.setFilterMode(FILTER_LINEAR); #petscIm = dgLinearSystemExtrusion(claw, groups, extrusion) #timeIter.getNewton().setVerb(3) #Verbosity solution0 = dgDofContainer(groups, claw.getNbFields()) solution0.copy(solution) `````` zhang committed Apr 18, 2013 202 203 ``````nbSteps = 300 `````` zhang committed Feb 09, 2013 204 205 206 ``````for iruns in range(0,5) : petscIm = linearSystemPETScBlockDouble() `````` zhang committed Apr 23, 2013 207 `````` #petscIm.setParameter("petscOptions", "-ksp_atol 0 -ksp_rtol 1e-14") `````` zhang committed Feb 09, 2013 208 209 `````` dofIm = dgDofManager.newDGBlock(groups, claw.getNbFields(), petscIm) #timeIter = dgIMEXDIMSIM(claw, dofIm, 2) #timeorder `````` zhang committed Apr 23, 2013 210 `````` timeIter = dgIMEXTSRK(claw, dofIm, 4) #timeorder `````` zhang committed Feb 09, 2013 211 212 213 `````` #timeIter = dgIMEXRK(claw, dofIm, 3) #timeorder #timeIter = dgDIRK(claw, dofIm, 2) #timeorder `````` zhang committed Apr 23, 2013 214 215 `````` #timeIter.getNewton().setAtol(1.e-13) #ATol #timeIter.getNewton().setRtol(1.e-13) #Rtol `````` zhang committed Feb 09, 2013 216 217 218 `````` solution.copy(solution0) #dt=claw.getMinOfTimeSteps(solution, extrusion)*.8 `````` zhang committed Apr 18, 2013 219 `````` dt = (Tf-Ti)/nbSteps `````` zhang committed Feb 09, 2013 220 221 222 223 `````` if (Msg.GetCommRank()==0): print "Time step:",dt `````` zhang committed Apr 18, 2013 224 `````` #nbSteps = int(round(Tf/dt)) `````` zhang committed Feb 09, 2013 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 `````` # Compute relative error def getRefSolSq(FCT, refSol) : for i in range(FCT.size1()): FCT.set(i,0, refSol(i,0)**2) FCT.set(i,1, refSol(i,1)**2) FCT.set(i,2, refSol(i,2)**2) FCT.set(i,3, refSol(i,3)**2) solRefSq=functionPython(4, getRefSolSq, [reloaded.getFunction()]) def getError(FCT, refSol, compSol) : for i in range(FCT.size1()): FCT.set(i,0,(refSol(i,0)-compSol(i,0))**2) FCT.set(i,1,(refSol(i,1)-compSol(i,1))**2) FCT.set(i,2,(refSol(i,2)-compSol(i,2))**2) FCT.set(i,3,(refSol(i,3)-compSol(i,3))**2) error = functionPython(4, getError, [reloaded.getFunction(), solution.getFunction()]) integratorError = dgFunctionIntegrator(groups, error) intErr = fullMatrixDouble(4,1) integratorRefSq = dgFunctionIntegrator(groups, solRefSq) intRefSq = fullMatrixDouble(4,1) #Export data def getExp(FCT, uv, rhop, thetap, pp) : for i in range (0,uv.size1()) : FCT.set(i,0,uv(i,0)) FCT.set(i,1,uv(i,1)) FCT.set(i,2,rhop(i,0)) FCT.set(i,3,thetap(i,0)) FCT.set(i,4,pp(i,0)) Exp=functionPython(5, getExp, [uv, rhop, thetap, pp]) nCompExp=[2,1,1,1] namesExp=["uv","rhop","thetap","pp"] #sBV = 2.0/3*(order+1.0) #muBV = 0.2 #filterBV = dgFilterBoydVandeven(groups, "", sBV, muBV) prefixFileName = 'output'+str(iruns)+'/export' t=Ti # starter for IMEX TSRK, move two sptes ahead here t=timeIter.starter(solution,dt,t,3) # starter for IMEX DIMSIM #timeIter.starter(solution,dt,dt,t,3) n_export=0 timeStart=time.clock(); #for i in range(0,nbSteps): for i in range(2,nbSteps): # if (i==nbSteps-1): # dt=Tf-t if (i%(100*2**iruns) == 0): solution.exportFunctionVtk(Exp,prefixFileName, t*1000, i,"solution",nCompExp,namesExp) #if (Msg.GetCommRank()==0): # print '\nWriting output',n_export,'at time',t,'and step',i,'over',nbSteps # print 'Time elapsed: ',time.clock()-timeStart n_export=n_export+1 norm = timeIter.iterate (solution, dt, t) #filterBV.apply(solution) t=t+dt if (Msg.GetCommRank()==0): sys.stdout.write('.') sys.stdout.flush() solution.exportFunctionVtk(Exp,prefixFileName, Tf*1000, nbSteps,"solution",nCompExp,namesExp) if (Msg.GetCommRank()==0): print '' print 'Time elapsed: ',time.clock()-timeStart integratorError.compute(intErr) integratorRefSq.compute(intRefSq) errp.append(sqrt(intErr(0,0)/intRefSq(0,0))) erru.append(sqrt(intErr(1,0)/intRefSq(1,0))) errv.append(sqrt(intErr(2,0)/intRefSq(2,0))) errthetap.append(sqrt(intErr(3,0)/intRefSq(3,0))) errall.append( sqrt((intErr(0,0)+intErr(1,0)+intErr(2,0)+intErr(3,0))/(intRefSq(0,0)+intRefSq(1,0)+intRefSq(2,0)+intRefSq(3,0))) ) stepsizes.append(dt) `````` zhang committed Apr 18, 2013 303 `````` nbSteps = nbSteps*2 `````` zhang committed Feb 09, 2013 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 `````` if (Msg.GetCommRank()==0): print "Error on rhop:",errp[-1],"rhou:",erru[-1],"rhov:", errv[-1],"rhothetap:",errthetap[-1],"all:",errall[-1] outFile = open('output/ErrorVsStep','w') outFile.write("h rhop rhou rhov rhothetap\n") for i in range(len(stepsizes)): outFile.write("%s %s %s %s %s %s\n" % (stepsizes[i], errp[i], erru[i], errv[i], errthetap[i], errall[i])) outFile.close() # pltP.set_data(stepsizes,errp) # pltU.set_data(stepsizes,erru) # pltV.set_data(stepsizes,errv) # pltThetap.set_data(stepsizes,errthetap) # pltAll.set_data(stepsizes,errall) # axes.relim() # axes.autoscale_view(True,True,True) # plt.draw() # fig.savefig('output/ErrorVsStep.pdf') # plt.draw() # plt.show() Msg.Exit(0)``````