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remesh.f90
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remesh.f90
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subroutine remesh
use arrays
include 'precision.inc'
include 'params.inc'
include 'arrays.inc'
include 'phases.inc'
common /remeshing/ pt(mnz*mnx*2,2,3),barcord(mnz+1,mnx+1,3), &
cold(mnz+1,mnx+1,2),cnew(mnz+1,mnx+1,2),numtr(mnz+1,mnx+1),nzt,nxt
allocatable :: dummy(:,:), cordo(:,:,:), dhnew(:), extnew(:)
allocate(cordo(1:nz,1:nx,1:2))
! Save old mesh for interpolations
cordo = cord
! Create The New grid (cord) using cordo(nz,i,2) for the bottom and cordo(1,i,2) for the surface
call rem_cord(cordo)
! Interpolate accumulated topo change
allocate(dhnew(nx-1), extnew(nx-1))
dhnew(:) = 0
extnew(:) = 0
i2 = 1
! for each new element i
do i = 1, nx-1
! for each old node, starting from i2
do i1 = i2, nx-1
if (cordo(1,i1,1) <= cord(1,i,1)) cycle
if (cordo(1,i1,1) < cord(1,i+1,1)) then
if (i1 /= 1) then
if (cordo(1,i1-1,1) >= cord(1,i,1)) then
dhnew(i) = dhnew(i) + dhacc(i1-1) * (cordo(1,i1,1) - cordo(1,i-1,1))
extnew(i) = extnew(i) + extr_acc(i1-1) * (cordo(1,i1,1) - cordo(1,i-1,1))
else
dhnew(i) = dhnew(i) + dhacc(i1-1) * (cordo(1,i1,1) - cord(1,i,1))
extnew(i) = extnew(i) + extr_acc(i1-1) * (cordo(1,i1,1) - cord(1,i,1))
end if
end if
else
if (i1 /= 1) then
dhnew(i) = dhnew(i) + dhacc(i1-1) * (cord(1,i+1,1) - cordo(1,i1-1,1))
extnew(i) = extnew(i) + extr_acc(i1-1) * (cord(1,i+1,1) - cordo(1,i1-1,1))
end if
i2 = i1
exit
end if
end do
end do
! special treatment for the last new element
i = nx - 1
i1 = i2
if (cordo(1,i1,1) <= cord(1,i,1)) then
dhnew(i) = dhnew(i) + dhacc(i1) * (cord(1,i+1,1) - cord(1,i,1))
extnew(i) = extnew(i) + extr_acc(i1) * (cord(1,i+1,1) - cord(1,i,1))
end if
dhacc(1:nx-1) = dhnew / (cord(1,2:nx,1) - cord(1,1:nx-1,1))
extr_acc(1:nx-1) = extnew / (cord(1,2:nx,1) - cord(1,1:nx-1,1))
deallocate(dhnew, extnew)
! REMESHING FOR ELEMENT-WISE PROPERTIES
! Linear interpolation in baricentric coordinates defined as centers of old mesh
nxt = nx-1
nzt = nz-1
allocate( dummy(nzt,nxt) )
! Old mesh - old-element centers
! New mesh - new-element centers
do i = 1, nx-1
do j = 1, nz-1
cold(j,i,1) = 0.25*( cordo(j,i,1)+cordo(j+1,i,1)+cordo(j,i+1,1)+cordo(j+1,i+1,1) )
cold(j,i,2) = 0.25*( cordo(j,i,2)+cordo(j+1,i,2)+cordo(j,i+1,2)+cordo(j+1,i+1,2) )
cnew(j,i,1) = 0.25*( cord(j,i,1)+cord(j+1,i,1)+cord(j,i+1,1)+cord(j+1,i+1,1) )
cnew(j,i,2) = 0.25*( cord(j,i,2)+cord(j+1,i,2)+cord(j,i+1,2)+cord(j+1,i+1,2) )
enddo
enddo
! Calculate parameters of old-mesh triangles
call rem_trpars
! Baricentric coordinates of new-elements centers
call rem_barcord
! Do interpolations
! Interpolate Stress (in quadralaterals)
do k = 1,4
do l = 1,4
dummy(1:nzt,1:nxt) = stress0(1:nzt,1:nxt,k,l)
call rem_interpolate( dummy )
stress0(1:nzt,1:nxt,k,l) = dummy(1:nzt,1:nxt)
end do
end do
! HOOK
! Remeshing mode 3 - see user_luc.f90
!if( mode_rem .eq. 3 ) call rem_stress_alt()
! Interpolate strains
do k = 1, 3
dummy(1:nzt,1:nxt) = strain(1:nzt,1:nxt,k)
call rem_interpolate( dummy )
strain(1:nzt,1:nxt,k) = dummy(1:nzt,1:nxt)
end do
! plastic strain
dummy(1:nzt,1:nxt) = aps(1:nzt,1:nxt)
call rem_interpolate( dummy )
do i = 1, nxt
do j = 1, nzt
if( dummy(j,i) .ge. 0. ) then
aps(j,i) = dummy(j,i)
else
aps(j,i) = 0.
endif
! write(*,*) i,j,aps(j,i)
end do
end do
! viscosity
dummy(1:nzt,1:nxt) = visn(1:nzt,1:nxt)
call rem_interpolate( dummy )
visn(1:nzt,1:nxt) = dummy(1:nzt,1:nxt)
! phases
! XXX: Assuming material is coming from the left or right boundary
! and is within 3-element distance from the boundary and has the
! same layered structure as the 4th element away from the boundary
idist = 2
if(incoming_left==1) then
aps(1:nz-1, 1:1+idist) = 0.0
do jj = 1, nz-1
if((cord(1,1,2) - 0.5*(cord(jj,1,2)+cord(jj+1,1,2))) > hc1(1)*1e3) exit
enddo
call newphase2marker(1, jj-1, 1, 1+idist, iph_col1(1))
j = jj
do jj = j, nz-1
if((cord(1,1,2) - 0.5*(cord(jj,1,2)+cord(jj+1,1,2))) > hc2(1)*1e3) exit
enddo
call newphase2marker(j, jj-1, 1, 1+idist, iph_col2(1))
j = jj
do jj = j, nz-1
if((cord(1,1,2) - 0.5*(cord(jj,1,2)+cord(jj+1,1,2))) > hc3(1)*1e3) exit
enddo
call newphase2marker(j, jj-1, 1, 1+idist, iph_col3(1))
j = jj
do jj = j, nz-1
if((cord(1,1,2) - 0.5*(cord(jj,1,2)+cord(jj+1,1,2))) > hc4(1)*1e3) exit
enddo
call newphase2marker(j, jj-1, 1, 1+idist, iph_col4(1))
j = jj
call newphase2marker(j, nz-1, 1, 1+idist, iph_col5(1))
endif
if(incoming_right==1) then
aps(1:nz-1, nx-1-idist:nx-1) = 0.0
do jj = 1, nz-1
if((cord(1,nx,2) - 0.5*(cord(jj,nx,2)+cord(jj+1,nx,2))) > hc1(nzone_age)*1e3) exit
enddo
call newphase2marker(1, jj-1, nx-1-idist, nx-1, iph_col1(nzone_age))
j = jj
do jj = j, nz-1
if((cord(1,nx,2) - 0.5*(cord(jj,nx,2)+cord(jj+1,nx,2))) > hc2(nzone_age)*1e3) exit
enddo
call newphase2marker(j, jj-1, nx-1-idist, nx-1, iph_col2(nzone_age))
j = jj
do jj = j, nz-1
if((cord(1,nx,2) - 0.5*(cord(jj,nx,2)+cord(jj+1,nx,2))) > hc3(nzone_age)*1e3) exit
enddo
call newphase2marker(j, jj-1, nx-1-idist, nx-1, iph_col3(nzone_age))
j = jj
do jj = j, nz-1
if((cord(1,nx,2) - 0.5*(cord(jj,nx,2)+cord(jj+1,nx,2))) > hc4(nzone_age)*1e3) exit
enddo
call newphase2marker(j, jj-1, nx-1-idist, nx-1, iph_col4(nzone_age))
j = jj
call newphase2marker(j, nz-1, nx-1-idist, nx-1, iph_col5(nzone_age))
endif
!!$! XXX: the bottom elements must be mantle material, otherwise
!!$! too much deformation can occur(?)
!!$aps(nz-3:nz-1, 1:nx-1) = 0.0
!!$call newphase2marker(nz-3, nz-1, 1, nx-1, kmant1)
! sources
dummy(1:nzt,1:nxt) = source(1:nzt,1:nxt)
call rem_interpolate( dummy )
source(1:nzt,1:nxt) = dummy(1:nzt,1:nxt)
deallocate( dummy )
! REMESHING FOR NODE-WISE PROPERTIES
! Linear interpolation in baricentric coordinates of old mesh
nxt = nx
nzt = nz
allocate( dummy(nzt,nxt) )
! Old mesh - old coordinates points
cold(1:nz,1:nx,1:2) = cordo(1:nz,1:nx,1:2)
temp0(1:nz,1:nx) = temp(1:nz,1:nx)
! New mesh - new coordinates points
cnew(1:nz,1:nx,1:2) = cord(1:nz,1:nx,1:2)
if (iac_rem.eq.1) cold(1:nz,1:nx,1:2) = cnew(1:nz,1:nx,1:2)
! Calculate parameters of triangles of this mesh
call rem_trpars
! Baricentric coordinates of new-elements centers
call rem_barcord
! Do node-wise interpolations
! Velocities (in nodes)
do k = 1, 2
dummy(1:nzt,1:nxt) = vel(1:nzt,1:nxt,k)
call rem_interpolate( dummy )
vel(1:nzt,1:nxt,k) = dummy(1:nzt,1:nxt)
end do
! Temperatures (in nodes)
dummy(1:nzt,1:nxt) = temp(1:nzt,1:nxt)
call rem_interpolate( dummy )
temp(1:nzt,1:nxt) = dummy(1:nzt,1:nxt)
deallocate( dummy )
! Changing the temperature of left-/right- most elements
! in accordance to initial temperature
if(incoming_left==1) call sidewalltemp(1,1+idist)
if(incoming_right==1) call sidewalltemp(nx-idist,nx)
! AFTER INTERPOLATIONS - RECALCULATE SOME DEPENDENT VARIABLES
! Calculation of areas of triangle
call init_areas
!if (iac_rem.eq.1) call init_phase
!if (iac_rem.eq.1) call init_temp
! reinitialize the stress in the 3 middle element if iac_rem 1
if (iac_rem.eq.1) then
do 522 i = iinj-1,iinj+1
rogh = 0.
do 522 j = 1,nz-1
iph = iphase(j,i)
tmpr = 0.25*(temp(j,i)+temp(j+1,i)+temp(j,i+1)+temp(j+1,i+1))
densT = den(iph) * ( 1 - alfa(iph)*tmpr )
dh1 = cord (j,i ,2) - cord (j+1,i ,2)
dh2 = cord (j,i+1,2) - cord (j+1,i+1,2)
dh = 0.5 * (dh1+dh2)
dPT = densT * g * dh
dP = dPT * ( 1 - beta(iph)*rogh ) / ( 1 + beta(iph)/2*dPT )
press = rogh + 0.5*dP
do ii = 1,4
stress0(j,i,1,ii) = -press
stress0(j,i,2,ii) = -press
stress0(j,i,3,ii) = 0.
stress0(j,i,4,ii) = -press
end do
rogh = rogh + dP
aps(j,i) = 0.
do k = 1,3
strain(j,i,k) = 0.
enddo
522 continue
endif
! Distribution of masses in nodes
call rmasses
! 1) Determine Inertial Masses with a given dt_scale (idt_scale=1)
! 2) dt_mech with a given Real Masses (idt_scale = 0)
call dt_mass
! drop the time step to the smallest one
dt = min(dt_elastic, dt_maxwell)
deallocate(cordo)
return
end
!===============================================
! parameters of triangles of a grid
!===============================================
subroutine rem_trpars
include 'precision.inc'
include 'arrays.inc'
common /remeshing/ pt(mnz*mnx*2,2,3),barcord(mnz+1,mnx+1,3), &
cold(mnz+1,mnx+1,2),cnew(mnz+1,mnx+1,2),numtr(mnz+1,mnx+1),nzt,nxt
do i = 1,nxt-1
do j = 1,nzt-1
do k = 1,2
! diagonal / :
! ii=1 ii=2
! 1---3 1
! | / / |
! 2 2---3
if (k.eq.1) then
x1 = cold(j ,i ,1)
x2 = cold(j+1,i ,1)
x3 = cold(j ,i+1,1)
y1 = cold(j ,i ,2)
y2 = cold(j+1,i ,2)
y3 = cold(j ,i+1,2)
else !if (k.eq.2) then
x1 = cold(j ,i+1,1)
x2 = cold(j+1,i ,1)
x3 = cold(j+1,i+1,1)
y1 = cold(j ,i+1,2)
y2 = cold(j+1,i ,2)
y3 = cold(j+1,i+1,2)
endif
det=( (x2*y3-y2*x3) - (x1*y3-y1*x3) + (x1*y2-y1*x2) )
n = 2*( (nzt-1)*(i-1)+j-1 ) + k
!Find the parameters ONLY for 2 vertices
pt(n,1,1)=(x2*y3-y2*x3)/det
pt(n,1,2)=(y2-y3)/det
pt(n,1,3)=(x3-x2)/det
pt(n,2,1)=(x3*y1-y3*x1)/det
pt(n,2,2)=(y3-y1)/det
pt(n,2,3)=(x1-x3)/det
end do
end do
end do
return
end
!===============================================
! baricentric coordinates of new mesh in old triangles
!===============================================
subroutine rem_barcord
include 'precision.inc'
include 'arrays.inc'
common /remeshing/ pt(mnz*mnx*2,2,3),barcord(mnz+1,mnx+1,3), &
cold(mnz+1,mnx+1,2),cnew(mnz+1,mnx+1,2),numtr(mnz+1,mnx+1),nzt,nxt
perr = 1.e-4
do i = 1, nxt
do j = 1, nzt
xx = cnew(j,i,1)
yy = cnew(j,i,2)
amodmin = 1.e+10
numtr(j,i) = 0
do l = 0, max( nxt-1, nzt-1 )
do lt = 1, max(8*l,1)
if( lt .le. 2*l ) then
jo = j - l
io = i + lt-1 - l
elseif( lt .le. 4*l ) then
jo = j + lt-2*l - l - 1
io = i + l
elseif( lt .le. 6*l ) then
jo = j + l
io = i + lt-4*l - l
elseif( lt .le. 8*l ) then
jo = j + lt-6*l - l
io = i - l
else ! only at l=0
jo = j
io = i
endif
if( io.lt.1 .or. io.gt.nxt-1 ) cycle
if( jo.lt.1 .or. jo.gt.nzt-1 ) cycle
do k = 1, 2
n = 2*( (nzt-1)*(io-1)+jo-1 ) + k
a1 = pt(n,1,1) + xx*pt(n,1,2) + yy*pt(n,1,3)
a2 = pt(n,2,1) + xx*pt(n,2,2) + yy*pt(n,2,3)
a3 = 1. - a1 - a2
amod = a1*a1 + a2*a2 + a3*a3
if( amod .lt. amodmin ) then
amodmin = amod
nmin = n
endif
if ( a1.le.-perr .or. a1.ge.(1.0+perr) ) cycle
if ( a2.le.-perr .or. a2.ge.(1.0+perr) ) cycle
if ( a3.le.-perr .or. a3.ge.(1.0+perr) ) cycle
numtr(j,i) = n
barcord(j,i,1) = a1
barcord(j,i,2) = a2
barcord(j,i,3) = a3
goto 10
end do
end do
end do
10 continue
! if a point is outside of the mesh
if( numtr(j,i) .eq. 0 ) then
numtr(j,i) = nmin
numqu = (numtr(j,i) + 1)/2
io = (numqu-1)/(nzt-1) + 1
jo = numqu - (io-1)*(nzt-1)
if( mod(numtr(j,i),2).eq.0 ) then
dist1 = sqrt((xx-cold(jo,io+1,1))**2 + (yy-cold(jo,io+1,2))**2)
dist2 = sqrt((xx-cold(jo+1,io,1))**2 + (yy-cold(jo+1,io,2))**2)
dist3 = sqrt((xx-cold(jo+1,io+1,1))**2 + (yy-cold(jo+1,io+1,2))**2)
else
dist1 = sqrt((xx-cold(jo,io,1))**2 + (yy-cold(jo,io,2))**2)
dist2 = sqrt((xx-cold(jo+1,io,1))**2 + (yy-cold(jo+1,io,2))**2)
dist3 = sqrt((xx-cold(jo,io+1,1))**2 + (yy-cold(jo,io+1,2))**2)
endif
! select two nearest points for interpolation
if( dist1 .gt. dist2 ) then
if( dist2 .gt. dist3 ) then
! 1,2,3
barcord(j,i,1) = 0.
barcord(j,i,2) = 1./dist2/(1./dist2+1./dist3)
barcord(j,i,3) = 1./dist3/(1./dist2+1./dist3)
else
if( dist1 .gt. dist3 ) then
! 1,3,2
barcord(j,i,1) = 0.
barcord(j,i,2) = 1./dist2/(1./dist2+1./dist3)
barcord(j,i,3) = 1./dist3/(1./dist2+1./dist3)
else
! 3,1,2
barcord(j,i,1) = 1./dist1/(1./dist1+1./dist2)
barcord(j,i,2) = 1./dist2/(1./dist1+1./dist2)
barcord(j,i,3) = 0.
endif
endif
else
if( dist3 .gt. dist1 ) then
if( dist2 .gt. dist3 ) then
! 2,3,1
barcord(j,i,1) = 1./dist1/(1./dist1+1./dist3)
barcord(j,i,2) = 0.
barcord(j,i,3) = 1./dist3/(1./dist1+1./dist3)
else
! 3,2,1
barcord(j,i,1) = 1./dist1/(1./dist1+1./dist2)
barcord(j,i,2) = 1./dist2/(1./dist1+1./dist2)
barcord(j,i,3) = 0.
endif
else
! 2,1,3
barcord(j,i,1) = 1./dist1/(1./dist1+1./dist3)
barcord(j,i,2) = 0.
barcord(j,i,3) = 1./dist3/(1./dist1+1./dist3)
endif
endif
endif
end do
end do
return
end
!===============================================
! interpolation
!===============================================
subroutine rem_interpolate( arr )
include 'precision.inc'
include 'arrays.inc'
include 'params.inc'
common /remeshing/ pt(mnz*mnx*2,2,3),barcord(mnz+1,mnx+1,3), &
cold(mnz+1,mnx+1,2),cnew(mnz+1,mnx+1,2),numtr(mnz+1,mnx+1),nzt,nxt
dimension dummy(nzt,nxt),arr(nzt,nxt)
dummy = arr
do i = 1, nxt
do j = 1, nzt
numq = (numtr(j,i)+1) / 2
io = (numq-1)/(nzt-1) + 1
jo = numq - (io-1)*(nzt-1)
! diagonal / :
! kk=1 kk=2
!
! 1---3 1
! | / / |
! 2 2---3
if( mod(numtr(j,i),2).eq.0 ) then
f1 = dummy(jo ,io+1)
f2 = dummy(jo+1,io )
f3 = dummy(jo+1,io+1)
else
f1 = dummy(jo ,io )
f2 = dummy(jo+1,io )
f3 = dummy(jo ,io+1)
endif
arr(j,i) = barcord(j,i,1)*f1 + barcord(j,i,2)*f2 + barcord(j,i,3)*f3
! For the phases make sure that you do not create new phases
! iph_int = 0
! if(iph_int.eq.1) then
! xmax1 = max(int(f1+0.5),int(f2+0.5))
! xmax2 = int(f3+0.5)
! xmax = max(xmax1,xmax2)
! xmin1 = min(int(f1+0.5),int(f2+0.5))
! xmin2 = int(f3+0.5)
! xmin = min(xmin1,xmin2)
! xnorm = abs(xmax -xmin)
! xavr = abs(xmax+xmin)*0.5
! if (xnorm.eq.0.) goto 132
! if(arr(j,i).lt.xavr) then
! xvalnorm = abs((xmin-arr(j,i))/xnorm)
! else
! xvalnorm = abs((xmax-arr(j,i))/xnorm)
! endif
! if (xvalnorm.ge.0.5) arr(j,i) = xmax-xvalnorm
! if (xvalnorm.lt.0.5) arr(j,i) = xmin+xvalnorm
!132 arr(j,i) = xmin
! if(arr(j,i).eq.0.) arr(j,i) = 1.
! endif
end do
end do
return
end