#include #include #include #include #include #include #include #include "common/Communication.h" #include "analysis/TwoPhase.h" #include "analysis/runAnalysis.h" #include "common/MPI_Helpers.h" #include "ProfilerApp.h" #include "threadpool/thread_pool.h" /* * Simulator for two-phase flow in porous media * James E. McClure 2013-2018 */ using namespace std; //************************************************************************* // Implementation of Two-Phase Immiscible LBM //************************************************************************* int main(int argc, char **argv) { // Initialize MPI int provided_thread_support = -1; MPI_Init_thread(&argc,&argv,MPI_THREAD_MULTIPLE,&provided_thread_support); MPI_Comm comm; MPI_Comm_dup(MPI_COMM_WORLD,&comm); int rank = comm_rank(comm); int nprocs = comm_size(comm); { // Limit scope so variables that contain communicators will free before MPI_Finialize if ( argc < 2 ) { std::cerr << "Invalid number of arguments, no input file specified\n"; return -1; } auto filename = argv[1]; auto db = std::make_shared( filename ); auto domain_db = db->getDatabase( "Domain" ); auto color_db = db->getDatabase( "Color" ); auto analysis_db = db->getDatabase( "Analysis" ); if (rank == 0){ printf("********************************************************\n"); printf("Running Color LBM \n"); printf("********************************************************\n"); } // Initialize compute device // int device=ScaLBL_SetDevice(rank); ScaLBL_DeviceBarrier(); MPI_Barrier(comm); PROFILE_ENABLE(1); //PROFILE_ENABLE_TRACE(); //PROFILE_ENABLE_MEMORY(); PROFILE_SYNCHRONIZE(); PROFILE_START("Main"); Utilities::setErrorHandlers(); // Variables that specify the computational domain string FILENAME; // Color Model parameters int timestepMax = color_db->getScalar( "timestepMax" ); double tauA = color_db->getScalar( "tauA" ); double tauB = color_db->getScalar( "tauB" ); double rhoA = color_db->getScalar( "rhoA" ); double rhoB = color_db->getScalar( "rhoB" ); double Fx = color_db->getVector( "F" )[0]; double Fy = color_db->getVector( "F" )[1]; double Fz = color_db->getVector( "F" )[2]; double alpha = color_db->getScalar( "alpha" ); double beta = color_db->getScalar( "beta" ); bool Restart = color_db->getScalar( "Restart" ); double din = color_db->getScalar( "din" ); double dout = color_db->getScalar( "dout" );; double inletA=1.f; double inletB=0.f; double outletA=0.f; double outletB=1.f; double flux = 10.f; // Read domain values auto L = domain_db->getVector( "L" ); auto size = domain_db->getVector( "n" ); auto nproc = domain_db->getVector( "nproc" ); int BoundaryCondition = domain_db->getScalar( "BC" ); int Nx = size[0]; int Ny = size[1]; int Nz = size[2]; double Lx = L[0]; double Ly = L[1]; double Lz = L[2]; int nprocx = nproc[0]; int nprocy = nproc[1]; int nprocz = nproc[2]; int timestep = 6; if (BoundaryCondition==4) flux = din*rhoA; // mass flux must adjust for density (see formulation for details // Get the rank info const RankInfoStruct rank_info(rank,nprocx,nprocy,nprocz); MPI_Barrier(comm); if (nprocs != nprocx*nprocy*nprocz){ printf("nprocx = %i \n",nprocx); printf("nprocy = %i \n",nprocy); printf("nprocz = %i \n",nprocz); INSIST(nprocs == nprocx*nprocy*nprocz,"Fatal error in processor count!"); } if (rank==0){ printf("********************************************************\n"); printf("tau (non-wetting) = %f \n", tauA); printf("tau (wetting) = %f \n", tauB); printf("density (non-wetting) = %f \n", rhoA); printf("density (wetting) = %f \n", rhoB); printf("alpha = %f \n", alpha); printf("beta = %f \n", beta); printf("gamma_{wn} = %f \n", 5.796*alpha); printf("Force(x) = %f \n", Fx); printf("Force(y) = %f \n", Fy); printf("Force(z) = %f \n", Fz); printf("Sub-domain size = %i x %i x %i\n",Nx,Ny,Nz); printf("Parallel domain size = %i x %i x %i\n",nprocx,nprocy,nprocz); if (BoundaryCondition==0) printf("Periodic boundary conditions will applied \n"); if (BoundaryCondition==1) printf("Pressure boundary conditions will be applied \n"); if (BoundaryCondition==2) printf("Velocity boundary conditions will be applied \n"); if (BoundaryCondition==3) printf("Dynamic pressure boundary conditions will be applied \n"); if (BoundaryCondition==4) printf("Average flux boundary conditions will be applied \n"); if (!Restart) printf("Initial conditions assigned from phase ID file \n"); if (Restart) printf("Initial conditions assigned from restart file \n"); printf("********************************************************\n"); } // Initialized domain and averaging framework for Two-Phase Flow bool pBC; if (BoundaryCondition==1 || BoundaryCondition==3 || BoundaryCondition == 4) pBC=true; else pBC=false; std::shared_ptr Dm (new Domain(domain_db)); for (int i=0; iNx*Dm->Ny*Dm->Nz; i++) Dm->id[i] = 1; Dm->CommInit(); std::shared_ptr Averages( new TwoPhase(Dm) ); // Mask that excludes the solid phase std::shared_ptr Mask (new Domain(domain_db)); MPI_Barrier(comm); Nx+=2; Ny+=2; Nz += 2; int N = Nx*Ny*Nz; //....................................................................... if (rank == 0) printf("Read input media... \n"); //....................................................................... //....................................................................... // Filenames used char LocalRankString[8]; char LocalRankFilename[40]; char LocalRestartFile[40]; sprintf(LocalRankString,"%05d",rank); sprintf(LocalRankFilename,"%s%s","ID.",LocalRankString); sprintf(LocalRestartFile,"%s%s","Restart.",LocalRankString); // printf("Local File Name = %s \n",LocalRankFilename); // .......... READ THE INPUT FILE ....................................... // char value; char *id; id = new char[N]; double sum, sum_local; double iVol_global = 1.0/(1.0*(Nx-2)*(Ny-2)*(Nz-2)*nprocs); if (BoundaryCondition > 0) iVol_global = 1.0/(1.0*(Nx-2)*nprocx*(Ny-2)*nprocy*((Nz-2)*nprocz-6)); //........................................................................... if (rank == 0) cout << "Reading in domain from signed distance function..." << endl; //....................................................................... // Read the signed distance sprintf(LocalRankString,"%05d",rank); sprintf(LocalRankFilename,"%s%s","SignDist.",LocalRankString); ReadBinaryFile(LocalRankFilename, Averages->SDs.data(), N); MPI_Barrier(comm); if (rank == 0) cout << "Domain set." << endl; //....................................................................... // Assign the phase ID field based on the signed distance //....................................................................... for (int k=0;kSDs(n) > 0.0){ id[n] = 2; } // compute the porosity (actual interface location used) if (Averages->SDs(n) > 0.0){ sum++; } } } } if (rank==0) printf("Initialize from segmented data: solid=0, NWP=1, WP=2 \n"); sprintf(LocalRankFilename,"ID.%05i",rank); size_t readID; FILE *IDFILE = fopen(LocalRankFilename,"rb"); if (IDFILE==NULL) ERROR("lbpm_color_simulator: Error opening file: ID.xxxxx"); readID=fread(id,1,N,IDFILE); if (readID != size_t(N)) printf("lbpm_color_simulator: Error reading ID (rank=%i) \n",rank); fclose(IDFILE); // Read id from restart if (Restart == true){ if (rank==0){ printf("Reading restart file! \n"); ifstream restart("Restart.txt"); if (restart.is_open()){ restart >> timestep; printf("Restarting from timestep =%i \n",timestep); } else{ printf("WARNING:No Restart.txt file, setting timestep=0 \n"); timestep=0; } } MPI_Bcast(×tep,1,MPI_INT,0,comm); FILE *RESTART = fopen(LocalRestartFile,"rb"); if (IDFILE==NULL) ERROR("lbpm_color_simulator: Error opening file: Restart.xxxxx"); readID=fread(id,1,N,RESTART); if (readID != size_t(N)) printf("lbpm_color_simulator: Error reading Restart (rank=%i) \n",rank); fclose(RESTART); /* // Read in the restart file to CPU buffers double *cDen = new double[2*Np]; double *cfq = new double[19*Np]; ReadCheckpoint(LocalRestartFile, cDen, cfq, Np); // Copy the restart data to the GPU ScaLBL_CopyToDevice(fq,cfq,19*Np*sizeof(double)); ScaLBL_CopyToDevice(Den,cDen,2*Np*sizeof(double)); ScaLBL_DeviceBarrier(); delete [] cDen; delete [] cfq; */ MPI_Barrier(comm); } //....................................................................... // Compute the media porosity, assign phase labels and solid composition //....................................................................... sum_local=0.0; int Np=0; // number of local pore nodes //....................................................................... for (int k=1;k 0){ sum_local+=1.0; Np++; } } } } MPI_Allreduce(&sum_local,&sum,1,MPI_DOUBLE,MPI_SUM,comm); double porosity = sum*iVol_global; if (rank==0) printf("Media porosity = %f \n",porosity); //......................................................... // If external boundary conditions are applied remove solid if (BoundaryCondition > 0 && Dm->kproc() == 0){ for (int k=0; k<3; k++){ for (int j=0;jSDs(n) = max(Averages->SDs(n),1.0*(2.5-k)); } } } } if (BoundaryCondition > 0 && Dm->kproc() == nprocz-1){ for (int k=Nz-3; kSDs(n) = max(Averages->SDs(n),1.0*(k-Nz+2.5)); } } } } //......................................................... // don't perform computations at the eight corners id[0] = id[Nx-1] = id[(Ny-1)*Nx] = id[(Ny-1)*Nx + Nx-1] = 0; id[(Nz-1)*Nx*Ny] = id[(Nz-1)*Nx*Ny+Nx-1] = id[(Nz-1)*Nx*Ny+(Ny-1)*Nx] = id[(Nz-1)*Nx*Ny+(Ny-1)*Nx + Nx-1] = 0; //......................................................... // Initialize communication structures in averaging domain for (int i=0; iNx*Mask->Ny*Mask->Nz; i++) Mask->id[i] = id[i]; Mask->CommInit(comm); double *PhaseLabel; PhaseLabel = new double[N]; Mask->AssignComponentLabels(PhaseLabel); //........................................................................... if (rank==0) printf ("Create ScaLBL_Communicator \n"); // Create a communicator for the device (will use optimized layout) //ScaLBL_Communicator ScaLBL_Comm(Mask); ScaLBL_Comm = std::shared_ptr(new ScaLBL_Communicator(Mask)); //Create a second communicator based on the regular data layout ScaLBL_Communicator ScaLBL_Comm_Regular(Mask); int Npad=(Np/16 + 2)*16; if (rank==0) printf ("Set up memory efficient layout \n"); IntArray Map(Nx,Ny,Nz); auto neighborList= new int[18*Npad]; Np = ScaLBL_Comm.MemoryOptimizedLayoutAA(Map,neighborList,Mask->id,Np); MPI_Barrier(comm); //........................................................................... // MAIN VARIABLES ALLOCATED HERE //........................................................................... // LBM variables if (rank==0) printf ("Allocating distributions \n"); //......................device distributions................................. int dist_mem_size = Np*sizeof(double); int neighborSize=18*(Np*sizeof(int)); int *NeighborList; int *dvcMap; double *fq, *Aq, *Bq; double *Den, *Phi; double *SolidPotential; double *Velocity; double *Gradient; double *Pressure; //........................................................................... ScaLBL_AllocateDeviceMemory((void **) &NeighborList, neighborSize); ScaLBL_AllocateDeviceMemory((void **) &dvcMap, sizeof(int)*Np); ScaLBL_AllocateDeviceMemory((void **) &fq, 19*dist_mem_size); ScaLBL_AllocateDeviceMemory((void **) &Aq, 7*dist_mem_size); ScaLBL_AllocateDeviceMemory((void **) &Bq, 7*dist_mem_size); ScaLBL_AllocateDeviceMemory((void **) &Den, 2*dist_mem_size); ScaLBL_AllocateDeviceMemory((void **) &Phi, sizeof(double)*Np); ScaLBL_AllocateDeviceMemory((void **) &Pressure, sizeof(double)*Np); ScaLBL_AllocateDeviceMemory((void **) &Velocity, 3*sizeof(double)*Np); ScaLBL_AllocateDeviceMemory((void **) &Gradient, 3*sizeof(double)*Np); ScaLBL_AllocateDeviceMemory((void **) &SolidPotential, 3*sizeof(double)*Np); //........................................................................... // Update GPU data structures if (rank==0) printf ("Setting up device map and neighbor list \n"); int *TmpMap; TmpMap=new int[Np]; for (int k=1; kUpdateMeshValues(); // this computes the gradient of distance field (among other things) // Create the distance stencil // Compute solid forces based on mean field approximation double *Dst; Dst = new double [5*5*5]; for (int kk=0; kk<5; kk++){ for (int jj=0; jj<5; jj++){ for (int ii=0; ii<5; ii++){ int index = kk*25+jj*5+ii; Dst[index] = sqrt(double(ii-2)*double(ii-2) + double(jj-2)*double(jj-2)+ double(kk-2)*double(kk-2)); } } } for (int k=1; kid[nn] > 0)){ double vec_x = double(ii-2); double vec_y = double(jj-2); double vec_z = double(kk-2); double ALPHA=PhaseLabel[nn]; double GAMMA=-2.f; if (distval > 2.f) ALPHA=0.f; // symmetric cutoff distance phi_x += ALPHA*exp(GAMMA*distval)*vec_x/distval; phi_y += ALPHA*exp(GAMMA*distval)*vec_y/distval; phi_z += ALPHA*exp(GAMMA*distval)*vec_z/distval; } } } } Tmp[idx] = phi_x; Tmp[idx+Np] = phi_y; Tmp[idx+2*Np] = phi_z; /* double d = Averages->SDs(n); double dx = Averages->SDs_x(n); double dy = Averages->SDs_y(n); double dz = Averages->SDs_z(n); double value=cns*exp(-bns*fabs(d))-cws*exp(-bns*fabs(d)); Tmp[idx] = value*dx; Tmp[idx+Np] = value*dy; Tmp[idx+2*Np] = value*dz; */ } } } } ScaLBL_CopyToDevice(SolidPotential, Tmp, 3*sizeof(double)*Np); ScaLBL_DeviceBarrier(); delete [] Tmp; delete [] Dst; DoubleArray Psx(Nx,Ny,Nz); DoubleArray Psy(Nx,Ny,Nz); DoubleArray Psz(Nx,Ny,Nz); DoubleArray Psnorm(Nx,Ny,Nz); ScaLBL_Comm.RegularLayout(Map,&SolidPotential[0],Psx); ScaLBL_Comm.RegularLayout(Map,&SolidPotential[Np],Psy); ScaLBL_Comm.RegularLayout(Map,&SolidPotential[2*Np],Psz); for (int n=0; nid[n] == 1) PhaseLabel[idx] = 1.0; else { PhaseLabel[idx] = -1.0; count_wet+=1.f; } } } } } //printf("sw=%f \n",count_wet/double(Np)); // copy the neighbor list ScaLBL_CopyToDevice(NeighborList, neighborList, neighborSize); // initialize phi based on PhaseLabel (include solid component labels) ScaLBL_CopyToDevice(Phi, PhaseLabel, Np*sizeof(double)); //........................................................................... if (rank==0) printf ("Initializing distributions \n"); ScaLBL_D3Q19_Init(fq, Np); if (rank==0) printf ("Initializing phase field \n"); ScaLBL_DFH_Init(Phi, Den, Aq, Bq, 0, ScaLBL_Comm.last_interior, Np); //....................................................................... // Once phase has been initialized, map solid to account for 'smeared' interface //for (i=0; iSDs(i) -= (1.0); // Make sure the id match for the two domains for (int i=0; iid[i] = Mask->id[i]; //....................................................................... // Finalize setup for averaging domain Averages->UpdateSolid(); //....................................................................... //ScaLBL_D3Q19_Pressure(fq,Pressure,Np); //ScaLBL_D3Q19_Momentum(fq,Velocity,Np); //........................................................................... // Copy the phase indicator field for the earlier timestep ScaLBL_DeviceBarrier(); ScaLBL_CopyToHost(Averages->Phase_tplus.data(),Phi,Np*sizeof(double)); //........................................................................... // Copy the data for for the analysis timestep //........................................................................... // Copy the phase from the GPU -> CPU //........................................................................... ScaLBL_DeviceBarrier(); ScaLBL_CopyToHost(Averages->Phase.data(),Phi,Np*sizeof(double)); ScaLBL_Comm.RegularLayout(Map,Pressure,Averages->Press); ScaLBL_Comm.RegularLayout(Map,&Velocity[0],Averages->Vel_x); ScaLBL_Comm.RegularLayout(Map,&Velocity[Np],Averages->Vel_y); ScaLBL_Comm.RegularLayout(Map,&Velocity[2*Np],Averages->Vel_z); //........................................................................... if (rank==0) printf("********************************************************\n"); if (rank==0) printf("No. of timesteps: %i \n", timestepMax); //.......create and start timer............ double starttime,stoptime,cputime; ScaLBL_DeviceBarrier(); MPI_Barrier(comm); starttime = MPI_Wtime(); //......................................... //************ MAIN ITERATION LOOP ***************************************/ PROFILE_START("Loop"); runAnalysis analysis( analysis_db, rank_info, ScaLBL_Comm, Dm, Np, pBC, beta, Map ); while (timestep < timestepMax ) { //if ( rank==0 ) { printf("Running timestep %i (%i MB)\n",timestep+1,(int)(Utilities::getMemoryUsage()/1048576)); } PROFILE_START("Update"); // *************ODD TIMESTEP************* timestep++; // Compute the Phase indicator field // Read for Aq, Bq happens in this routine (requires communication) ScaLBL_Comm.BiSendD3Q7AA(Aq,Bq); //READ FROM NORMAL ScaLBL_D3Q7_AAodd_DFH(NeighborList, Aq, Bq, Den, Phi, ScaLBL_Comm.first_interior, ScaLBL_Comm.last_interior, Np); ScaLBL_Comm.BiRecvD3Q7AA(Aq,Bq); //WRITE INTO OPPOSITE ScaLBL_D3Q7_AAodd_DFH(NeighborList, Aq, Bq, Den, Phi, 0, ScaLBL_Comm.next, Np); // compute the gradient ScaLBL_D3Q19_Gradient_DFH(NeighborList, Phi, Gradient, SolidPotential, ScaLBL_Comm.first_interior, ScaLBL_Comm.last_interior, Np); ScaLBL_Comm.SendHalo(Phi); ScaLBL_D3Q19_Gradient_DFH(NeighborList, Phi, Gradient, SolidPotential, 0, ScaLBL_Comm.next, Np); ScaLBL_Comm.RecvGrad(Phi,Gradient); // Perform the collision operation ScaLBL_Comm.SendD3Q19AA(fq); //READ FROM NORMAL ScaLBL_D3Q19_AAodd_DFH(NeighborList, fq, Aq, Bq, Den, Phi, Gradient, rhoA, rhoB, tauA, tauB, alpha, beta, Fx, Fy, Fz, ScaLBL_Comm.first_interior, ScaLBL_Comm.last_interior, Np); ScaLBL_Comm.RecvD3Q19AA(fq); //WRITE INTO OPPOSITE // Set BCs if (BoundaryCondition > 0){ ScaLBL_Comm.Color_BC_z(dvcMap, Phi, Den, inletA, inletB); ScaLBL_Comm.Color_BC_Z(dvcMap, Phi, Den, outletA, outletB); } if (BoundaryCondition == 3){ ScaLBL_Comm.D3Q19_Pressure_BC_z(NeighborList, fq, din, timestep); ScaLBL_Comm.D3Q19_Pressure_BC_Z(NeighborList, fq, dout, timestep); } if (BoundaryCondition == 4){ din = ScaLBL_Comm.D3Q19_Flux_BC_z(NeighborList, fq, flux, timestep); ScaLBL_Comm.D3Q19_Pressure_BC_Z(NeighborList, fq, dout, timestep); } ScaLBL_D3Q19_AAodd_DFH(NeighborList, fq, Aq, Bq, Den, Phi, Gradient, rhoA, rhoB, tauA, tauB, alpha, beta, Fx, Fy, Fz, 0, ScaLBL_Comm.next, Np); ScaLBL_DeviceBarrier(); MPI_Barrier(comm); // *************EVEN TIMESTEP************* timestep++; // Compute the Phase indicator field ScaLBL_Comm.BiSendD3Q7AA(Aq,Bq); //READ FROM NORMAL ScaLBL_D3Q7_AAeven_DFH(Aq, Bq, Den, Phi, ScaLBL_Comm.first_interior, ScaLBL_Comm.last_interior, Np); ScaLBL_Comm.BiRecvD3Q7AA(Aq,Bq); //WRITE INTO OPPOSITE ScaLBL_D3Q7_AAeven_DFH(Aq, Bq, Den, Phi, 0, ScaLBL_Comm.next, Np); // compute the gradient ScaLBL_D3Q19_Gradient_DFH(NeighborList, Phi, Gradient, SolidPotential, ScaLBL_Comm.first_interior, ScaLBL_Comm.last_interior, Np); ScaLBL_Comm.SendHalo(Phi); ScaLBL_D3Q19_Gradient_DFH(NeighborList, Phi, Gradient, SolidPotential, 0, ScaLBL_Comm.next, Np); ScaLBL_Comm.RecvGrad(Phi,Gradient); // Perform the collision operation ScaLBL_Comm.SendD3Q19AA(fq); //READ FORM NORMAL ScaLBL_D3Q19_AAeven_DFH(NeighborList, fq, Aq, Bq, Den, Phi, Gradient, rhoA, rhoB, tauA, tauB, alpha, beta, Fx, Fy, Fz, ScaLBL_Comm.first_interior, ScaLBL_Comm.last_interior, Np); ScaLBL_Comm.RecvD3Q19AA(fq); //WRITE INTO OPPOSITE // Set boundary conditions if (BoundaryCondition > 0){ ScaLBL_Comm.Color_BC_z(dvcMap, Phi, Den, inletA, inletB); ScaLBL_Comm.Color_BC_Z(dvcMap, Phi, Den, outletA, outletB); } if (BoundaryCondition == 3){ ScaLBL_Comm.D3Q19_Pressure_BC_z(NeighborList, fq, din, timestep); ScaLBL_Comm.D3Q19_Pressure_BC_Z(NeighborList, fq, dout, timestep); } else if (BoundaryCondition == 4){ din = ScaLBL_Comm.D3Q19_Flux_BC_z(NeighborList, fq, flux, timestep); ScaLBL_Comm.D3Q19_Pressure_BC_Z(NeighborList, fq, dout, timestep); } ScaLBL_D3Q19_AAeven_DFH(NeighborList, fq, Aq, Bq, Den, Phi, Gradient, rhoA, rhoB, tauA, tauB, alpha, beta, Fx, Fy, Fz, 0, ScaLBL_Comm.next, Np); ScaLBL_DeviceBarrier(); MPI_Barrier(comm); //************************************************************************ MPI_Barrier(comm); PROFILE_STOP("Update"); // Run the analysis analysis.run( timestep, *Averages, Phi, Pressure, Velocity, fq, Den ); } analysis.finish(); PROFILE_STOP("Loop"); PROFILE_SAVE("lbpm_color_simulator",1); //************************************************************************ ScaLBL_DeviceBarrier(); MPI_Barrier(comm); stoptime = MPI_Wtime(); if (rank==0) printf("-------------------------------------------------------------------\n"); // Compute the walltime per timestep cputime = (stoptime - starttime)/timestep; // Performance obtained from each node double MLUPS = double(Np)/cputime/1000000; if (rank==0) printf("********************************************************\n"); if (rank==0) printf("CPU time = %f \n", cputime); if (rank==0) printf("Lattice update rate (per core)= %f MLUPS \n", MLUPS); MLUPS *= nprocs; if (rank==0) printf("Lattice update rate (total)= %f MLUPS \n", MLUPS); if (rank==0) printf("********************************************************\n"); // ************************************************************************ // Copy back final phase indicator field and convert to regular layout DoubleArray PhaseField(Nx,Ny,Nz); ScaLBL_Comm.RegularLayout(Map,Phi,PhaseField); FILE *OUTFILE; sprintf(LocalRankFilename,"Phase.%05i.raw",rank); OUTFILE = fopen(LocalRankFilename,"wb"); fwrite(PhaseField.data(),8,N,OUTFILE); fclose(OUTFILE); PROFILE_STOP("Main"); PROFILE_SAVE("lbpm_color_simulator",1); // **************************************************** MPI_Barrier(comm); } // Limit scope so variables that contain communicators will free before MPI_Finialize MPI_Comm_free(&comm); MPI_Finalize(); }