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4687 lines (4685 loc) · 161 KB
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C=====================================================================
C CA-DENDRITIC MICROSTRUCTURES
C Two-Dimensional Cellular Automaton Model for Primary Dendritic
C Solidification in Binary Alloys
C
C Copyright (c) 2026 David R. Johnson
C Licensed under the MIT License (see LICENSE file for details)
C
C Compile:
C gfortran -O3 -Wall -Wextra -o CAsim <source>.f
C
C Note:
C This code is intended for teaching, experimentation, and
C preservation of a legacy cellular automaton solidification model.
C It is not a validated solidification simulation package.
C=====================================================================
C OVERVIEW
C --------
C This program implements a 2-D cellular automaton (CA) model for
C primary dendritic solidification in binary alloys.
C
C Scope:
C Primary solidification using an effective binary alloy.
C Multicomponent alloys may be approximated using an effective
C binary description of the primary solidification path.
C
C Full mushy-zone evolution and multiphase reactions are outside the
C intended model scope. The model is intended to generate
C mass-balanced primary microstructure states that may be used as
C starting points for subsequent higher-fidelity simulations.
C
C Main features:
C - Explicit liquid-phase solute diffusion on the CA grid
C - Local equilibrium partitioning during interface solidification
C - 4-fold anisotropic growth through orientation-based weighting
C - Analytical tip-scale guidance from KGT/marginal stability models
C - Macro-scale thermal histories coupled to local thermal analysis
C
C APPROACH
C --------
C The CA grid resolves evolving morphology and liquid-phase transport,
C while unresolved dendrite-tip physics is supplied analytically
C through the KGT/marginal-stability framework.
C
C Interface growth couples these two descriptions through:
C - Local equilibrium partitioning
C - Orientation-dependent capture rules
C - Staged solute release from unresolved local reservoirs
C
C INPUT & OUTPUT WORKFLOW
C -----------------------
C Input files:
C xparam.txt : simulation parameters
C xgrid.txt : starting CA grid
C xthermal.csv : imposed macro thermal history
C Output files:
C data.csv : runtime diagnostics
C grid.txt : final CA grid state
C outN.ppm : optional PPM movie frames
C
C BOUNDARY CONDITIONS
C -------------------
C IBCTYPE = 0 : closed X, closed Y
C IBCTYPE = 1 : periodic X, closed Y (default)
C IBCTYPE = 2 : closed X, periodic Y
C IBCTYPE = 3 : periodic X, periodic Y
C
C THERMAL INPUT
C -------------
C The macro-thermal field is read from THFIL, normally xthermal.csv,
C by LOADTHERMCSV().
C
C IEMBED controls the initial thermal alignment:
C IEMBED = 1: use imposed thermal history directly
C IEMBED = 0: shift imposed thermal history so the initial seed/front
C aligns with TL0 - DTSEED (standalone, default)
C
C NUMERICAL NOTES & CONSTRAINTS
C -----------------------------
C - ZUNITS controls subcell resolution within each CA cell
C - Explicit solute diffusion uses ALPHA = D*DT/DX^2
C - Stability and resolution depend on DCOEFF, VEL, DX, timestep size,
C thermal history, and interface update frequency
C - DFRZ is the local freezing/capture scale used by the interface
C update; it is evaluated internally from the current KGT-based
C tip-scale estimate.
C
C DIAGNOSTICS
C -----------
C - Tip velocity
C - Tip temperature
C - KGT curvature/radius
C - Peclet number
C - Supersaturation comparison (OmegaCA vs OmegaKGT)
C
C REFERENCES & MODEL BASIS
C ------------------------
C Cellular automaton solidification framework
C -------------------------------------------
C Rappaz, M. and Gandin, C.-A.,
C "Probabilistic modelling of microstructure formation in
C solidification processes,"
C Acta Metallurgica et Materialia, 41 (1993) 345-360.
C
C Dendrite growth theory, marginal stability, and KGT routines
C ------------------------------------------------------------
C Kurz, W., Giovanola, B., and Trivedi, R.,
C "Theory of microstructural development during rapid solidification,"
C Acta Metallurgica, 34 (1986) 823-830.
C
C W. Kurz, D.J. Fisher, "Fundamentals of Solidification, 4th Ed.,"
C Trans Tech Publications, 1998, pp. 242-244.
C
C Ivantsov diffusion solution and supersaturation relationships
C --------------------------------------------------------------
C Ivantsov, G.P.,
C "Temperature field around a spherical, cylindrical, and
C needle-shaped crystal growing in a supercooled melt,"
C Doklady Akademii Nauk SSSR, 58 (1947) 567-569.
C
C Walter Gautschi and William F. Cahill, "Exponential Integral and
C Related Functions," in Handbook of Mathematical Functions,
C Milton Abramowitz and I.A. Stegun, eds., Dover Publications
C New York, 1965, pp. 227-254.
C
C Solute trapping & velocity-dependent partition coefficient
C ----------------------------------------------------------
C Aziz, M.J.,
C "Model for solute redistribution during rapid solidification,"
C Journal of Applied Physics, 53 (1982) 1158-1168.
C
C Gibbs-Thomson capillarity relation
C ----------------------------------
C Standard Gibbs-Thomson curvature undercooling relation used in
C dendritic solidification theory and KGT marginal-stability models.
C
C Notes
C -----
C Specific routine references are noted directly in the in-line
C comments. Otherwise, the present implementation combines analytical
C dendrite-tip physics, explicit liquid-phase solute diffusion, and
C cellular automaton interface capture/growth logic.
C
C The staged-solute transport and DFRZ update rule used here are part
C of the present CA model.
C
C Fixed code parameters:
C GRID slot names and the CA subcell scale are defined consistently
C throughout the code using PARAMETER constants:
C
C INTEGER LCELLS, LIQUID, SOLID, PHASE, TCELL, CELLDIR
C PARAMETER (LCELLS=1, LIQUID=2, SOLID=3, PHASE=4)
C PARAMETER (TCELL=5, CELLDIR=6)
C
C REAL ZUNITS
C PARAMETER (ZUNITS=1000.0)
C=====================================================================
PROGRAM CADEN
IMPLICIT NONE
C Size limits
INTEGER NXMAX, NYMAX
PARAMETER (NXMAX=1000, NYMAX=1000)
C Sparse-list capacities
C These scale with maximum compiled grid size.
C Active use is normally much smaller and is guarded at runtime.
INTEGER MAXUPD, MAXREJ, MAXTOUCH
PARAMETER (MAXUPD = NXMAX*NYMAX/5)
PARAMETER (MAXREJ = NXMAX*NYMAX/50)
PARAMETER (MAXTOUCH = NXMAX*NYMAX/5)
C Grid slot tags
C Fixed CA & geometry constants
INTEGER BOX2, TOPEDGE
REAL TOL
PARAMETER (BOX2=3, TOPEDGE=60)
PARAMETER (TOL=1.0E-6)
C Boundary-condition type
C 0 = closed X, closed Y
C 1 = periodic X, closed Y current default
C 2 = closed X, periodic Y
C 3 = periodic X, periodic Y
INTEGER IBCTYPE
DATA IBCTYPE/1/
C Main arrays
REAL GRID(NXMAX, NYMAX, 6, 2)
REAL XADD(NXMAX, NYMAX)
REAL XRES(NXMAX, NYMAX)
REAL XRESADD(NXMAX, NYMAX)
REAL XRND(NXMAX, NYMAX)
C Domain size
INTEGER XLEN, YLEN
DATA XLEN/200/, YLEN/400/
C Screen & loop control
INTEGER I, J
INTEGER SCRN, SCUR, SNEW
INTEGER IEMBED
INTEGER DONE
INTEGER NTOK, NPRINTS
DATA IEMBED/0/
DATA DONE/0/
C Boundary & seeding controls
INTEGER WTOP, WBOT, WLEFT, WRIGHT
DATA WTOP/1/, WBOT/1/, WLEFT/1/, WRIGHT/1/
C I/O control
INTEGER IUNIT, DSPNUM, ISTOPMODE
CHARACTER*128 PARFIL, GRIDFIL
PARAMETER (IUNIT=21, DSPNUM=200)
LOGICAL MOVIE
DATA MOVIE /.TRUE./
C Counters
INTEGER GCOUNT1, GCOUNT2
INTEGER GINCFRZ, GINCPRI, GINCEUT
INTEGER ECOUNT, NGROW
C Tip & live diagnostic variables
INTEGER TIPX, TIPY, OTIPY
REAL VELMEAS, CURVKGT
REAL OTIME, TTIP
REAL TSTART
REAL GTIME, DEUTE
DATA OTIPY/0/
DATA GTIME/0.0/
DATA OTIME/0.25/
C Runtime control & closure parameters
REAL DFRZ, DTSEED
REAL DTAD
REAL FIN, FIN2
LOGICAL CASTOP
DATA DFRZ/150.0/, DTSEED/1.0/
DATA DTAD/10.0/
DATA FIN/10.0/
C Transport & growth parameters
REAL DCOEFF, DT, DX
REAL GRAD, VEL
REAL DMASK
REAL DEFF, DALPHA
DATA DCOEFF/1.0E-9/, DT/1.0E-4/, DX/1.0E-6/
DATA GRAD/0.015/, VEL/200.0/
DATA DMASK/0.60/
C Phase diagram & alloy system
REAL TMP, MLIQ, KALPHA
REAL C0, CEUT, TL0, TEUT
REAL TLIQBIN
EXTERNAL TLIQBIN
DATA TMP/327.502/, MLIQ/-2.326/, KALPHA/0.296/
DATA C0/8.0/, CEUT/61.9/
C Capillarity / anisotropy / orientation
REAL THETA1, THETA2, FR, GKGT0, VV
REAL GIBT, DD, SPARE
DATA THETA1/1.04720/, THETA2/1.39626/
DATA GIBT/2.0E-7/, DD/0.05/, SPARE/1.0/
C Sparse work arrays
INTEGER IUPD(MAXUPD), JUPD(MAXUPD)
INTEGER IREJ(MAXREJ), JREJ(MAXREJ)
INTEGER ITCH(MAXTOUCH), JITCH(MAXTOUCH)
C Thermal terms
REAL QLAT(NXMAX, NYMAX)
REAL ATHERM, LHEAT, CPHEAT
DATA ATHERM/2.5E-9/, LHEAT/1.0E4/, CPHEAT/5.0E2/
C Imposed macro thermal-history table
INTEGER MAXTHERM, NTHERM
PARAMETER (MAXTHERM=20000)
REAL TTAB(MAXTHERM), TREFTAB(MAXTHERM), GTAB(MAXTHERM)
REAL RTAB(MAXTHERM), VTAB(MAXTHERM)
CHARACTER*128 THFIL
INTEGER JREFTH
REAL TSHIFT
C -------------------------------------------------------------------
C Batch input file and I/O preference
C -------------------------------------------------------------------
PARFIL = 'xparam.txt'
GRIDFIL = 'xgrid.txt'
THFIL = 'xthermal.csv'
WRITE(*,*) 'Dendritic CA simulation'
WRITE(*,*)
WRITE(*,*) 'Enter solidification parameter file:'
READ(*,*) PARFIL
WRITE(*,*)
WRITE(*,*) 'Stop control:'
WRITE(*,*) '1=time, 2=dendrite at top, 3=whichever occurs first'
READ (*,*) ISTOPMODE
WRITE(*,*)
WRITE(*,*) 'Make movie? 1=yes, 0=no'
READ (*,*) I
MOVIE = .FALSE.
IF (I.EQ.1) MOVIE = .TRUE.
C-------------------------------------------------------------------
C Initialize CA update screens
C-------------------------------------------------------------------
SCRN = 1
SNEW = 3 - SCRN
SCUR = SCRN
C -------------------------------------------------------------------
C Open CSV output and write header
C--------------------------------------------------------------------
OPEN(UNIT=IUNIT, FILE='data.csv', STATUS='UNKNOWN',
& FORM='FORMATTED')
CALL CSVHEAD(IUNIT)
C -------------------------------------------------------------------
C Load parameters from CAparam.txt
C -------------------------------------------------------------------
CALL LOADCA(PARFIL, PARFIL, GRIDFIL, THFIL,
& TMP, MLIQ, KALPHA, C0, CEUT, GIBT,
& DD, DCOEFF, DT, DX, FIN, GRAD, VEL, SPARE,
& THETA1, THETA2, DTSEED, DMASK, DTAD,
& XLEN, YLEN, ATHERM, LHEAT, IEMBED, IBCTYPE, CPHEAT)
IF (XLEN .GT. NXMAX .OR. YLEN .GT. NYMAX) THEN
WRITE(*,*) 'ERROR: Requested grid size exceeds limits!'
STOP
ENDIF
C -------------------------------------------------------------------
C Update derived quantities after file load
C -------------------------------------------------------------------
NTHERM = 0
JREFTH = 1
TSHIFT = 0.0
CALL LOADTHERMCSV(THFIL,TTAB,TREFTAB,GTAB,RTAB,VTAB,
& MAXTHERM,NTHERM)
TL0 = TLIQBIN(C0,TMP,MLIQ,0.0)
TEUT = TLIQBIN(CEUT,TMP,MLIQ,0.0)
TSTART = TL0 - DTSEED
VV = VEL*DX
GKGT0 = GRAD/DX
FR = TL0 - TEUT
DEFF = DCOEFF/2.0
DALPHA = DCOEFF*DT/(DX*DX)
FIN2 = FIN
C --------------------------------------------------------------------
C Stage A: load prepared starting GRID from xgrid.txt
C --------------------------------------------------------------------
CALL GETGRID(GRID, XLEN, YLEN, GRIDFIL)
C The loaded grid may contain an old thermal field from setup.
C Reset TCELL to the imposed macro field at t=0 so that the initial
C perturbation is zero. Otherwise the first HEATPERT2D call would
C interpret the old TCELL field as a huge latent-heat perturbation.
CALL INITTHERMCSV(GRID, XLEN, YLEN, SCRN, SNEW, DX,
& GRAD, VEL, TTAB, TREFTAB, GTAB, RTAB, VTAB, NTHERM,
& IEMBED, TL0, DTSEED, JREFTH, TSHIFT)
C --------------------------------------------------------------------
C Initialize counters and runtime variables
C --------------------------------------------------------------------
CASTOP = .FALSE.
GTIME = 0.0
ECOUNT = 0
GCOUNT1 = 0
GCOUNT2 = 0
NGROW = 0
DONE = 0
C --------------------------------------------------------------------
C Initialize diagnostic counters and accumulators
C --------------------------------------------------------------------
NTOK = 0
NPRINTS = 0
GINCFRZ = 0
GINCPRI = 0
GINCEUT = 0
DEUTE = 0.0
C --------------------------------------------------------------------
C Initialize thermal analysis variables
C --------------------------------------------------------------------
DO J=1,YLEN
DO I=1,XLEN
XRES(I,J) = 0.0
XADD(I,J) = 0.0
XRESADD(I,J) = 0.0
XRND(I,J) = 0.0
QLAT(I,J) = 0.0
ENDDO
ENDDO
C --------------------------------------------------------------------
C Main CA simulation loop
C --------------------------------------------------------------------
IF (.NOT. CASTOP) THEN
CALL CALOOP(
C State arrays
& GRID, XADD, XRES, XRESADD, XRND, QLAT,
C Domain size
& XLEN, YLEN,
C Screen state
& SCRN,
C Time and grid scales
& GTIME, FIN, DT, DX, TOL,
C Runtime control and output
& IUNIT, DSPNUM,
C Transport and thermal driving
& VEL, GRAD,
& DCOEFF, DMASK, DALPHA,
& ATHERM, LHEAT, CPHEAT,
& TTAB, TREFTAB, GTAB, RTAB, VTAB, NTHERM,
& JREFTH, TSHIFT,
C Interface / capillarity / closure
& DD, GIBT, DFRZ, DTSEED,
C Phase diagram / alloy parameters
& TEUT, TL0, MLIQ, KALPHA, C0, CEUT,
C KGT and box-scale diagnostics
& CURVKGT,
& BOX2, TOPEDGE,
C Tip tracking / time history
& OTIPY, OTIME, TTIP,
C Counters and run statistics
& GCOUNT1, GCOUNT2, ECOUNT, NGROW,
& GINCFRZ, GINCPRI, GINCEUT,
& DEUTE, DONE,
C Measured outputs
& VELMEAS, TIPX, TIPY,
C Sparse work lists
& IUPD, JUPD, MAXUPD,
& IREJ, JREJ, MAXREJ,
& ITCH, JITCH, MAXTOUCH, IBCTYPE,
C Stop flag
& MOVIE, CASTOP, ISTOPMODE)
ENDIF
C Save at least one ppm-image of the CA run.
CALL MOVPPM(GRID, XLEN, YLEN, SCRN, C0, CEUT)
C --------------------------------------------------------------------
C Finalize run and write output files
C --------------------------------------------------------------------
CLOSE(IUNIT)
CALL DOTABLE(GRID, SCRN, XLEN, YLEN)
WRITE(*,*)
WRITE(*,*) ' --Finished--'
WRITE(*,*) ' Parameters used: ', PARFIL
WRITE(*,*) ' Starting grid: ', GRIDFIL
WRITE(*,*) ' Runtime data: data.csv'
WRITE(*,*) ' Final grid: grid.txt'
WRITE(*,*) ' Bitmap image: out#.ppm'
WRITE(*,*)
IF (MOVIE) THEN
WRITE(*,*) 'Possible command for movie scripting:'
WRITE(*,*) 'ffmpeg -framerate 20 -i out%d.ppm movie.mp4'
ENDIF
END
C
C=====================================================================
C CALOOP == Main CA time-stepping loop
C=====================================================================
SUBROUTINE CALOOP(
& GRID, XADD, XRES, XRESADD, XRND, QLAT,
& XLEN, YLEN,
& SCRN,
& GTIME, FIN, DT, DX, TOL,
& IUNIT, DSPNUM,
& VEL, GRAD,
& DCOEFF, DMASK, DALPHA,
& ATHERM, LHEAT, CPHEAT,
& TTAB, TREFTAB, GTAB, RTAB, VTAB, NTHERM,
& JREFTH, TSHIFT,
& DD, GIBT, DFRZ, DTSEED,
& TEUT, TL0, MLIQ, KALPHA, C0, CEUT,
& CURVKGT,
& BOX2, TOPEDGE,
& OTIPY, OTIME, TTIP,
& GCOUNT1, GCOUNT2, ECOUNT, NGROW,
& GINCFRZ, GINCPRI, GINCEUT,
& DEUTE, DONE,
& VELMEAS, TIPX, TIPY,
& IUPD, JUPD, MAXUPD,
& IREJ, JREJ, MAXREJ,
& ITCH, JITCH, MAXTOUCH, IBCTYPE,
& MOVIE, CASTOP, ISTOPMODE)
IMPLICIT NONE
C Parameters
INTEGER NXMAX, NYMAX, LENBOX, IBCTYPE
PARAMETER (NXMAX=1000, NYMAX=1000)
PARAMETER (LENBOX=7)
C Arrays
REAL GRID(NXMAX,NYMAX,6,2)
REAL XADD(NXMAX,NYMAX)
REAL XRES(NXMAX,NYMAX)
REAL XRESADD(NXMAX,NYMAX)
REAL XRND(NXMAX,NYMAX)
REAL QLAT(NXMAX,NYMAX)
C Scalars
INTEGER XLEN,YLEN
INTEGER SCRN,IUNIT,DSPNUM
REAL GTIME,FIN,DT,DX,TOL
REAL VEL,GRAD,DCOEFF,DMASK,DALPHA
REAL ATHERM, LHEAT, CPHEAT
INTEGER NTHERM, JREFTH
REAL TTAB(*), TREFTAB(*), GTAB(*), RTAB(*), VTAB(*)
REAL TSHIFT
REAL DD,GIBT,DFRZ,DTSEED
REAL TEUT,TL0,MLIQ,KALPHA,C0, CEUT
REAL CURVKGT
INTEGER BOX2,TOPEDGE
INTEGER OTIPY
REAL OTIME,TTIP
INTEGER GCOUNT1,GCOUNT2,ECOUNT,NGROW
INTEGER GINCFRZ,GINCPRI,GINCEUT
REAL DEUTE
INTEGER DONE, ISTOPMODE
REAL VELMEAS
INTEGER TIPX,TIPY
INTEGER MAXUPD,MAXREJ,MAXTOUCH
INTEGER IUPD(MAXUPD),JUPD(MAXUPD)
INTEGER IREJ(MAXREJ),JREJ(MAXREJ)
INTEGER ITCH(MAXTOUCH),JITCH(MAXTOUCH)
LOGICAL MOVIE, CASTOP
C Locals
INTEGER I,J,NREJ,NTOUCH,NSTAGEBOX
INTEGER OTIPX,ITIPLOAD
INTEGER ISTAGEBOX(64),JSTAGEBOX(64),IFRZSTAGE(64)
LOGICAL HAVETIP,VINIT,EINIT,CINIT,UINIT
DOUBLE PRECISION MASSBAL,M0
REAL OEMATIME,CTAVG,UNCLAVG
REAL DTBEST,TLBEST
REAL VELAVG,VKGTMS,GGKGTUSE
REAL GX,GY
REAL GTXTIP,GTYTIP,GGTIP
REAL DT2KGT,VV,GKGT,RTIP,PE,IVR,DELT0
REAL DFRZKGT,DFRZMS,PHIKGT,RHOTIP
REAL VDTRAP,KEQ,KPART
REAL TLX,TLY,TLGX,TLGY,TLCLTIP,TLLDIF,TLWID,TLLEN
REAL TOTDEUTE,MAXFRATE,MTDIFF
INTEGER TOTFRZ,TOTPRI,TOTEUT
C External
REAL KPARTBIN
EXTERNAL MASSBAL,KPARTBIN
C Initialization
M0 = MASSBAL(GRID, XADD,XRES,XRND,XLEN,YLEN,SCRN,CASTOP)
DO J=1,YLEN
DO I=1,XLEN
XADD(I,J)=0.0
XRESADD(I,J)=0.0
ENDDO
ENDDO
TIPX=1
TIPY=1
OTIPX=TIPX
OTIPY=TIPY
OTIME=GTIME
TTIP=TL0-DTSEED
VELMEAS=0.0
VELAVG=0.0
VKGTMS=0.0
GGKGTUSE=0.0
GX=0.0
GY=1.0
VINIT=.FALSE.
HAVETIP=.FALSE.
OEMATIME=0.0
CTAVG=0.0
UNCLAVG=0.0
EINIT=.FALSE.
CINIT=.FALSE.
UINIT=.FALSE.
DTBEST=1.0E30
TLBEST=-1.0E30
DT2KGT=DTSEED
VV=0.0
GKGT=0.0
RTIP=0.0
PE=0.0
IVR=0.0
DELT0=0.0
DFRZKGT=0.0
DFRZMS=DFRZ
PHIKGT=1.0
RHOTIP=0.0
VDTRAP=1.0E-2
KEQ=KALPHA
TLX=0.0
TLY=0.0
TLGX=0.0
TLGY=1.0
GTXTIP=0.0
GTYTIP=1.0
GGTIP=ABS(GRAD)/DX
TLCLTIP=C0
TLLDIF=0.0
TLWID=0.0
TLLEN=0.0
ITIPLOAD=0
DEUTE=0.0
MTDIFF=0.0
IF (DALPHA > 0.25) THEN
WRITE(*,*) 'Error: DALPHA > 0.25; stability issues!'
CASTOP = .TRUE.
ENDIF
CALL FNDTDR(GRID,XLEN,YLEN,SCRN,GX,GY,TIPX,TIPY,HAVETIP)
IF (.NOT. HAVETIP) THEN
TIPX = XLEN/2
TIPY = 1
ENDIF
CALL DIAGINIT(TOTFRZ,TOTPRI,TOTEUT,TOTDEUTE,MAXFRATE)
C=====================================================================
C Runtime loop
C=====================================================================
IF (.NOT. CASTOP) THEN
DO WHILE (.NOT. CASTOP)
C Runtime advance
C -------------------------
CALL STEPINC(GTIME,DT,ECOUNT,GCOUNT1,GCOUNT2,NREJ)
C -------------------------
C Block A: transport
C Energy transport is updated first.
C -------------------------
CALL HEATPERT2D(GRID,QLAT,XLEN,YLEN,SCRN,
& DT,DX,ATHERM,GTIME,VEL,GRAD,
& TTAB,TREFTAB,GTAB,RTAB,VTAB,NTHERM,
& JREFTH,TSHIFT)
C Solute transport follows the thermal update.
CALL DIFFUSE(GRID,XLEN,YLEN,SCRN,DALPHA,DMASK, IBCTYPE)
C ----------------------------------
C Block B: runtime interface state
C ----------------------------------
CALL XRUNSTATE(VEL,GRAD,DX,DCOEFF,DT,
& GIBT,MLIQ,KALPHA,C0,
& DT2KGT,VV,GKGT,RTIP,CURVKGT,PE,IVR,DELT0,
& DFRZKGT,DFRZMS,PHIKGT,RHOTIP,DFRZ)
KEQ = KPARTBIN(TLCLTIP,TTIP,TL0,MLIQ,KALPHA,C0)
CALL XKPARTRUN(VV,KEQ,VDTRAP,KPART)
C Select scan-band mode from the current geometric tip direction.
C FNDTDR locates the active tip; the tip's stored CELLDIR selects
C vertical, horizontal, or rectangular banding for XSTAGE.
CALL DTINFC(GRID,XLEN,YLEN,SCRN)
C -----------------------------------------------------------
C Block C: dendrite growth. Note the two separate variables:
C - DFRZKGT controls how much solid is staged at the tip
C - DFRZ controls when remaining liquid is flushed outward
C-------------------------------------------------------------
CALL XTIPBLD(GRID,XLEN,YLEN,SCRN,BOX2,
& TIPX,TIPY,TTIP,
& MLIQ,TL0,C0, IBCTYPE,
& DFRZKGT,64,NSTAGEBOX,ISTAGEBOX,JSTAGEBOX,
& IFRZSTAGE,3)
C --
C Current leading-tip thermal-gradient state for local KGT use.
C This is kept separate from the diagnostic XDIAGTIP cadence.
CALL TIPGRAD(GRID,XLEN,YLEN,SCRN,TIPX,TIPY,DX,
& GTXTIP,GTYTIP,GGTIP)
C --
CALL XGROW(GRID,XADD,XRES,XRND,QLAT,XLEN,YLEN,
& SCRN,BOX2,TOL,TEUT,TL0,MLIQ,KPART,C0,
& GIBT,DD,DFRZ,CURVKGT,LHEAT,CPHEAT,
& VEL,GRAD,DX,DCOEFF,DT,
& GINCFRZ,GINCPRI,GINCEUT,
& DTBEST,TLBEST,TIPX,TIPY,HAVETIP,TTIP,
& TLX,TLY,TLGX,TLGY,
& GTXTIP,GTYTIP,GGTIP,
& TLCLTIP,TLLDIF,TLWID,TLLEN,
& ITIPLOAD,
& NSTAGEBOX,ISTAGEBOX,JSTAGEBOX,IFRZSTAGE,
& IUPD,JUPD,MAXUPD,NGROW,LENBOX, IBCTYPE, CASTOP)
C --------------------------------
C Block D0: staged solute transfer and mass balance
C --------------------------------
CALL CATRANSFER(GRID,XLEN,YLEN,SCRN,
& XADD,XRES,XRESADD,XRND,
& NREJ,IREJ,JREJ,MAXREJ,
& NTOUCH,ITCH,JITCH,MAXTOUCH,
& MLIQ,TL0,C0,
& GCOUNT1,DSPNUM,M0,MTDIFF, IBCTYPE, CASTOP)
C --------------------------------
C Block D: diagnostics and output
C Diagnostic KGT state only
C --------------------------------
IF (MOD(GCOUNT1,DSPNUM).EQ.0) THEN
CALL XDIAGTIP(GRID,XRES,XLEN,YLEN,SCRN,
& GTIME,DT,DX,DSPNUM,
& IUNIT,
& TEUT,TL0,DFRZ,
& OTIPX,OTIPY,OTIME,OEMATIME,EINIT,TTIP,
& VELAVG,VINIT,VKGTMS,GGKGTUSE,
& TIPX,TIPY,DONE,
& CTAVG,UNCLAVG,CINIT,UINIT, IBCTYPE,
& C0,MLIQ,KALPHA,DD,GIBT,DCOEFF,GX,GY)
CALL XUPDATE(GCOUNT1,GINCFRZ,GINCPRI,GINCEUT,
& DEUTE,XLEN,YLEN,MTDIFF,
& TOTFRZ,TOTPRI,TOTEUT,TOTDEUTE,MAXFRATE)
IF (MOVIE) CALL MOVPPM(GRID, XLEN, YLEN, SCRN, C0, CEUT)
ENDIF
C Loop tail
CALL XRESET(GINCFRZ,GINCPRI,GINCEUT,DEUTE)
C Stop control:
C ISTOPMODE = 1 : stop at FIN only
C ISTOPMODE = 2 : stop when dendrite reaches TOPEDGE
C ISTOPMODE = 3 : stop at FIN or TOPEDGE, whichever comes first
IF (ISTOPMODE .EQ. 1) THEN
IF (GTIME .GE. FIN) CASTOP = .TRUE.
ELSE IF (ISTOPMODE .EQ. 2) THEN
CALL XFINISH(TIPY,YLEN,TOPEDGE,GTIME,FIN)
ELSE
IF (GTIME .GE. FIN) CASTOP = .TRUE.
CALL XFINISH(TIPY,YLEN,TOPEDGE,GTIME,FIN)
ENDIF
IF (CASTOP) GTIME = FIN
ENDDO
ENDIF
RETURN
END
C
C=====================================================================
C Binary primary-solidification thermodynamic wrappers
C
C Default model: linear liquidus with constant partition coefficient.
C The CA growth logic should call these routines rather than embedding
C liquidus/solidus equations directly.
C=====================================================================
C Liquidus temperature
REAL FUNCTION TLIQBIN(CL,TREF,MLIQ,CREF)
IMPLICIT NONE
REAL CL,TREF,MLIQ,CREF
TLIQBIN = TREF + MLIQ*(CL - CREF)
RETURN
END
C Liquid composition
REAL FUNCTION CLIQBIN(T,TREF,MLIQ,CREF)
IMPLICIT NONE
REAL T,TREF,MLIQ,CREF
CLIQBIN = CREF
IF (ABS(MLIQ) .GT. 1.0E-12) THEN
CLIQBIN = CREF + (T - TREF)/MLIQ
ENDIF
RETURN
END
C Partition coefficient
REAL FUNCTION KPARTBIN(CL,T,TREF,MLIQ,KALPHA,CREF)
IMPLICIT NONE
REAL CL,T,TREF,MLIQ,KALPHA,CREF
C Current equilibrium model is constant k. The extra arguments are
C retained for later T- or C-dependent thermodynamic partitioning.
KPARTBIN = KALPHA + 0.0*(CL+T+TREF+MLIQ+CREF)
RETURN
END
C Solid composition
REAL FUNCTION CSOLBIN(CL,T,TREF,MLIQ,KALPHA,CREF)
IMPLICIT NONE
REAL CL,T,TREF,MLIQ,KALPHA,CREF
REAL KPARTBIN
EXTERNAL KPARTBIN
CSOLBIN = KPARTBIN(CL,T,TREF,MLIQ,KALPHA,CREF)*CL
RETURN
END
C
C ===============================================================
C LOADCA -- read simulation starting data as named value pairs
C Numeric entries: NAME VALUE
C String/file entries:
C PARFIL filename
C GRIDFIL filename
C THFIL filename
C ===============================================================
SUBROUTINE LOADCA(FNAME, PARFIL, GRIDFIL, THFIL,
& TMP, MLIQ, KALPHA, C0, CEUT, GIBT,
& DD, DCOEFF, DT, DX, FIN, GRAD, VEL, SPARE,
& THETA1, THETA2, DTSEED, DMASK, DTAD, XLEN, YLEN,
& ATHERM, LHEAT, IEMBED, IBCTYPE, CPHEAT)
IMPLICIT NONE
CHARACTER*(*) FNAME, PARFIL, GRIDFIL, THFIL
CHARACTER*128 LINE, NAME, STRVAL
INTEGER IOS, JSTAT, UNIT, XLEN, YLEN, IFOUND, NFOUND
INTEGER IEMBED, IBCTYPE
REAL TMP, MLIQ, KALPHA, C0, CEUT, GIBT
REAL DD, DCOEFF, DT, DX, FIN, GRAD, VEL
REAL THETA1, THETA2, VALUE, DTSEED, SPARE
REAL DMASK, DTAD, ATHERM, LHEAT, CPHEAT
UNIT = 20
NFOUND = 0
OPEN(UNIT=UNIT, FILE=FNAME, STATUS='OLD', IOSTAT=IOS)
IF (IOS .EQ. 0) THEN
READ(UNIT,'(A)',IOSTAT=IOS) LINE
DO WHILE (IOS .EQ. 0)
IF (LINE .NE. ' ') THEN
IF (LINE(1:1) .NE. '#') THEN
IFOUND = 0
C First try numeric named-value input.
READ(LINE,*,IOSTAT=JSTAT) NAME, VALUE
IF (JSTAT .EQ. 0) THEN
CALL SETPARNUM(NAME, VALUE,
& TMP, MLIQ, KALPHA, C0, CEUT, GIBT,
& DD, DCOEFF, DT, DX, FIN,
& GRAD, VEL, THETA1, THETA2, DTSEED, DMASK,
& DTAD, XLEN, YLEN, SPARE,
& ATHERM, LHEAT, CPHEAT,
& IEMBED, IBCTYPE, IFOUND)
ELSE
C If numeric read fails, try string/file input.
READ(LINE,*,IOSTAT=JSTAT) NAME, STRVAL
IF (JSTAT .EQ. 0) THEN
CALL SETPARSTR(NAME, STRVAL,
& PARFIL, GRIDFIL, THFIL, IFOUND)
ENDIF
ENDIF
IF (IFOUND .EQ. 0) THEN
WRITE(*,*) 'LOADCA: unknown name ignored: ',NAME
ELSE
NFOUND = NFOUND + 1
ENDIF
ENDIF
ENDIF
READ(UNIT,'(A)',IOSTAT=IOS) LINE
END DO
CLOSE(UNIT)
WRITE(*,*) 'LOADCA: loaded ', NFOUND,
& ' parameters from ', FNAME
ELSE
WRITE(*,*) 'LOADCA: could not open file ', FNAME
ENDIF
RETURN
END
C
C=====================================================================
C SETPARNUM -- assign one numeric named parameter.
C=====================================================================
SUBROUTINE SETPARNUM(NAME, VALUE,
& TMP, MLIQ, KALPHA, C0, CEUT, GIBT,
& DD, DCOEFF, DT, DX, FIN, GRAD, VEL,
& THETA1, THETA2, DTSEED, DMASK,
& DTAD, XLEN, YLEN, SPARE,
& ATHERM, LHEAT, CPHEAT, IEMBED, IBCTYPE, IFOUND)
IMPLICIT NONE
CHARACTER*(*) NAME
INTEGER XLEN, YLEN, IEMBED, IBCTYPE, IFOUND
REAL VALUE
REAL TMP, MLIQ, KALPHA, C0, CEUT, GIBT
REAL DD, DCOEFF, DT, DX, FIN, GRAD, VEL
REAL THETA1, THETA2, DTSEED, DMASK, DTAD, SPARE
REAL ATHERM, LHEAT, CPHEAT
IFOUND = 1
IF (NAME .EQ. 'TMP') THEN
TMP = VALUE
ELSE IF (NAME .EQ. 'MLIQ') THEN
MLIQ = VALUE
ELSE IF (NAME .EQ. 'KALPHA') THEN
KALPHA = VALUE
ELSE IF (NAME .EQ. 'C0') THEN
C0 = VALUE
ELSE IF (NAME .EQ. 'CEUT') THEN
CEUT = VALUE
ELSE IF (NAME .EQ. 'GIBT') THEN
GIBT = VALUE
ELSE IF (NAME .EQ. 'DD') THEN
DD = VALUE
ELSE IF (NAME .EQ. 'DCOEFF') THEN
DCOEFF = VALUE
ELSE IF (NAME .EQ. 'DT') THEN
DT = VALUE
ELSE IF (NAME .EQ. 'DX') THEN
DX = VALUE
ELSE IF (NAME .EQ. 'FIN') THEN
FIN = VALUE
ELSE IF (NAME .EQ. 'GRAD') THEN
GRAD = VALUE
ELSE IF (NAME .EQ. 'VEL') THEN
VEL = VALUE
ELSE IF (NAME .EQ. 'THETA1') THEN
THETA1 = VALUE
ELSE IF (NAME .EQ. 'THETA2') THEN
THETA2 = VALUE
ELSE IF (NAME .EQ. 'DTSEED') THEN
DTSEED = VALUE
ELSE IF (NAME .EQ. 'DMASK') THEN
DMASK = VALUE
ELSE IF (NAME .EQ. 'DTAD') THEN
DTAD = VALUE
ELSE IF (NAME .EQ. 'XLEN') THEN
XLEN = INT(VALUE)
ELSE IF (NAME .EQ. 'YLEN') THEN
YLEN = INT(VALUE)
ELSE IF (NAME .EQ. 'SPARE') THEN
SPARE = VALUE
ELSE IF (NAME .EQ. 'ATHERM') THEN
ATHERM = VALUE
ELSE IF (NAME .EQ. 'LHEAT') THEN
LHEAT = VALUE
ELSE IF (NAME .EQ. 'CPHEAT') THEN
CPHEAT = VALUE
ELSE IF (NAME .EQ. 'IEMBED') THEN
IEMBED = INT(VALUE)
ELSE IF (NAME .EQ. 'IBCTYPE') THEN
IBCTYPE = INT(VALUE)
ELSE
IFOUND = 0
ENDIF
RETURN
END
C
C=====================================================================
C SETPARSTR -- assign one string/file named parameter.
C=====================================================================
SUBROUTINE SETPARSTR(NAME,STRVAL,PARFIL, GRIDFIL, THFIL, IFOUND)
IMPLICIT NONE
CHARACTER*(*) NAME, STRVAL
CHARACTER*(*) PARFIL, GRIDFIL, THFIL
INTEGER IFOUND
IFOUND = 1
IF (NAME .EQ. 'PARFIL') THEN
PARFIL = STRVAL
ELSE IF (NAME .EQ. 'GRIDFIL') THEN
GRIDFIL = STRVAL
ELSE IF (NAME .EQ. 'THFIL') THEN
THFIL = STRVAL
ELSE
IFOUND = 0
ENDIF
RETURN
END
C
C=====================================================================
C CSVHEAD -- write CSV header
C=====================================================================
SUBROUTINE CSVHEAD(IUNIT)
IMPLICIT NONE
INTEGER IUNIT
WRITE(IUNIT,1000)
1000 FORMAT('time(s),vel(um/s),tipX,tipY,tipT(degC),',
& 'tipCavg(wt%),undercoolavg(degC),',
& 'radiusKGT(um),curvKGT(1/m),theta(rad),DFRZ,',
& 'DTKGT(degC),peclet,Clstar(wt%),OmegaCA,OmegaKGT')
RETURN
END
C
C ====================================================================
C GETGRID -- read the CA grid from a text file
C and load into BOTH screens
C ====================================================================
SUBROUTINE GETGRID(GRID, XLEN, YLEN, FILNAM)
IMPLICIT NONE
INTEGER NXMAX, NYMAX
PARAMETER (NXMAX=1000, NYMAX=1000)
INTEGER XLEN, YLEN
REAL GRID(NXMAX, NYMAX, 6, 2)
CHARACTER FILNAM*128
INTEGER UNIT, IOS, I, J, K, IX, IY
INTEGER LCELLS, LIQUID, SOLID, PHASE, TCELL, CELLDIR
REAL LQCELLS, LCOMP, SCOMP, PHASEV, TEMP, ANGLE
PARAMETER (LCELLS=1, LIQUID=2, SOLID=3, PHASE=4, TCELL=5)
PARAMETER (CELLDIR=6)
CHARACTER LINE*120
LOGICAL ERROR
UNIT = 20
ERROR = .FALSE.
OPEN (UNIT=UNIT, FILE=FILNAM, STATUS='OLD', IOSTAT=IOS)
IF (IOS .EQ. 0) THEN
C Skip the header line
READ (UNIT, '(A)', IOSTAT=IOS) LINE
IF (IOS .NE. 0) THEN
WRITE (*,*) ' *** ERROR reading header in ', FILNAM
ERROR = .TRUE.
ENDIF
C Read the data into BOTH screens (K=1,2)
J = 1
DO WHILE (J .LE. YLEN .AND. .NOT. ERROR)
I = 1
DO WHILE (I .LE. XLEN .AND. .NOT. ERROR)
READ (UNIT, *, IOSTAT=IOS) IX, IY,
& LQCELLS, LCOMP, SCOMP, PHASEV, TEMP, ANGLE
IF (IOS .NE. 0) THEN
WRITE (*,*) ' *** ERROR reading data at I,J =',I,J
ERROR = .TRUE.
ELSE
IF (IX .NE. I .OR. IY .NE. J) THEN
WRITE(*,*) ' *** GETGRID order mismatch: I,J=',I,J,
& ' IX,IY=',IX,IY
ENDIF
C Success: Fill both time-steps (SCUR/SNEW)
DO K = 1, 2
GRID(I,J,LCELLS,K) = LQCELLS
GRID(I,J,LIQUID,K) = LCOMP
GRID(I,J,SOLID,K) = SCOMP
GRID(I,J,PHASE,K) = PHASEV
GRID(I,J,TCELL,K) = TEMP
GRID(I,J,CELLDIR,K) = ANGLE
END DO
ENDIF
I = I + 1
END DO
J = J + 1
END DO
IF (.NOT. ERROR) THEN
WRITE(*,*) 'Successfully loaded grid from ', FILNAM
ENDIF
CLOSE (UNIT)
ELSE
WRITE (*,*) ' *** ERROR opening file ', FILNAM
ENDIF
RETURN
END
C
C ====================================================================
C DOTABLE - Save the full GRID as a text file (grid.txt)
C ====================================================================
SUBROUTINE DOTABLE (GRID,SCRNUM,XLEN,YLEN)
IMPLICIT NONE
INTEGER NXMAX, NYMAX
PARAMETER (NXMAX=1000, NYMAX=1000)
INTEGER SCRNUM, XLEN, YLEN
REAL GRID(NXMAX, NYMAX, 6, 2)
INTEGER LCELLS, LIQUID, SOLID, PHASE, TCELL, CELLDIR
INTEGER I,J,UNIT
CHARACTER*20 FILENAME
PARAMETER (LCELLS=1, LIQUID=2, SOLID=3, PHASE=4, TCELL=5)
PARAMETER (CELLDIR=6)
DATA FILENAME /'grid.txt'/
UNIT = 10
OPEN(UNIT, FILE=FILENAME, STATUS='UNKNOWN')
WRITE(UNIT,'(A)') ' X Y #liqCells Lcomp Scomp Phase Temp Orient'
DO J = 1, YLEN
DO I = 1, XLEN
WRITE(UNIT, '(2I4,3F10.3,2F10.2,F10.4)') I, J,
& GRID(I, J, LCELLS, SCRNUM),