MODFLOW 6  version 6.7.0.dev3
USGS Modular Hydrologic Model
Enumerations | Functions/Subroutines | Variables
gwfconductanceutilsmodule Module Reference

This module contains stateless conductance functions. More...

Enumerations

enum  { ccond_lmean = 1 , ccond_amtlmk = 2 , ccond_amthmk = 3 }
 enumerator that defines the conductance options More...
 

Functions/Subroutines

real(dp) function, public hcond (ibdn, ibdm, ictn, ictm, iupstream, ihc, icellavg, condsat, hn, hm, satn, satm, hkn, hkm, topn, topm, botn, botm, cln, clm, fawidth)
 Horizontal conductance between two cells. More...
 
real(dp) function convertible_upstream (hn, hm, satn, satm, condsat)
 Convertible cell(s) with upstream weighted horizontal conductance. More...
 
real(dp) function convertible_standard (ihc, icellavg, satn, satm, hkn, hkm, topn, topm, botn, botm, cln, clm, fawidth)
 Convertible cell(s) with standard weighted horizontal conductance. More...
 
real(dp) function, public vcond (ibdn, ibdm, ictn, ictm, inewton, ivarcv, idewatcv, condsat, hn, hm, vkn, vkm, satn, satm, topn, topm, botn, botm, flowarea)
 Vertical conductance between two cells. More...
 
real(dp) function, public condmean (k1, k2, thick1, thick2, cl1, cl2, width, iavgmeth)
 Calculate the conductance between two cells. More...
 
real(dp) function logmean (d1, d2)
 Calculate the the logarithmic mean of two double precision numbers. More...
 
real(dp) function, public thksatnm (ibdn, ibdm, ictn, ictm, iupstream, ihc, hn, hm, satn, satm, topn, topm, botn, botm)
 Calculate wetted cell thickness at interface between two cells. More...
 
real(dp) function, public staggered_thkfrac (top, bot, sat, topc, botc)
 Calculate the thickness fraction for staggered grids. More...
 

Variables

@, public ccond_hmean = 0
 Harmonic mean. More...
 

Detailed Description

This module contains the functions to calculate the horizontal and vertical conductance between two cells that are used in the the node property flow (NPF) package. It also contains functions to calculate the wetted cell fraction. This module does not depend on the NPF package.

Enumeration Type Documentation

◆ anonymous enum

anonymous enum
private
Enumerator
ccond_lmean 

Logarithmic mean.

ccond_amtlmk 

Arithmetic-mean thickness and logarithmic-mean hydraulic conductivity.

ccond_amthmk 

Arithmetic-mean thickness and harmonic-mean hydraulic conductivity.

Definition at line 27 of file GwfConductanceUtils.f90.

Function/Subroutine Documentation

◆ condmean()

real(dp) function, public gwfconductanceutilsmodule::condmean ( real(dp), intent(in)  k1,
real(dp), intent(in)  k2,
real(dp), intent(in)  thick1,
real(dp), intent(in)  thick2,
real(dp), intent(in)  cl1,
real(dp), intent(in)  cl2,
real(dp), intent(in)  width,
integer(i4b), intent(in)  iavgmeth 
)
Returns
mean conductance between two cells
Parameters
[in]k1hydraulic conductivity for cell n (in the direction of cell m)
[in]k2hydraulic conductivity for cell m (in the direction of celln)
[in]thick1saturated thickness for cell 1
[in]thick2saturated thickness for cell 2
[in]cl1distance from the center of cell n to the shared face with cell m
[in]cl2distance from the center of cell m to the shared face with cell n
[in]widthwidth of cell perpendicular to flow
[in]iavgmethaveraging method

Definition at line 236 of file GwfConductanceUtils.f90.

237  ! return variable
238  real(DP) :: condmean !< mean conductance between two cells
239  ! dummy
240  real(DP), intent(in) :: k1 !< hydraulic conductivity for cell n (in the direction of cell m)
241  real(DP), intent(in) :: k2 !< hydraulic conductivity for cell m (in the direction of celln)
242  real(DP), intent(in) :: thick1 !< saturated thickness for cell 1
243  real(DP), intent(in) :: thick2 !< saturated thickness for cell 2
244  real(DP), intent(in) :: cl1 !< distance from the center of cell n to the shared face with cell m
245  real(DP), intent(in) :: cl2 !< distance from the center of cell m to the shared face with cell n
246  real(DP), intent(in) :: width !< width of cell perpendicular to flow
247  integer(I4B), intent(in) :: iavgmeth !< averaging method
248  ! local
249  real(DP) :: t1
250  real(DP) :: t2
251  real(DP) :: tmean
252  real(DP) :: kmean
253  real(DP) :: denom
254  !
255  ! Initialize
256  t1 = k1 * thick1
257  t2 = k2 * thick2
258 
259  ! Averaging method
260  select case (iavgmeth)
261 
262  case (ccond_hmean)
263  if (t1 * t2 > dzero) then
264  condmean = width * t1 * t2 / (t1 * cl2 + t2 * cl1)
265  else
266  condmean = dzero
267  end if
268 
269  case (ccond_lmean)
270  if (t1 * t2 > dzero) then
271  tmean = logmean(t1, t2)
272  else
273  tmean = dzero
274  end if
275  condmean = tmean * width / (cl1 + cl2)
276 
277  case (ccond_amtlmk)
278  if (k1 * k2 > dzero) then
279  kmean = logmean(k1, k2)
280  else
281  kmean = dzero
282  end if
283  condmean = kmean * dhalf * (thick1 + thick2) * width / (cl1 + cl2)
284 
285  case (ccond_amthmk)
286  denom = (k1 * cl2 + k2 * cl1)
287  if (denom > dzero) then
288  kmean = k1 * k2 / denom
289  else
290  kmean = dzero
291  end if
292  condmean = kmean * dhalf * (thick1 + thick2) * width
293  end select
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◆ convertible_standard()

real(dp) function gwfconductanceutilsmodule::convertible_standard ( integer(i4b), intent(in)  ihc,
integer(i4b), intent(in)  icellavg,
real(dp), intent(in)  satn,
real(dp), intent(in)  satm,
real(dp), intent(in)  hkn,
real(dp), intent(in)  hkm,
real(dp), intent(in)  topn,
real(dp), intent(in)  topm,
real(dp), intent(in)  botn,
real(dp), intent(in)  botm,
real(dp), intent(in)  cln,
real(dp), intent(in)  clm,
real(dp), intent(in)  fawidth 
)
private
Returns
horizontal conductance between two cells
Parameters
[in]ihcconnection type
[in]icellavgcell averaging option
[in]satncell n wetted cell fraction
[in]satmcell m wetted cell fraction
[in]hknhorizontal hydraulic conductivity for cell n (in the direction of cell m)
[in]hkmhorizontal hydraulic conductivity for cell m (in the direction of cell n)
[in]topntop of cell n
[in]topmtop of cell m
[in]botnbottom of cell n
[in]botmbottom of cell m
[in]clndistance from the center of cell n to the shared face with cell m
[in]clmdistance from the center of cell m to the shared face with cell n
[in]fawidthwidth of cell perpendicular to flow

Definition at line 113 of file GwfConductanceUtils.f90.

116  ! return variable
117  real(DP) :: condnm !< horizontal conductance between two cells
118  ! dummy
119  integer(I4B), intent(in) :: ihc !< connection type
120  integer(I4B), intent(in) :: icellavg !< cell averaging option
121  real(DP), intent(in) :: satn !< cell n wetted cell fraction
122  real(DP), intent(in) :: satm !< cell m wetted cell fraction
123  real(DP), intent(in) :: hkn !< horizontal hydraulic conductivity for cell n (in the direction of cell m)
124  real(DP), intent(in) :: hkm !< horizontal hydraulic conductivity for cell m (in the direction of cell n)
125  real(DP), intent(in) :: topn !< top of cell n
126  real(DP), intent(in) :: topm !< top of cell m
127  real(DP), intent(in) :: botn !< bottom of cell n
128  real(DP), intent(in) :: botm !< bottom of cell m
129  real(DP), intent(in) :: cln !< distance from the center of cell n to the shared face with cell m
130  real(DP), intent(in) :: clm !< distance from the center of cell m to the shared face with cell n
131  real(DP), intent(in) :: fawidth !< width of cell perpendicular to flow
132  ! local
133  real(DP) :: thksatn
134  real(DP) :: thksatm
135 
136  if (ihc == c3d_staggered) then
137  thksatn = staggered_thkfrac(topn, botn, satn, topm, botm)
138  thksatm = staggered_thkfrac(topm, botm, satm, topn, botn)
139  else
140  thksatn = satn * (topn - botn)
141  thksatm = satm * (topm - botm)
142  end if
143  condnm = condmean(hkn, hkm, thksatn, thksatm, cln, clm, &
144  fawidth, icellavg)
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◆ convertible_upstream()

real(dp) function gwfconductanceutilsmodule::convertible_upstream ( real(dp), intent(in)  hn,
real(dp), intent(in)  hm,
real(dp), intent(in)  satn,
real(dp), intent(in)  satm,
real(dp), intent(in)  condsat 
)
private
Returns
horizontal conductance between two cells
Parameters
[in]condsatsaturated conductance
[in]hncell n head
[in]hmcell m head
[in]satncell n wetted cell fraction
[in]satmcell m wetted cell fraction

Definition at line 90 of file GwfConductanceUtils.f90.

92  ! return variable
93  real(DP) :: condnm !< horizontal conductance between two cells
94  ! dummy
95  real(DP), intent(in) :: condsat !< saturated conductance
96  real(DP), intent(in) :: hn !< cell n head
97  real(DP), intent(in) :: hm !< cell m head
98  real(DP), intent(in) :: satn !< cell n wetted cell fraction
99  real(DP), intent(in) :: satm !< cell m wetted cell fraction
100  ! local
101  real(DP) :: sat_up
102 
103  if (hn > hm) then
104  sat_up = satn
105  else
106  sat_up = satm
107  end if
108  condnm = sat_up * condsat
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◆ hcond()

real(dp) function, public gwfconductanceutilsmodule::hcond ( integer(i4b), intent(in)  ibdn,
integer(i4b), intent(in)  ibdm,
integer(i4b), intent(in)  ictn,
integer(i4b), intent(in)  ictm,
integer(i4b), intent(in)  iupstream,
integer(i4b), intent(in)  ihc,
integer(i4b), intent(in)  icellavg,
real(dp), intent(in)  condsat,
real(dp), intent(in)  hn,
real(dp), intent(in)  hm,
real(dp), intent(in)  satn,
real(dp), intent(in)  satm,
real(dp), intent(in)  hkn,
real(dp), intent(in)  hkm,
real(dp), intent(in)  topn,
real(dp), intent(in)  topm,
real(dp), intent(in)  botn,
real(dp), intent(in)  botm,
real(dp), intent(in)  cln,
real(dp), intent(in)  clm,
real(dp), intent(in)  fawidth 
)

This function uses a weighted transmissivity in the harmonic mean conductance calculations. This differs from the MODFLOW-NWT and MODFLOW-USG conductance calculations for the Newton-Raphson formulation which use a weighted hydraulic conductivity.

Returns
horizontal conductance between two cells
Parameters
[in]ibdncell n active flag
[in]ibdmcell m active flag
[in]ictncell n convertible cell flag
[in]ictmcell m convertible cell flag
[in]iupstreamflag for upstream weighting
[in]ihcconnection type
[in]icellavgcell averaging option
[in]condsatsaturated conductance
[in]hncell n head
[in]hmcell m head
[in]satncell n wetted cell fraction
[in]satmcell m wetted cell fraction
[in]hknhorizontal hydraulic conductivity for cell n (in the direction of cell m)
[in]hkmhorizontal hydraulic conductivity for cell m (in the direction of cell n)
[in]topntop of cell n
[in]topmtop of cell m
[in]botnbottom of cell n
[in]botmbottom of cell m
[in]clndistance from the center of cell n to the shared face with cell m
[in]clmdistance from the center of cell m to the shared face with cell n
[in]fawidthwidth of cell perpendicular to flow

Definition at line 43 of file GwfConductanceUtils.f90.

47  ! return variable
48  real(DP) :: condnm !< horizontal conductance between two cells
49  ! dummy
50  integer(I4B), intent(in) :: ibdn !< cell n active flag
51  integer(I4B), intent(in) :: ibdm !< cell m active flag
52  integer(I4B), intent(in) :: ictn !< cell n convertible cell flag
53  integer(I4B), intent(in) :: ictm !< cell m convertible cell flag
54  integer(I4B), intent(in) :: iupstream !< flag for upstream weighting
55  integer(I4B), intent(in) :: ihc !< connection type
56  integer(I4B), intent(in) :: icellavg !< cell averaging option
57  real(DP), intent(in) :: condsat !< saturated conductance
58  real(DP), intent(in) :: hn !< cell n head
59  real(DP), intent(in) :: hm !< cell m head
60  real(DP), intent(in) :: satn !< cell n wetted cell fraction
61  real(DP), intent(in) :: satm !< cell m wetted cell fraction
62  real(DP), intent(in) :: hkn !< horizontal hydraulic conductivity for cell n (in the direction of cell m)
63  real(DP), intent(in) :: hkm !< horizontal hydraulic conductivity for cell m (in the direction of cell n)
64  real(DP), intent(in) :: topn !< top of cell n
65  real(DP), intent(in) :: topm !< top of cell m
66  real(DP), intent(in) :: botn !< bottom of cell n
67  real(DP), intent(in) :: botm !< bottom of cell m
68  real(DP), intent(in) :: cln !< distance from the center of cell n to the shared face with cell m
69  real(DP), intent(in) :: clm !< distance from the center of cell m to the shared face with cell n
70  real(DP), intent(in) :: fawidth !< width of cell perpendicular to flow
71 
72  ! n or m is inactive
73  if (ibdn == 0 .or. ibdm == 0) then
74  condnm = dzero
75  ! both cells are non-convertible
76  elseif (ictn == 0 .and. ictm == 0) then
77  condnm = condsat
78  else if (iupstream == 1) then
79  condnm = convertible_upstream(hn, hm, satn, satm, condsat)
80  else
81  condnm = convertible_standard(ihc, icellavg, &
82  satn, satm, hkn, hkm, &
83  topn, topm, botn, botm, &
84  cln, clm, fawidth)
85  end if
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◆ logmean()

real(dp) function gwfconductanceutilsmodule::logmean ( real(dp), intent(in)  d1,
real(dp), intent(in)  d2 
)
private

Use an approximation if the ratio is near 1

Returns
logarithmic mean for two number
Parameters
[in]d1first number
[in]d2second number

Definition at line 300 of file GwfConductanceUtils.f90.

301  ! return variable
302  real(DP) :: logmean !< logarithmic mean for two number
303  ! dummy
304  real(DP), intent(in) :: d1 !< first number
305  real(DP), intent(in) :: d2 !< second number
306  ! local
307  real(DP) :: drat
308 
309  drat = d2 / d1
310  if (drat <= dlnlow .or. drat >= dlnhigh) then
311  logmean = (d2 - d1) / log(drat)
312  else
313  logmean = dhalf * (d1 + d2)
314  end if
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◆ staggered_thkfrac()

real(dp) function, public gwfconductanceutilsmodule::staggered_thkfrac ( real(dp)  top,
real(dp)  bot,
real(dp)  sat,
real(dp)  topc,
real(dp)  botc 
)
Returns
staggered thickness fraction for cell
Parameters
toptop of cell
botbottom of cell
satcell saturation
topctop of connected cell
botcbottom of connected cells

Definition at line 385 of file GwfConductanceUtils.f90.

386  ! return variable
387  real(DP) :: res !< staggered thickness fraction for cell
388  ! dummy
389  real(DP) :: top !< top of cell
390  real(DP) :: bot !< bottom of cell
391  real(DP) :: sat !< cell saturation
392  real(DP) :: topc !< top of connected cell
393  real(DP) :: botc !< bottom of connected cells
394  ! local
395  real(DP) :: sill_top
396  real(DP) :: sill_bot
397  real(DP) :: tp
398 
399  sill_top = min(top, topc)
400  sill_bot = max(bot, botc)
401  tp = bot + sat * (top - bot)
402  res = max(min(tp, sill_top) - sill_bot, dzero)
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◆ thksatnm()

real(dp) function, public gwfconductanceutilsmodule::thksatnm ( integer(i4b), intent(in)  ibdn,
integer(i4b), intent(in)  ibdm,
integer(i4b), intent(in)  ictn,
integer(i4b), intent(in)  ictm,
integer(i4b), intent(in)  iupstream,
integer(i4b), intent(in)  ihc,
real(dp), intent(in)  hn,
real(dp), intent(in)  hm,
real(dp), intent(in)  satn,
real(dp), intent(in)  satm,
real(dp), intent(in)  topn,
real(dp), intent(in)  topm,
real(dp), intent(in)  botn,
real(dp), intent(in)  botm 
)
Returns
wetted cell thickness for connection nm
Parameters
[in]ibdncell n active flag
[in]ibdmcell m active flag
[in]ictncell n convertible cell flag
[in]ictmcell m convertible cell flag
[in]iupstreamflag for upstream weighting
[in]ihcconnection type
[in]hncell n head
[in]hmcell m head
[in]satncell n wetted cell fraction
[in]satmcell m wetted cell fraction
[in]topntop of cell n
[in]topmtop of cell m
[in]botnbottom of cell n
[in]botmbottom of cell m

Definition at line 319 of file GwfConductanceUtils.f90.

321  ! return variable
322  real(DP) :: res !< wetted cell thickness for connection nm
323  ! dummy
324  integer(I4B), intent(in) :: ibdn !< cell n active flag
325  integer(I4B), intent(in) :: ibdm !< cell m active flag
326  integer(I4B), intent(in) :: ictn !< cell n convertible cell flag
327  integer(I4B), intent(in) :: ictm !< cell m convertible cell flag
328  integer(I4B), intent(in) :: iupstream !< flag for upstream weighting
329  integer(I4B), intent(in) :: ihc !< connection type
330  real(DP), intent(in) :: hn !< cell n head
331  real(DP), intent(in) :: hm !< cell m head
332  real(DP), intent(in) :: satn !< cell n wetted cell fraction
333  real(DP), intent(in) :: satm !< cell m wetted cell fraction
334  real(DP), intent(in) :: topn !< top of cell n
335  real(DP), intent(in) :: topm !< top of cell m
336  real(DP), intent(in) :: botn !< bottom of cell n
337  real(DP), intent(in) :: botm !< bottom of cell m
338  ! local
339  real(DP) :: thksatn
340  real(DP) :: thksatm
341  real(DP) :: sill_top
342  real(DP) :: sill_bot
343  !
344  ! n or m is inactive
345  if (ibdn == 0 .or. ibdm == 0) then
346  res = dzero
347  !
348  ! both cells are non-convertible
349  elseif (ictn == 0 .and. ictm == 0) then
350  if (ihc == c3d_staggered) then
351  sill_top = min(topn, topm)
352  sill_bot = max(botn, botm)
353 
354  thksatn = max(sill_top - sill_bot, dzero)
355  thksatm = thksatn
356  else
357  thksatn = topn - botn
358  thksatm = topm - botm
359  end if
360  res = dhalf * (thksatn + thksatm)
361  !
362  ! At least one of the cells is convertible
363  elseif (iupstream == 1) then
364  if (hn > hm) then
365  res = satn * (topn - botn)
366  else
367  res = satm * (topm - botm)
368  end if
369  !
370  ! At least one of the cells is convertible and not upstream weighted
371  else
372  if (ihc == c3d_staggered) then
373  thksatn = staggered_thkfrac(topn, botn, satn, topm, botm)
374  thksatm = staggered_thkfrac(topm, botm, satm, topn, botn)
375  else
376  thksatn = satn * (topn - botn)
377  thksatm = satm * (topm - botm)
378  end if
379  res = dhalf * (thksatn + thksatm)
380  end if
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◆ vcond()

real(dp) function, public gwfconductanceutilsmodule::vcond ( integer(i4b), intent(in)  ibdn,
integer(i4b), intent(in)  ibdm,
integer(i4b), intent(in)  ictn,
integer(i4b), intent(in)  ictm,
integer(i4b), intent(in)  inewton,
integer(i4b), intent(in)  ivarcv,
integer(i4b), intent(in)  idewatcv,
real(dp), intent(in)  condsat,
real(dp), intent(in)  hn,
real(dp), intent(in)  hm,
real(dp), intent(in)  vkn,
real(dp), intent(in)  vkm,
real(dp), intent(in)  satn,
real(dp), intent(in)  satm,
real(dp), intent(in)  topn,
real(dp), intent(in)  topm,
real(dp), intent(in)  botn,
real(dp), intent(in)  botm,
real(dp), intent(in)  flowarea 
)
Parameters
[in]ibdncell n active flag
[in]ibdmcell m active flag
[in]ictncell n convertible cell flag
[in]ictmcell m convertible cell flag
[in]inewtonflag for Newton-Raphson formulation
[in]ivarcvvariable vertical conductance flag
[in]idewatcvdewatered vertical conductance flag
[in]condsatsaturated conductance
[in]hncell n head
[in]hmcell m head
[in]vknvertical hydraulic conductivity for cell n (in the direction of cell m)
[in]vkmvertical hydraulic conductivity for cell m (in the direction of cell n)
[in]satncell n wetted cell fraction
[in]satmcell m wetted cell fraction
[in]topntop of cell n
[in]topmtop of cell m
[in]botnbottom of cell n
[in]botmbottom of cell m
[in]flowareaflow area between cell n and m

Definition at line 149 of file GwfConductanceUtils.f90.

152  ! return variable
153  real(DP) :: condnm
154  ! dummy
155  integer(I4B), intent(in) :: ibdn !< cell n active flag
156  integer(I4B), intent(in) :: ibdm !< cell m active flag
157  integer(I4B), intent(in) :: ictn !< cell n convertible cell flag
158  integer(I4B), intent(in) :: ictm !< cell m convertible cell flag
159  integer(I4B), intent(in) :: inewton !< flag for Newton-Raphson formulation
160  integer(I4B), intent(in) :: ivarcv !< variable vertical conductance flag
161  integer(I4B), intent(in) :: idewatcv !< dewatered vertical conductance flag
162  real(DP), intent(in) :: condsat !< saturated conductance
163  real(DP), intent(in) :: hn !< cell n head
164  real(DP), intent(in) :: hm !< cell m head
165  real(DP), intent(in) :: vkn !< vertical hydraulic conductivity for cell n (in the direction of cell m)
166  real(DP), intent(in) :: vkm !< vertical hydraulic conductivity for cell m (in the direction of cell n)
167  real(DP), intent(in) :: satn !< cell n wetted cell fraction
168  real(DP), intent(in) :: satm !< cell m wetted cell fraction
169  real(DP), intent(in) :: topn !< top of cell n
170  real(DP), intent(in) :: topm !< top of cell m
171  real(DP), intent(in) :: botn !< bottom of cell n
172  real(DP), intent(in) :: botm !< bottom of cell m
173  real(DP), intent(in) :: flowarea !< flow area between cell n and m
174  ! local
175  real(DP) :: satntmp
176  real(DP) :: satmtmp
177  real(DP) :: bovk1
178  real(DP) :: bovk2
179  real(DP) :: denom
180  !
181  ! Either n or m is inactive
182  if (ibdn == 0 .or. ibdm == 0) then
183  condnm = dzero
184  !
185  ! constantcv
186  elseif (ivarcv == 0) then
187  condnm = condsat
188  !
189  ! both cells are non-convertible
190  elseif (ictn == 0 .and. ictm == 0) then
191  condnm = condsat
192  !
193  ! both cells are fully saturated
194  elseif (hn >= topn .and. hm >= topm) then
195  condnm = condsat
196  !
197  ! At least one cell is partially saturated, so recalculate vertical
198  ! conductance for this connection
199  ! todo: upstream weighting?
200  else
201  !
202  ! Default is for CV correction (dewatered option); use underlying
203  ! saturation of 1.
204  satntmp = satn
205  satmtmp = satm
206  if (idewatcv == 0) then
207  if (botn > botm) then
208  satmtmp = done
209  else
210  satntmp = done
211  end if
212  else
213  if (botn > botm) then
214  if (satmtmp < done) then
215  satmtmp = dzero
216  end if
217  else
218  if (satntmp < done) then
219  satntmp = dzero
220  end if
221  end if
222  end if
223  bovk1 = satntmp * (topn - botn) * dhalf / vkn
224  bovk2 = satmtmp * (topm - botm) * dhalf / vkm
225  denom = (bovk1 + bovk2)
226  if (denom /= dzero) then
227  condnm = flowarea / denom
228  else
229  condnm = dzero
230  end if
231  end if
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Variable Documentation

◆ ccond_hmean

@, public gwfconductanceutilsmodule::ccond_hmean = 0

Definition at line 28 of file GwfConductanceUtils.f90.

28  ENUMERATOR :: CCOND_HMEAN = 0 !< Harmonic mean