177841947SLeila Ghaffari // Copyright (c) 2017, Lawrence Livermore National Security, LLC. Produced at 277841947SLeila Ghaffari // the Lawrence Livermore National Laboratory. LLNL-CODE-734707. All Rights 377841947SLeila Ghaffari // reserved. See files LICENSE and NOTICE for details. 477841947SLeila Ghaffari // 577841947SLeila Ghaffari // This file is part of CEED, a collection of benchmarks, miniapps, software 677841947SLeila Ghaffari // libraries and APIs for efficient high-order finite element and spectral 777841947SLeila Ghaffari // element discretizations for exascale applications. For more information and 877841947SLeila Ghaffari // source code availability see http://github.com/ceed. 977841947SLeila Ghaffari // 1077841947SLeila Ghaffari // The CEED research is supported by the Exascale Computing Project 17-SC-20-SC, 1177841947SLeila Ghaffari // a collaborative effort of two U.S. Department of Energy organizations (Office 1277841947SLeila Ghaffari // of Science and the National Nuclear Security Administration) responsible for 1377841947SLeila Ghaffari // the planning and preparation of a capable exascale ecosystem, including 1477841947SLeila Ghaffari // software, applications, hardware, advanced system engineering and early 1577841947SLeila Ghaffari // testbed platforms, in support of the nation's exascale computing imperative. 1677841947SLeila Ghaffari 1777841947SLeila Ghaffari /// @file 1877841947SLeila Ghaffari /// Utility functions for setting up ADVECTION 1977841947SLeila Ghaffari 2077841947SLeila Ghaffari #include "../navierstokes.h" 2177841947SLeila Ghaffari #include "../qfunctions/setupgeo.h" 2277841947SLeila Ghaffari #include "../qfunctions/advection.h" 2377841947SLeila Ghaffari 2477841947SLeila Ghaffari PetscErrorCode NS_ADVECTION(ProblemData *problem, void *setup_ctx, void *ctx) { 2577841947SLeila Ghaffari WindType wind_type; 2677841947SLeila Ghaffari BubbleType bubble_type; 2777841947SLeila Ghaffari BubbleContinuityType bubble_continuity_type; 2877841947SLeila Ghaffari StabilizationType stab; 2977841947SLeila Ghaffari SetupContext setup_context = *(SetupContext *)setup_ctx; 3077841947SLeila Ghaffari User user = *(User *)ctx; 3177841947SLeila Ghaffari MPI_Comm comm = PETSC_COMM_WORLD; 3277841947SLeila Ghaffari PetscBool implicit; 3377841947SLeila Ghaffari PetscBool has_curr_time = PETSC_FALSE; 3477841947SLeila Ghaffari PetscInt ierr; 3577841947SLeila Ghaffari PetscFunctionBeginUser; 3677841947SLeila Ghaffari 3777841947SLeila Ghaffari ierr = PetscCalloc1(1, &user->phys->advection_ctx); CHKERRQ(ierr); 3877841947SLeila Ghaffari 3977841947SLeila Ghaffari // ------------------------------------------------------ 4077841947SLeila Ghaffari // SET UP ADVECTION 4177841947SLeila Ghaffari // ------------------------------------------------------ 4277841947SLeila Ghaffari problem->dim = 3; 4377841947SLeila Ghaffari problem->q_data_size_vol = 10; 4477841947SLeila Ghaffari problem->q_data_size_sur = 4; 4577841947SLeila Ghaffari problem->setup_vol = Setup; 4677841947SLeila Ghaffari problem->setup_vol_loc = Setup_loc; 4777841947SLeila Ghaffari problem->setup_sur = SetupBoundary; 4877841947SLeila Ghaffari problem->setup_sur_loc = SetupBoundary_loc; 4977841947SLeila Ghaffari problem->ics = ICsAdvection; 5077841947SLeila Ghaffari problem->ics_loc = ICsAdvection_loc; 5177841947SLeila Ghaffari problem->apply_vol_rhs = Advection; 5277841947SLeila Ghaffari problem->apply_vol_rhs_loc = Advection_loc; 5377841947SLeila Ghaffari problem->apply_vol_ifunction = IFunction_Advection; 5477841947SLeila Ghaffari problem->apply_vol_ifunction_loc = IFunction_Advection_loc; 5577841947SLeila Ghaffari problem->apply_sur = Advection_Sur; 5677841947SLeila Ghaffari problem->apply_sur_loc = Advection_Sur_loc; 5777841947SLeila Ghaffari problem->bc = Exact_Advection; 58d0b732dbSLeila Ghaffari problem->setup_ctx = SetupContext_ADVECTION; 5977841947SLeila Ghaffari problem->bc_func = BC_ADVECTION; 6077841947SLeila Ghaffari problem->non_zero_time = PETSC_FALSE; 6177841947SLeila Ghaffari problem->print_info = PRINT_ADVECTION; 6277841947SLeila Ghaffari 6377841947SLeila Ghaffari // ------------------------------------------------------ 6477841947SLeila Ghaffari // Create the libCEED context 6577841947SLeila Ghaffari // ------------------------------------------------------ 6677841947SLeila Ghaffari PetscScalar lx = 8000.; // m 6777841947SLeila Ghaffari PetscScalar ly = 8000.; // m 6877841947SLeila Ghaffari PetscScalar lz = 4000.; // m 6977841947SLeila Ghaffari CeedScalar rc = 1000.; // m (Radius of bubble) 7077841947SLeila Ghaffari CeedScalar CtauS = 0.; // dimensionless 7177841947SLeila Ghaffari CeedScalar strong_form = 0.; // [0,1] 7277841947SLeila Ghaffari CeedScalar E_wind = 1.e6; // J 7377841947SLeila Ghaffari PetscReal wind[3] = {1., 0, 0}; // m/s 7477841947SLeila Ghaffari 7577841947SLeila Ghaffari // ------------------------------------------------------ 7677841947SLeila Ghaffari // Create the PETSc context 7777841947SLeila Ghaffari // ------------------------------------------------------ 7877841947SLeila Ghaffari PetscScalar meter = 1e-2; // 1 meter in scaled length units 7977841947SLeila Ghaffari PetscScalar kilogram = 1e-6; // 1 kilogram in scaled mass units 8077841947SLeila Ghaffari PetscScalar second = 1e-2; // 1 second in scaled time units 8177841947SLeila Ghaffari PetscScalar Joule; 8277841947SLeila Ghaffari 8377841947SLeila Ghaffari // ------------------------------------------------------ 8477841947SLeila Ghaffari // Command line Options 8577841947SLeila Ghaffari // ------------------------------------------------------ 8677841947SLeila Ghaffari ierr = PetscOptionsBegin(comm, NULL, "Options for ADVECTION problem", 8777841947SLeila Ghaffari NULL); CHKERRQ(ierr); 8877841947SLeila Ghaffari // -- Physics 8977841947SLeila Ghaffari ierr = PetscOptionsScalar("-lx", "Length scale in x direction", 9077841947SLeila Ghaffari NULL, lx, &lx, NULL); CHKERRQ(ierr); 9177841947SLeila Ghaffari ierr = PetscOptionsScalar("-ly", "Length scale in y direction", 9277841947SLeila Ghaffari NULL, ly, &ly, NULL); CHKERRQ(ierr); 9377841947SLeila Ghaffari ierr = PetscOptionsScalar("-lz", "Length scale in z direction", 9477841947SLeila Ghaffari NULL, lz, &lz, NULL); CHKERRQ(ierr); 9577841947SLeila Ghaffari ierr = PetscOptionsScalar("-rc", "Characteristic radius of thermal bubble", 9677841947SLeila Ghaffari NULL, rc, &rc, NULL); CHKERRQ(ierr); 9777841947SLeila Ghaffari PetscBool translation; 9877841947SLeila Ghaffari ierr = PetscOptionsEnum("-wind_type", "Wind type in Advection", 9977841947SLeila Ghaffari NULL, WindTypes, 10077841947SLeila Ghaffari (PetscEnum)(wind_type = WIND_ROTATION), 10177841947SLeila Ghaffari (PetscEnum *)&wind_type, &translation); CHKERRQ(ierr); 10277841947SLeila Ghaffari if (translation) user->phys->has_neumann = PETSC_TRUE; 10377841947SLeila Ghaffari PetscInt n = problem->dim; 10477841947SLeila Ghaffari PetscBool user_wind; 10577841947SLeila Ghaffari ierr = PetscOptionsRealArray("-wind_translation", "Constant wind vector", 10677841947SLeila Ghaffari NULL, wind, &n, &user_wind); CHKERRQ(ierr); 10777841947SLeila Ghaffari ierr = PetscOptionsScalar("-CtauS", 10877841947SLeila Ghaffari "Scale coefficient for tau (nondimensional)", 10977841947SLeila Ghaffari NULL, CtauS, &CtauS, NULL); CHKERRQ(ierr); 11077841947SLeila Ghaffari ierr = PetscOptionsScalar("-strong_form", 11177841947SLeila Ghaffari "Strong (1) or weak/integrated by parts (0) advection residual", 11277841947SLeila Ghaffari NULL, strong_form, &strong_form, NULL); CHKERRQ(ierr); 11377841947SLeila Ghaffari ierr = PetscOptionsScalar("-E_wind", "Total energy of inflow wind", 11477841947SLeila Ghaffari NULL, E_wind, &E_wind, NULL); CHKERRQ(ierr); 11577841947SLeila Ghaffari ierr = PetscOptionsEnum("-bubble_type", "Sphere (3D) or cylinder (2D)", 11677841947SLeila Ghaffari NULL, BubbleTypes, 11777841947SLeila Ghaffari (PetscEnum)(bubble_type = BUBBLE_SPHERE), 11877841947SLeila Ghaffari (PetscEnum *)&bubble_type, NULL); CHKERRQ(ierr); 11977841947SLeila Ghaffari ierr = PetscOptionsEnum("-bubble_continuity", "Smooth, back_sharp, or thick", 12077841947SLeila Ghaffari NULL, BubbleContinuityTypes, 12177841947SLeila Ghaffari (PetscEnum)(bubble_continuity_type = BUBBLE_CONTINUITY_SMOOTH), 12277841947SLeila Ghaffari (PetscEnum *)&bubble_continuity_type, NULL); CHKERRQ(ierr); 12377841947SLeila Ghaffari ierr = PetscOptionsEnum("-stab", "Stabilization method", NULL, 12477841947SLeila Ghaffari StabilizationTypes, (PetscEnum)(stab = STAB_NONE), 12577841947SLeila Ghaffari (PetscEnum *)&stab, NULL); CHKERRQ(ierr); 12677841947SLeila Ghaffari ierr = PetscOptionsBool("-implicit", "Use implicit (IFunction) formulation", 12777841947SLeila Ghaffari NULL, implicit=PETSC_FALSE, &implicit, NULL); 12877841947SLeila Ghaffari CHKERRQ(ierr); 12977841947SLeila Ghaffari 13077841947SLeila Ghaffari // -- Units 13177841947SLeila Ghaffari ierr = PetscOptionsScalar("-units_meter", "1 meter in scaled length units", 13277841947SLeila Ghaffari NULL, meter, &meter, NULL); CHKERRQ(ierr); 13377841947SLeila Ghaffari meter = fabs(meter); 13477841947SLeila Ghaffari ierr = PetscOptionsScalar("-units_kilogram","1 kilogram in scaled mass units", 13577841947SLeila Ghaffari NULL, kilogram, &kilogram, NULL); CHKERRQ(ierr); 13677841947SLeila Ghaffari kilogram = fabs(kilogram); 13777841947SLeila Ghaffari ierr = PetscOptionsScalar("-units_second","1 second in scaled time units", 13877841947SLeila Ghaffari NULL, second, &second, NULL); CHKERRQ(ierr); 13977841947SLeila Ghaffari second = fabs(second); 14077841947SLeila Ghaffari 14177841947SLeila Ghaffari // -- Warnings 14277841947SLeila Ghaffari if (wind_type == WIND_ROTATION && user_wind) { 14377841947SLeila Ghaffari ierr = PetscPrintf(comm, 14477841947SLeila Ghaffari "Warning! Use -wind_translation only with -wind_type translation\n"); 14577841947SLeila Ghaffari CHKERRQ(ierr); 14677841947SLeila Ghaffari } 14777841947SLeila Ghaffari if (wind_type == WIND_TRANSLATION 14877841947SLeila Ghaffari && bubble_type == BUBBLE_CYLINDER && wind[2] != 0.) { 14977841947SLeila Ghaffari wind[2] = 0; 15077841947SLeila Ghaffari ierr = PetscPrintf(comm, 15177841947SLeila Ghaffari "Warning! Background wind in the z direction should be zero (-wind_translation x,x,0) with -bubble_type cylinder\n"); 15277841947SLeila Ghaffari CHKERRQ(ierr); 15377841947SLeila Ghaffari } 15477841947SLeila Ghaffari if (stab == STAB_NONE && CtauS != 0) { 15577841947SLeila Ghaffari ierr = PetscPrintf(comm, 15677841947SLeila Ghaffari "Warning! Use -CtauS only with -stab su or -stab supg\n"); 15777841947SLeila Ghaffari CHKERRQ(ierr); 15877841947SLeila Ghaffari } 15977841947SLeila Ghaffari if (stab == STAB_SUPG && !implicit) { 16077841947SLeila Ghaffari ierr = PetscPrintf(comm, 16177841947SLeila Ghaffari "Warning! Use -stab supg only with -implicit\n"); 16277841947SLeila Ghaffari CHKERRQ(ierr); 16377841947SLeila Ghaffari } 16477841947SLeila Ghaffari 16577841947SLeila Ghaffari ierr = PetscOptionsEnd(); CHKERRQ(ierr); 16677841947SLeila Ghaffari 16777841947SLeila Ghaffari // ------------------------------------------------------ 16877841947SLeila Ghaffari // Set up the PETSc context 16977841947SLeila Ghaffari // ------------------------------------------------------ 17077841947SLeila Ghaffari // -- Define derived units 17177841947SLeila Ghaffari Joule = kilogram * PetscSqr(meter) / PetscSqr(second); 17277841947SLeila Ghaffari 17377841947SLeila Ghaffari user->units->meter = meter; 17477841947SLeila Ghaffari user->units->kilogram = kilogram; 17577841947SLeila Ghaffari user->units->second = second; 17677841947SLeila Ghaffari user->units->Joule = Joule; 17777841947SLeila Ghaffari 17877841947SLeila Ghaffari // ------------------------------------------------------ 17977841947SLeila Ghaffari // Set up the libCEED context 18077841947SLeila Ghaffari // ------------------------------------------------------ 18177841947SLeila Ghaffari // -- Scale variables to desired units 18277841947SLeila Ghaffari E_wind *= Joule; 18377841947SLeila Ghaffari lx = fabs(lx) * meter; 18477841947SLeila Ghaffari ly = fabs(ly) * meter; 18577841947SLeila Ghaffari lz = fabs(lz) * meter; 18677841947SLeila Ghaffari rc = fabs(rc) * meter; 187e535bb46SLeila Ghaffari for (int i=0; i<3; i++) wind[i] = wind[i] * (meter/second); 18877841947SLeila Ghaffari 18977841947SLeila Ghaffari // -- Setup Context 19077841947SLeila Ghaffari setup_context->rc = rc; 19177841947SLeila Ghaffari setup_context->lx = lx; 19277841947SLeila Ghaffari setup_context->ly = ly; 19377841947SLeila Ghaffari setup_context->lz = lz; 19477841947SLeila Ghaffari setup_context->wind[0] = wind[0]; 19577841947SLeila Ghaffari setup_context->wind[1] = wind[1]; 19677841947SLeila Ghaffari setup_context->wind[2] = wind[2]; 19777841947SLeila Ghaffari setup_context->wind_type = wind_type; 19877841947SLeila Ghaffari setup_context->bubble_type = bubble_type; 19977841947SLeila Ghaffari setup_context->bubble_continuity_type = bubble_continuity_type; 20077841947SLeila Ghaffari setup_context->time = 0; 20177841947SLeila Ghaffari 20277841947SLeila Ghaffari // -- QFunction Context 20377841947SLeila Ghaffari user->phys->stab = stab; 20477841947SLeila Ghaffari user->phys->wind_type = wind_type; 20577841947SLeila Ghaffari user->phys->bubble_type = bubble_type; 20677841947SLeila Ghaffari user->phys->bubble_continuity_type = bubble_continuity_type; 20777841947SLeila Ghaffari // if passed correctly 20877841947SLeila Ghaffari user->phys->implicit = implicit; 20977841947SLeila Ghaffari user->phys->has_curr_time = has_curr_time; 21077841947SLeila Ghaffari user->phys->advection_ctx->CtauS = CtauS; 21177841947SLeila Ghaffari user->phys->advection_ctx->E_wind = E_wind; 21277841947SLeila Ghaffari user->phys->advection_ctx->implicit = implicit; 21377841947SLeila Ghaffari user->phys->advection_ctx->strong_form = strong_form; 21477841947SLeila Ghaffari user->phys->advection_ctx->stabilization = stab; 21577841947SLeila Ghaffari 21677841947SLeila Ghaffari PetscFunctionReturn(0); 21777841947SLeila Ghaffari } 21877841947SLeila Ghaffari 219d0b732dbSLeila Ghaffari PetscErrorCode SetupContext_ADVECTION(Ceed ceed, CeedData ceed_data, 220d0b732dbSLeila Ghaffari AppCtx app_ctx, SetupContext setup_ctx, Physics phys) { 221d0b732dbSLeila Ghaffari PetscFunctionBeginUser; 222d0b732dbSLeila Ghaffari 223d0b732dbSLeila Ghaffari CeedQFunctionContextCreate(ceed, &ceed_data->setup_context); 224d0b732dbSLeila Ghaffari CeedQFunctionContextSetData(ceed_data->setup_context, CEED_MEM_HOST, 225d0b732dbSLeila Ghaffari CEED_USE_POINTER, sizeof(*setup_ctx), setup_ctx); 226d0b732dbSLeila Ghaffari CeedQFunctionSetContext(ceed_data->qf_ics, ceed_data->setup_context); 227d0b732dbSLeila Ghaffari CeedQFunctionContextCreate(ceed, &ceed_data->advection_context); 228d0b732dbSLeila Ghaffari CeedQFunctionContextSetData(ceed_data->advection_context, CEED_MEM_HOST, 229d0b732dbSLeila Ghaffari CEED_USE_POINTER, 230d0b732dbSLeila Ghaffari sizeof(*phys->advection_ctx), phys->advection_ctx); 231d0b732dbSLeila Ghaffari if (ceed_data->qf_rhs_vol) 232d0b732dbSLeila Ghaffari CeedQFunctionSetContext(ceed_data->qf_rhs_vol, ceed_data->advection_context); 233d0b732dbSLeila Ghaffari if (ceed_data->qf_ifunction_vol) 234d0b732dbSLeila Ghaffari CeedQFunctionSetContext(ceed_data->qf_ifunction_vol, 235d0b732dbSLeila Ghaffari ceed_data->advection_context); 236d0b732dbSLeila Ghaffari if (ceed_data->qf_apply_sur) 237d0b732dbSLeila Ghaffari CeedQFunctionSetContext(ceed_data->qf_apply_sur, ceed_data->advection_context); 238d0b732dbSLeila Ghaffari 239d0b732dbSLeila Ghaffari PetscFunctionReturn(0); 240d0b732dbSLeila Ghaffari } 241d0b732dbSLeila Ghaffari 24277841947SLeila Ghaffari PetscErrorCode BC_ADVECTION(DM dm, SimpleBC bc, Physics phys, 24377841947SLeila Ghaffari void *setup_ctx) { 24477841947SLeila Ghaffari PetscErrorCode ierr; 24577841947SLeila Ghaffari PetscFunctionBeginUser; 24677841947SLeila Ghaffari 24777841947SLeila Ghaffari // Define boundary conditions 24877841947SLeila Ghaffari if (phys->wind_type == WIND_TRANSLATION) { 24977841947SLeila Ghaffari bc->num_wall = bc->num_slip[2] = 0; 25077841947SLeila Ghaffari } else if (phys->wind_type == WIND_ROTATION && 25177841947SLeila Ghaffari phys->bubble_type == BUBBLE_CYLINDER) { 25277841947SLeila Ghaffari bc->num_slip[2] = 2; bc->slips[2][0] = 1; bc->slips[2][1] = 2; 25377841947SLeila Ghaffari bc->num_wall = 4; 25477841947SLeila Ghaffari bc->walls[0] = 3; bc->walls[1] = 4; bc->walls[2] = 5; bc->walls[3] = 6; 25577841947SLeila Ghaffari } else { 25677841947SLeila Ghaffari bc->num_slip[2] = 0; 25777841947SLeila Ghaffari bc->num_wall = 6; 25877841947SLeila Ghaffari bc->walls[0] = 1; bc->walls[1] = 2; bc->walls[2] = 3; 25977841947SLeila Ghaffari bc->walls[3] = 4; bc->walls[4] = 5; bc->walls[5] = 6; 26077841947SLeila Ghaffari } 26177841947SLeila Ghaffari 26277841947SLeila Ghaffari { 26377841947SLeila Ghaffari // Set slip boundary conditions 26477841947SLeila Ghaffari DMLabel label; 26577841947SLeila Ghaffari ierr = DMGetLabel(dm, "Face Sets", &label); CHKERRQ(ierr); 26677841947SLeila Ghaffari PetscInt comps[1] = {3}; 267*b8962995SJeremy L Thompson ierr = DMAddBoundary(dm, DM_BC_ESSENTIAL, "slipz", label, 26877841947SLeila Ghaffari bc->num_slip[2], bc->slips[2], 0, 1, comps, 26977841947SLeila Ghaffari (void(*)(void))NULL, NULL, setup_ctx, NULL); 27077841947SLeila Ghaffari CHKERRQ(ierr); 27177841947SLeila Ghaffari } 27277841947SLeila Ghaffari 27377841947SLeila Ghaffari // Set wall boundary conditions 27477841947SLeila Ghaffari // zero energy density and zero flux 27577841947SLeila Ghaffari { 27677841947SLeila Ghaffari DMLabel label; 27777841947SLeila Ghaffari PetscInt comps[1] = {4}; 27877841947SLeila Ghaffari ierr = DMGetLabel(dm, "Face Sets", &label); CHKERRQ(ierr); 279*b8962995SJeremy L Thompson ierr = DMAddBoundary(dm, DM_BC_ESSENTIAL, "wall", label, 28077841947SLeila Ghaffari bc->num_wall, bc->walls, 0, 28177841947SLeila Ghaffari 1, comps, (void(*)(void))Exact_Advection, NULL, 28277841947SLeila Ghaffari setup_ctx, NULL); CHKERRQ(ierr); 28377841947SLeila Ghaffari } 28477841947SLeila Ghaffari 28577841947SLeila Ghaffari PetscFunctionReturn(0); 28677841947SLeila Ghaffari } 28777841947SLeila Ghaffari 28877841947SLeila Ghaffari PetscErrorCode PRINT_ADVECTION(Physics phys, SetupContext setup_ctx, 28977841947SLeila Ghaffari AppCtx app_ctx) { 29077841947SLeila Ghaffari MPI_Comm comm = PETSC_COMM_WORLD; 29177841947SLeila Ghaffari PetscErrorCode ierr; 29277841947SLeila Ghaffari PetscFunctionBeginUser; 29377841947SLeila Ghaffari 29477841947SLeila Ghaffari ierr = PetscPrintf(comm, 29577841947SLeila Ghaffari " Problem:\n" 29677841947SLeila Ghaffari " Problem Name : %s\n" 29777841947SLeila Ghaffari " Stabilization : %s\n" 29877841947SLeila Ghaffari " Bubble Type : %s (%dD)\n" 29977841947SLeila Ghaffari " Bubble Continuity : %s\n" 30077841947SLeila Ghaffari " Wind Type : %s\n", 30177841947SLeila Ghaffari app_ctx->problem_name, StabilizationTypes[phys->stab], 30277841947SLeila Ghaffari BubbleTypes[phys->bubble_type], 30377841947SLeila Ghaffari phys->bubble_type == BUBBLE_SPHERE ? 3 : 2, 30477841947SLeila Ghaffari BubbleContinuityTypes[phys->bubble_continuity_type], 30577841947SLeila Ghaffari WindTypes[phys->wind_type]); CHKERRQ(ierr); 30677841947SLeila Ghaffari 30777841947SLeila Ghaffari if (phys->wind_type == WIND_TRANSLATION) { 30877841947SLeila Ghaffari ierr = PetscPrintf(comm, 30977841947SLeila Ghaffari " Background Wind : %f,%f,%f\n", 31077841947SLeila Ghaffari setup_ctx->wind[0], setup_ctx->wind[1], setup_ctx->wind[2]); CHKERRQ(ierr); 31177841947SLeila Ghaffari } 31277841947SLeila Ghaffari PetscFunctionReturn(0); 31377841947SLeila Ghaffari } 314