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Computational Cell M95000220W North Face i, j + l, k V Top Face i, j, k i, j, k + 1 i + 1, j, k W U East Face

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Fortran Symbols 4 C_pgFluid-phase specific heat, C pg 4 C_psSolids-phase specific heat, C psm 4 F_gsFluid-solids drag coefficient, F gm 4 F_ssFluid-solids drag coefficient, F slm EP_gVoid fraction, g GAMMA_gsFluid-solids heat transfer coefficient, gs 4 HOR_gHeat of reaction for fluid phase, H rg 4 HOR_sHeats of reaction for solids phases, H rs 4 IX-direction index 4 IJKindex for i, j, k 4 IMJKindex for i ‑ 1, j, k 4 IPJKindex for i+1, j, k 4 IJMKindex for i, j ‑ 1, k

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Fortran Symbols 4 IJPKindex for i, j+1, k 4 IJKMindex for i, j, k ‑ 1 4 IJKPindex for i, j, k+1 4 IJKW= IMJK, if IMJK is a fluid cell; else IJK 4 IJKE= IPJK, if IPJK is a fluid cell; else IJK 4 IJKS= IJMK, if IJMK is a fluid cell; else IJK 4 IJKN= IJPK, if IJPK is a fluid cell; else IJK 4 IJKB= IJKM, if IJKM is a fluid cell; else IJK 4 IJKT= IJKP, if IJKP is a fluid cell; else IJK 4 JY-direction index 4 KZ-direction index 4 K_gFluid-phase thermal conductivity, k g 4 K_sSolids-phase thermal conductivity, k sm

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Fortran Symbols LAMBDA_sSolids-phase second coefficient of viscosity, sm 4 MIndex for solids phase 4 MU_gFluid viscosity, µ g 4 MU_sSolids-phase viscosity, µ sm 4 NIndex of gas or solids species 4 P_gFluid pressure, P g 4 P_sSolids pressure, P s 4 P_starSolids pressure in plastic regime, P * 4 R_gpRate of production of gas species n (part of R gn ) 4 RoX_gcRate of consumption of gas species n divided by X gn (part of R gn /X gn )

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Fortran Symbols 4 R_spRate of production of solids species n (part of R smn ) 4 RoX_scRate of consumption of solids species n divided by X smn (part of R smn /X smn ) RO_gFluid density, g ROP_gMacroscopic (effective) density of the fluid: g ' ~=~ g g SUM_R_g R_gn SUM_R_s R_smn 4 Theta_mgranular temperature 4 T_gFluid temperature, T g 4 T_sSolids phase temperature, T s

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Fortran Symbols 4 U_gX-component of fluid velocity, u g 4 U_sX-component of solids velocity, u sm 4 V_gY-component of fluid velocity, v g 4 V_sY-component of solids velocity, v sm 4 W_gZ-component of fluid velocity, w g 4 W_sZ-component of solids velocity, w sm 4 X_gFluid species mass fraction, X gn 4 X_sSolids species mass fraction, X sm

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List of Functions 4 BOTTOM_OF (IJK)IJKB. 4 EAST_OF (IJK)IJKE. 4 EP_s (IJK, M)volume fraction of the M th solids phase. 4 FLUID_AT (IJK)determine whether the cell IJK is a fluid cell. 4 FUNIJK (I, J, K,)find index IJK from I, J, and K values. 4 IM_OF (IJK)IMJK. 4 IP_OF (IJK)IPJK. 4 IS_AT_E (IJK)determine whether east face is an internal surface 4 IS_AT_N (IJK)determine whether north face is an internal surface 4 IS_AT_T (IJK)determine whether top face is an internal surface 4 JM_OF (IJK)IJMK. 4 JP_OF (IJK)IJPK.

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List of Functions 4 KM_OF (IJK)IJKM. 4 KP_OF (IJK)IJKP. 4 NORTH_OF (IJK)IJKN. 4 SOUTH_OF (IJK)IJKS. 4 TOP_OF (IJK)IJKT. 4 WALL_AT (IJK)determine whether the cell IJK is a wall cell. 4 WEST_OF (IJK)IJKW. 4 In addition to the above, there are a number of functions in function.inc and several averaging functions in the files fun_avg1.inc and fun_avg2.inc.

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List of Include Files 4 bc.incCommon blocks for boundary condition variables 4 b_force1.incDeclarations for body force functions 4 b_force2.incDefinitions for body force functions 4 constant.incCommon blocks for constants 4 fldvar.incCommon blocks for field variables 4 funits.incAssignment of file unit numbers 4 function.incMiscellaneous statement functions 4 fun_avg1.incDeclarations for averaging functions 4 fun_avg2.incDefinitions for averaging functions 4 geometry.incCommon blocks for geometry variables 4 ic.incCommon blocks for initial condition variables 4 indices.incCommon blocks for cell indices

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List of Include Files 4 is.incCommon blocks for internal surface variables 4 machine.incMachine-dependent constants 4 namelist.incNamelist declarations 4 output.incCommon blocks for output control variables 4 param.incParameter definitions for array dimensions and constants 4 physprop.incCommon blocks for physical property variables 4 run.incCommon blocks for run control variables 4 s_pr1.incDeclarations for solids pressure function 4 s_pr2.incDefinitions for solids pressure function 4 time_cpu.incCommon block for CPU time variables 4 tolerance.incVarious convergence criteria and iteration limits 4 usrnlst.incuser-defined variables and namelist variables

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List of Subroutines 4 calc_drag.fCalculate fluid-solids and solids-solids drag. 4 calc_gamma.fCalculate fluid-solids heat transfer coefficient. 4 calc_mu_g.fCalculate turbulent viscosity for fluid. 4 calc_mu_s.fCalculate granular viscosity for solids. 4 calc_resid.fCalculate residuals. 4 check_data_...fRoutines for error checking. 4 conv_dif_…fRoutines for calculating convection-diffusion terms 4 discretize.fHigher discretization schemes 4 drag_gs.fCalculate fluid-solids drag coefficient. 4 drag_ss.fCalculate solids-solids drag coefficient. 4 eosg.fCalculate fluid density. 4 g_0.fCalculate radial distribution function at contact.

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List of Subroutines 4 get_data.fRead and process input data. 4 iterate.fControl iterative solution. 4 machine.fMachine dependent constants. 4 mfix.fMain program. 4 partial_elim.fDo partial elimination. 4 physical_prop.fCalculate physical properties. 4 read_namelist.fRead namelist variables. 4 rrates.fCalculate reaction rates and heats of reactions. 4 set_bc0.fSet boundary conditions initially. 4 set_bc1.fSet boundary conditions after every time step. 4 set_flags.fSet the cell flags. 4 set_geometry.fSet geometry variables.

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List of Subroutines 4 set_ic.fSet initial conditions. 4 set_index1.fSet the indices for neighboring cells. 4 solve_energy_eq.fSolve energy equations. 4 solve_epp.fSolve volume fraction correction equation. 4 solve_lin_eq.fInterface to linear equation solvers. 4 solve_pp_g.fSolve fluid pressure correction equation. 4 solve_species_eq.fSolve species mass balance equations. 4 solve_vel_star.fSolve momentum equations. 4 source_….fRoutines for calculating source terms. 4 time_march.fControl marching in time.

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