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init.f90
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!> SWiM - a semi-Lagrangian, semi-implicit shallow water model in
!! Cartesian coordiates
!! Copyright (C) 2008-2012 Christian Lerrahn
!!
!! This program is free software: you can redistribute it and/or modify
!! it under the terms of the GNU General Public License as published by
!! the Free Software Foundation, either version 3 of the License, or
!! (at your option) any later version.
!!
!! This program is distributed in the hope that it will be useful,
!! but WITHOUT ANY WARRANTY; without even the implied warranty of
!! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
!! GNU General Public License for more details.
!!
!! You should have received a copy of the GNU General Public License
!! along with this program. If not, see <http://www.gnu.org/licenses/>.
!> init.f90
!> Initialises the grid with height, velocities and orography.
!! If off-centring used, the profile for epsilon_n is set here as well.
module init
use grid
implicit none
contains
!> Initialises the grid.
!> @param testcase Testcase to run (if configured)
subroutine initialise_grid(testcase)
integer :: i
integer :: j
integer :: testcase
! allocate arrays
allocate(x(xdim+2*gc))
allocate(y(ydim+2*gc))
allocate(uold(xdim+2*gc,ydim+2*gc))
allocate(vold(xdim+2*gc,ydim+2*gc))
allocate(phiold(xdim+2*gc,ydim+2*gc))
allocate(u(xdim+2*gc,ydim+2*gc))
allocate(v(xdim+2*gc,ydim+2*gc))
allocate(phi(xdim+2*gc,ydim+2*gc))
allocate(exact(xdim+2*gc,ydim+2*gc))
allocate(unew(xdim+2*gc,ydim+2*gc))
allocate(vnew(xdim+2*gc,ydim+2*gc))
allocate(phinew(xdim+2*gc,ydim+2*gc))
allocate(phioro(xdim+2*gc,ydim+2*gc))
allocate(alpha(xdim+2*gc,ydim+2*gc,2,3))
allocate(epsilon(xdim+2*gc,ydim+2*gc,3))
! initialise the grid
do j = (gc+1),(ydim+gc)
y(j) = real(j-gc-1) * deltay
do i = (gc+1),(xdim+gc)
x(i) = real(i-gc-1) * deltax
! linear advection
if (testcase.eq.2) then ! in x
call linear_horizontal(i,j)
elseif (testcase.eq.3) then ! in y
call linear_vertical(i,j)
elseif (testcase.eq.6) then ! in x and y
call linear_diagonal(i,j)
elseif (testcase.eq.16) then ! rotating Gaussian
call rotating_gaussian(i,j)
elseif (testcase.eq.26) then ! differentially rotating bar
call differentially_rotating_bar(i,j)
elseif ((testcase.ge.30.and.testcase.lt.50).and.&
&(mod(testcase,10).eq.0.or.&
&mod(mod(testcase,10),2).eq.0.or.&
&mod(mod(testcase,10),3).eq.0)) then ! geostrophic motion
call geostrophic_motion(i,j)
else ! default
u(i,j) = 50. ! m/s
v(i,j) = 0. ! m/s
phi(i,j) = 0. ! kg*m^2/s^2
end if
! last time step
phiold(i,j) = phi(i,j)
! off-centring parameter from config file
epsilon(i,j,1) = (alpha1-.5)*2.
epsilon(i,j,2) = (alpha2-.5)*2.
epsilon(i,j,3) = (alpha3-.5)*2.
! set orographic profile
! flat
phioro(i,j) = 0.
! one peak
!phioro(i,j) = phibar/2. * exp(-3.5e-2*(i-3.*xdim/4.-gc+1.)**2. - 2.5e-2*(j-ydim/2.-gc+1.)**2.)
! two peaks
! phioro(i,j) = phibar/2. * (&
! &exp(-3.5e-2*(i-3.*xdim/4.-gc+1.)**2. - 2.5e-2*(j-ydim/2.-gc+1.)**2.) + &
! &exp(-3.5e-2*(i-xdim/2.-gc+1.)**2. - 2.5e-2*(j-ydim/2.-gc+1.)**2.))
! six peaks
!phioro(i,j) = phibar/2. * (&
! &exp(-3.5e-2*(i-3.*xdim/4.-gc+1.)**2. - 2.5e-2*(j-ydim/2.-gc+1.)**2.) + &
! &exp(-3.5e-2*(i-xdim/2.-gc+1.)**2. - 2.5e-2*(j-ydim/2.-gc+1.)**2.) + &
! &exp(-3.5e-2*(i-3.*xdim/4.-gc+1.)**2. - 2.5e-2*(j-3*ydim/4.-gc+1.)**2.) + &
! &exp(-3.5e-2*(i-xdim/2.-gc+1.)**2. - 2.5e-2*(j-3*ydim/4.-gc+1.)**2.) + &
! &exp(-3.5e-2*(i-3.*xdim/4.-gc+1.)**2. - 2.5e-2*(j-ydim/4.-gc+1.)**2.) + &
! &exp(-3.5e-2*(i-xdim/2.-gc+1.)**2. - 2.5e-2*(j-ydim/4.-gc+1.)**2.))
!
! set epsilon(x,y)
! epsilon(i,j,:) = 0.
! epsilon(i,j,3) = exp(-3.5e-3*(i-3.*xdim/4.-gc+1.)**2. - 2.5e-3*(j-ydim/2.-gc+1.)**2.)*0.5
! if (i.le.int(xdim/2.+gc+1)) then
! epsilon(i,j,3) = exp(-3.5e-3*(i-1.*xdim/2.-gc+1.)**2.)*0.5
! elseif (i.ge.int(3.*xdim/4.+gc+1)) then
! epsilon(i,j,3) = exp(-3.5e-3*(i-3.*xdim/4.-gc+1.)**2.)*0.5
! else
! epsilon(i,j,3) = .5
! end if
end do
end do
end subroutine initialise_grid
!> Initialises test case for linear horizonal advection
! (test case 2)
subroutine linear_horizontal(i,j)
integer :: i,j
u(i,j) = 50. ! m/s
v(i,j) = 0. ! m/s
phi(i,j) = .1*phibar*exp(-5.e-3*(i-xdim/2.-gc+1.)**2. - 5.e-4*(j-ydim/2.-gc+1.)**2.)
end subroutine linear_horizontal
!> Initialises test case for linear vertical advection
! (test case 3)
subroutine linear_vertical(i,j)
integer :: i,j
u(i,j) = 0. ! m/s
v(i,j) = 50. ! m/s
phi(i,j) = .1*phibar*exp(-5.e-3*(i-xdim/2.-gc+1.)**2. - 5.e-4*(j-ydim/2.-gc+1.)**2.)
end subroutine linear_vertical
!> Initialises test case for simultaneous linear horizonal and
! vertical advection
! (test case 6)
subroutine linear_diagonal(i,j)
integer :: i,j
u(i,j) = 50. ! m/s
v(i,j) = 50. ! m/s
phi(i,j) = .1*phibar*exp(-5.e-3*(i-xdim/2.-gc+1.)**2. - 5.e-4*(j-ydim/2.-gc+1.)**2.)
end subroutine linear_diagonal
!> Initialises test case for rotating Gaussian (advection test)
! (test case 16)
subroutine rotating_gaussian(i,j)
integer :: i,j,ix,iy
real :: r
ix = i-xdim/2-gc
iy = j-ydim/2-gc
r = sqrt(real(ix)**2.+real(iy)**2.)
if (r.le.(.75*real(min(xdim,ydim)/2))) then
u(i,j) = -1.*real(iy)
elseif (r.lt.real(min(xdim,ydim)/2)) then
u(i,j) = -1.*(1.-r/real(min(xdim,ydim)/2))/(1.-.75)*real(iy)
else
u(i,j) = 0.
end if
if (r.le.(.75*real(min(xdim,ydim)/2))) then
v(i,j) = 1.*real(ix)
elseif (r.lt.real(min(xdim,ydim)/2)) then
v(i,j) = 1.*(1.-r/real(min(xdim,ydim)/2))/(1.-.75)*real(ix)
else
v(i,j) = 0.
end if
phi(i,j) = .1*phibar*exp(-5.e-3*(i-xdim/2.-gc+1.)**2. - 5.e-4*(j-ydim/2.-gc+1.)**2.)
end subroutine rotating_gaussian
!> Initialises test case for differentially rotating bar (advection test)
! (test case 26)
subroutine differentially_rotating_bar(i,j)
integer :: i,j,ix,iy
real :: r
ix = i-xdim/2-gc
iy = j-ydim/2-gc
r = sqrt(real(ix)**2.+real(iy)**2.)
if (r.le.(.75*real(min(xdim,ydim)/2))) then
u(i,j) = -1.*real(iy)
elseif (r.lt.real(min(xdim,ydim)/2)) then
u(i,j) = -1.*(1.-r/real(min(xdim,ydim)/2))/(1.-.75)*real(iy)
else
u(i,j) = 0.
end if
if (r.le.(.75*real(min(xdim,ydim)/2))) then
v(i,j) = 1.*real(ix)
elseif (r.lt.real(min(xdim,ydim)/2)) then
v(i,j) = 1.*(1.-r/real(min(xdim,ydim)/2))/(1.-.75)*real(ix)
else
v(i,j) = 0.
end if
! bar (width is gc)
if (i.gt.(xdim/2+1).and.&
&i.lt.(xdim/2+gc+1)) then
phi(i,j) = 100.
else
phi(i,j) = 1.
end if
end subroutine differentially_rotating_bar
!> Initialises test case for linearised geostrophic motion
! (test cases
! 30 (u and v free), 32 (v free), 33 (u free)
! 40 (u & v initialised, phi free)
! 44 (phi & u initialised, v free), 49 (phi & v initialised, u free)
subroutine geostrophic_motion(i,j)
integer :: i,j
real :: kvec,lvec
kvec = 2.*pi/real(xdim)
lvec = 2.*pi/real(ydim)
if (test.ne.49) then
u(i,j) = 1.e-3*phibar*lvec/(f*deltay)*sin(kvec*real(i-gc-.5)+lvec*real(j-gc))
else
u(i,j) = 0.
end if
if (test.ne.44) then
v(i,j) = -1.e-3*phibar*kvec/(f*deltax)*sin(kvec*real(i-gc)+lvec*real(j-gc-.5))
else
v(i,j) = 0.
end if
if (test.lt.40.or.test.eq.44.or.test.eq.49) then
phi(i,j) = 1.e-3*phibar*cos(kvec*real(i-gc)+lvec*real(j-gc))
else
phi(i,j) = 0.
end if
end subroutine geostrophic_motion
end module init