F90-bgk/0000755000175000017500000000000010452465573011176 5ustar jonasjonasF90-bgk/gpl.txt0000644000175000017500000004313310452465573012525 0ustar jonasjonas GNU GENERAL PUBLIC LICENSE
Version 2, June 1991
Copyright (C) 1989, 1991 Free Software Foundation, Inc.
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F90-bgk/Makefile0000644000175000017500000000236710452465573012646 0ustar jonasjonas# Lattice Boltzmann sample, written in Fortran 90
#
# Copyright (C) 2006 Orestis Malaspinas
# Address: EPFL STI ISE LIN, ME A2 398, 1015 Lausanne, Switzerland
# E-mail: orestis.malaspinas@epfl.ch
#
# 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 2
# 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, write to the Free
# Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
# Boston, MA 02110-1301, USA.
SHELL = /bin/sh
FC = gfortran
default: unsteady
.SUFFIXES: .f90 .o
.f90.o:
$(FC) $(IFORTOPT) $<
OBJunsteady = unsteady.o
# IFORTOPT = -fast -mp1 -inline all -mcpu=itanium -mtune=itanium -c
IFORTOPT = -O3 -ipo -w -c
unsteady: $(OBJunsteady)
$(FC) -ipo -o unsteady $(OBJunsteady)
clean:
/bin/rm -f *.o unsteady *.mod *.dat
all:
make unsteady
F90-bgk/unsteady.f900000644000175000017500000004161510452465573013361 0ustar jonasjonas! Lattice Boltzmann sample, written in Fortran 90
!
! Copyright (C) 2006 Orestis Malaspinas
! Address: EPFL STI ISE LIN, ME A2 398, 1015 Lausanne, Switzerland
! E-mail: orestis.malaspinas@epfl.ch
!
! 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 2
! 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, write to the Free
! Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
! Boston, MA 02110-1301, USA.
! unsteady.f90:
! This example examines an unsteady flow past a cylinder placed in a channel.
! The cylinder is offset somewhat from the center of the flow to make the
! steady-state symmetrical flow unstable. At the inlet and outlet, a Poiseuille
! profile is imposed on the velocity. At Reynolds numbers around 100,
! an unstable periodic pattern is created, the Karman vortex street.
! Note that with the implemented Zou/He boundary condition, you must
! increase the resolution to keep the simulation stable if you increase
! the Reynolds number.
! ========================================================
! Constants that identify different cell-types according
! to the dynamics they implement
! ========================================================
MODULE cellConst
integer, parameter:: fluid = 0, wall = 1, inlet = 10, outlet = 11
END MODULE cellConst
! ========================================================
! Lattice constants for the D2Q9 lattice
! ========================================================
MODULE D2Q9Const
! D2Q9 Weights
double precision,parameter:: t(0:8) = (/4.0d0/9.0d0,1.0d0/9.0d0,1.0d0/9.0d0,1.0d0/9.0d0,1.0d0/9.0d0&
&,1.0d0/36.0d0,1.0d0/36.0d0,1.0d0/36.0d0,1.0d0/36.0d0/)
! D2Q9 Directions
integer:: v(0:8,0:1)
! = (/(/0,1,0,-1,0,1,-1,-1,1/),(/0,0,1,0,-1,1,1,-1,-1/)/)
integer, parameter:: opposite(0:8) = (/0,3,4,1,2,7,8,5,6/)
END MODULE D2Q9Const
! ========================================================
! Constants for simulation setup
! ========================================================
MODULE simParam
integer, parameter:: xDim = 250
integer, parameter:: yDim = 50
integer, parameter:: obstX = xDim/5
integer, parameter:: obstY = yDim/2
integer, parameter:: obstR = yDim/10+1
integer, parameter:: tMax = 1000
double precision, parameter:: uMax = 0.02d0
double precision, parameter:: Re = 10.0d0
END MODULE simParam
! ========================================================
! The main program, implementing a flow past a cylinder
! ========================================================
PROGRAM unsteady
USE simParam, ONLY: xDim, yDim, tMax
implicit none
double precision:: omega, time1, time2, timeTot
double precision, dimension(:,:,:), allocatable:: f, fEq, u
double precision, dimension(:,:), allocatable:: rho, uSqr
integer, dimension(:,:), allocatable:: image
integer:: tStep
allocate(f(yDim,xDim,0:8))
allocate(fEq(yDim,xDim,0:8))
allocate(u(yDim,xDim,0:1))
allocate(uSqr(yDim,xDim))
allocate(rho(yDim,xDim))
allocate(image(yDim,xDim))
CALL constructImage(image)
CALL computeOmega(omega)
CALL writeInput(omega)
CALL initMacro(rho,u,uSqr)
CALL computeFeq(fEq,rho,u,uSqr)
f = fEq
timeTot = 0.0d0
do tStep = 1, tMax
CALL CPU_TIME(time1)
CALL inletOutlet(f,rho,u,image)
CALL boundaries(f,image)
CALL computeMacros(f,rho,u,uSqr)
CALL computeFeq(fEq,rho,u,uSqr)
CALL collide(f,fEq,omega,image)
CALL stream(f)
CALL CPU_TIME(time2)
timeTot = timeTot + (time2-time1)
end do
CALL writeImage(image)
CALL writeOutput(u,0)
write(*,*) dble(tMax) * (dble(yDim * xDim)) / timeTot ,'cells per second'
deallocate(f)
deallocate(fEq)
deallocate(u)
deallocate(uSqr)
deallocate(rho)
deallocate(image)
END PROGRAM unsteady
! ========================================================
! Compute the relaxation parameter from the Reynolds number
! ========================================================
SUBROUTINE computeOmega(omega)
USE simParam, ONLY: Re,uMax,obstR
implicit none
double precision, INTENT(INOUT):: omega
double precision:: nu
nu = uMax * 2.0d0 * dble(obstR) / Re
omega = 1.0d0 / (3.0d0*nu+0.5d0)
END SUBROUTINE computeOmega
! ========================================================
! Construct an array the defines the flow geometry
! ========================================================
SUBROUTINE constructImage(image)
USE cellConst
USE simParam, ONLY: xDim, yDim, obstX, obstY, obstR
USE D2Q9Const, ONLY: v
implicit none
integer, INTENT(INOUT):: image(yDim,xDim)
integer:: x,y
v(0:8,0) = (/0,1,0,-1,0,1,-1,-1,1/)
v(0:8,1) = (/0,0,1,0,-1,1,1,-1,-1/)
image = fluid
image(:,1) = inlet
image(:,xDim) = outlet
image(1,:) = wall
image(yDim,:) = wall
do x = 1, xDim
do y = 1, yDim
if (((x-obstX)**2 + (y-obstY)**2) <= (obstR**2) ) image(y,x) = wall
end do
end do
END SUBROUTINE constructImage
! ========================================================
! Initialize the simulation to Poiseuille profile at
! an equilibrium distribution
! ========================================================
SUBROUTINE initMacro(rho,u,uSqr)
USE simParam, ONLY: xDim, yDim
implicit none
double precision, INTENT(INOUT):: rho(yDim,xDim), u(yDim,xDim,0:1), uSqr(yDim,xDim)
double precision:: uProf
integer:: y
do y = 1, yDim
u(y,:,0) = uProf(y)
u(y,:,1) = 0.0d0
end do
rho = 1.0d0
uSqr = u(:,:,0) * u(:,:,0) + u(:,:,1) * u(:,:,1)
END SUBROUTINE initMacro
! ========================================================
! Compute equilibrium distribution
! ========================================================
SUBROUTINE computeFeq(fEq,rho,u,uSqr)
USE D2Q9COnst, ONLY: t, v
USE simParam, ONLY: xDim, yDim
implicit none
double precision, INTENT(IN):: rho(yDim,xDim), uSqr(yDim,xDim), u(yDim,xDim,0:1)
double precision, INTENT(INOUT):: fEq(yDim,xDim,0:8)
integer:: i, x, y
double precision:: uxy
do i = 0, 8
do x = 1, xDim
do y = 1, yDim
uxy = u(y,x,0) * v(i,0) + u(y,x,1) * v(i,1)
fEq(y,x,i) = t(i) * rho(y,x) * (1.0d0 + 3.0d0 * uxy + 4.5d0 * uxy * uxy - 1.5d0 * uSqr(y,x))
end do
end do
end do
END SUBROUTINE computeFeq
! ========================================================
! Compute density and velocity from distribution functions
! ========================================================
SUBROUTINE computeMacros(f,rho,u,uSqr)
USE simParam, ONLY: xDIm, yDim
implicit none
double precision, INTENT(IN):: f(yDim,xDim,0:8)
double precision, INTENT(INOUT):: u(yDim,xDim,0:1), rho(yDim, xDim), uSqr(yDim, xDim)
integer:: x,y
do x = 1, xDim
do y = 1, yDim
rho(y,x) = f(y,x,0) + f(y,x,1) + f(y,x,2) + f(y,x,3) + f(y,x,4) + f(y,x,5) + f(y,x,6) + f(y,x,7) + f(y,x,8)
u(y,x,0) = (f(y,x,1) - f(y,x,3) + f(y,x,5) - f(y,x,6) - f(y,x,7) + f(y,x,8)) / rho(y,x)
u(y,x,1) = (f(y,x,2) - f(y,x,4) + f(y,x,5) + f(y,x,6) - f(y,x,7) - f(y,x,8)) / rho(y,x)
uSqr(y,x) = u(y,x,0) * u(y,x,0) + u(y,x,1) * u(y,x,1)
end do
end do
END SUBROUTINE computeMacros
! ========================================================
! Implement Bounce-back on upper/lower boundaries
! ========================================================
SUBROUTINE boundaries(f,image)
USE D2Q9Const, ONLY: opposite
USE cellConst, ONLY: wall
USE simParam, ONLY: xDim, yDim
implicit none
integer, INTENT(IN):: image(yDim,xDim)
double precision, INTENT(INOUT):: f(yDim,xDim,0:8)
double precision:: fTmp(0:8)
integer:: i, x, y
do x = 1, xDim
do y = 1, yDim
if (image(y,x) == wall) then
do i = 0, 8
fTmp(i) = f(y,x,opposite(i))
end do
do i = 0, 8
f(y,x,i) = fTmp(i)
end do
end if
end do
end do
END SUBROUTINE boundaries
! ========================================================
! Use Zou/He boundary condition to implement Dirichlet
! boundaries on inlet/outlet
! ========================================================
SUBROUTINE inletOutlet(f,rho,u,image)
USE cellConst, ONLY: inlet, outlet
USE simParam
implicit none
double precision, INTENT(INOUT):: f(yDim,xDim,0:8), u(yDim,xDim,0:1), rho(yDim,xDim)
integer, INTENT(IN):: image(yDim,xDim)
double precision:: uProf
integer:: x, y
do x = 1, xDim
do y = 1, yDim
if (image(y,x) == inlet) then
u(y,x,0) = uProf(y)
u(y,x,1) = 0.0d0
CALL inletZou(f(y,x,:),u(y,x,:),rho(y,x))
else if (image(y,x) == outlet) then
u(y,x,0) = uProf(y)
u(y,x,1) = 0.0d0
CALL outletZou(f(y,x,:),u(y,x,:),rho(y,x))
end if
end do
end do
CONTAINS
! ========================================================
! Zou/He boundary on inlet
! ========================================================
SUBROUTINE inletZou(f,u,rho)
implicit none
double precision, INTENT(INOUT):: f(0:8),rho
double precision, INTENT(IN):: u(0:1)
double precision:: fInt, fInt2
fInt = f(0) + f(2) + f(4)
fInt2 = f(3) + f(6) + f(7)
rho = (fInt + 2.0d0 * fInt2) / (1.0d0 - u(0))
CALL zouWestWall(f,rho,u)
END SUBROUTINE inletZou
SUBROUTINE zouWestWall(f,rho,u)
implicit none
double precision, INTENT(INOUT):: f(0:8)
double precision, INTENT(IN):: rho, u(0:1)
double precision:: fDiff, rhoUx, rhoUy
fDiff = 0.5d0 * (f(2) - f(4))
rhoUx = rho * u(0) / 6.0d0
rhoUy = 0.5d0 * rho * u(1)
f(1) = f(3) + 4.0d0 * rhoUx
f(5) = f(7) - fDiff + rhoUx + rhoUy
f(8) = f(6) + fDiff + rhoUx - rhoUy
END SUBROUTINE zouWestWall
! ========================================================
! Zou/He boundary on outlet
! ========================================================
SUBROUTINE outletZou(f,u,rho)
implicit none
double precision, INTENT(INOUT):: f(0:8),rho,u(0:1)
double precision:: fInt, fInt2
fInt = f(0) + f(2) + f(4)
fInt2 = f(1) + f(8) + f(5)
rho = (fInt + 2.0d0 * fInt2) / (1.0d0 + u(0))
CALL zouEastWall(f,rho,u)
END SUBROUTINE outletZou
SUBROUTINE zouEastWall(f,rho,u)
implicit none
double precision, INTENT(INOUT):: f(0:8)
double precision, INTENT(IN):: rho, u(0:1)
double precision:: fDiff, rhoUx, rhoUy
fDiff = 0.5d0 * (f(2) - f(4))
rhoUx = rho * u(0) / 6.0d0
rhoUy = 0.5d0 * rho * u(1)
f(3) = f(1) - 4.0d0 * rhoUx
f(7) = f(5) + fDiff - rhoUx - rhoUy
f(6) = f(8) - fDiff - rhoUx + rhoUy
END SUBROUTINE zouEastWall
END SUBROUTINE inletOutlet
! ========================================================
! Computation of Poiseuille profile for the inlet/outlet
! ========================================================
FUNCTION uProf(y)
USE simParam, ONLY: yDIm, uMax
implicit none
integer, INTENT(IN):: y
double precision:: radius, uProf
radius = dble(yDim-1) * 0.5d0
uProf = -uMax * ((abs(1 - dble(y-1) / radius))**2 - 1.0d0)
END FUNCTION uProf
! ========================================================
! Streaming step: the population functions are shifted
! one site along their corresponding lattice direction
! (no temporary memory is needed)
! ========================================================
SUBROUTINE stream(f)
USE simParam
implicit none
double precision, INTENT(INOUT):: f(yDim,xDim,0:8)
double precision:: periodicHor(yDim), periodicVert(xDim)
! -------------------------------------
! right direction
periodicHor = f(:,xDim,1)
f(:,2:xDim,1) = f(:,1:xDim-1,1)
f(:,1,1) = periodicHor
! -------------------------------------
! up direction
periodicVert = f(1,:,2)
f(1:yDim-1,:,2) = f(2:yDim,:,2)
f(yDim,:,2) = periodicVert
! -------------------------------------
! left direction
periodicHor = f(:,1,3)
f(:,1:xDim-1,3) = f(:,2:xDim,3)
f(:,xDim,3) = periodicHor
! -------------------------------------
! down direction
periodicVert = f(yDim,:,4)
f(2:yDim,:,4) = f(1:yDim-1,:,4)
f(1,:,4) = periodicVert
! -------------------------------------
! up-right direction
periodicVert = f(1,:,5)
periodicHor = f(:,xDim,5)
f(1:yDim-1,2:xDim,5) = f(2:yDim,1:xDim-1,5)
f(yDim,2:xDim,5) = periodicVert(1:xDim-1)
f(yDim,1,5) = periodicVert(xDim)
f(1:yDim-1,1,5) = periodicHor(2:yDim)
! -------------------------------------
! up-left direction
periodicVert = f(1,:,6)
periodicHor = f(:,1,6)
f(1:yDim-1,1:xDim-1,6) = f(2:yDim,2:xDim,6)
f(yDim,1:xDim-1,6) = periodicVert(2:xDim)
f(yDim,xDim,6) = periodicVert(1)
f(1:yDim-1,xDim,6) = periodicHor(2:yDim)
! -------------------------------------
! down-left direction
periodicVert = f(yDim,:,7)
periodicHor = f(:,1,7)
f(2:yDim,1:xDim-1,7) = f(1:yDim-1,2:xDim,7)
f(1,1:xDim-1,7) = periodicVert(2:xDim)
f(1,xDim,7) = periodicVert(1)
f(2:yDim,xDim,7) = periodicHor(1:yDim-1)
! -------------------------------------
! down-right direction
periodicVert = f(yDim,:,8)
periodicHor = f(:,xDim,8)
f(2:yDim,2:xDim,8) = f(1:yDim-1,1:xDim-1,8)
f(1,2:xDim,8) = periodicVert(1:xDim-1)
f(1,1,8) = periodicVert(xDim)
f(2:yDim,1,8) = periodicHor(1:yDim-1)
END SUBROUTINE stream
! ========================================================
! LBGK collision step
! ========================================================
SUBROUTINE collide(f,fEq,omega,image)
USE simParam, ONLY: xDim, yDim
USE cellConst, ONLY: wall
implicit none
integer, INTENT(IN):: image(yDim,xDim)
double precision, INTENT(IN):: fEq(yDim,xDim,0:8), omega
double precision, INTENT(INOUT):: f(yDim,xDim,0:8)
integer:: x,y,i
do i = 0, 8
do x = 1, xDim
do y = 1, yDim
if (image(y,x) /= wall) f(y,x,i) = (1.0d0 - omega) * f(y,x,i) + omega * feq(y,x,i)
end do
end do
end do
END SUBROUTINE collide
! ========================================================
! Write the components of the velocity to a text file,
! with indices (x,y)
! ========================================================
SUBROUTINE writeOutput(u,tStep)
USE simParam, ONLY: xDim, yDim
implicit none
integer, INTENT(IN):: tStep
double precision, INTENT(IN):: u(yDim,xDim,0:1)
integer:: x,y
character (LEN=100):: fileName
write(fileName,*) tStep
fileName = adjustl(fileName)
open(14,file='outputUx_'//trim(fileName)//'.dat')
open(15,file='outputUy_'//trim(fileName)//'.dat')
do x=1, xDim
do y=1, yDim
write(14,101) x,y,u(y,x,0)
write(15,101) x,y,u(y,x,1)
end do
end do
101 format(2i10,f20.10)
close(14)
close(15)
END SUBROUTINE writeOutput
! ========================================================
! Write the flow geometry to a file
! ========================================================
SUBROUTINE writeImage(image)
USE simParam, ONLY: xDim, yDim
implicit none
integer, INTENT(IN):: image(yDim,xDim)
integer:: x,y
open(13,file='outputImage.dat')
do x=1, xDim
do y=1, yDim
write(13,102) image(y,x)
end do
end do
102 format(3i10)
close(15)
END SUBROUTINE writeImage
! ========================================================
! Print out simulation parameters to screen
! ========================================================
SUBROUTINE writeInput(omega)
USE simParam
implicit none
double precision, INTENT(IN):: omega
write(*,*) 'xDim = ', xDim
write(*,*) 'yDim = ', yDim
write(*,*) 'Obstacle X = ', obstX
write(*,*) 'Obstacle Y = ', obstY
write(*,*) 'Obstacle Radius = ', obstR
write(*,*) 'tMax = ', tMax
write(*,*) 'uMax = ', uMax
write(*,*) 'Re = ', Re
write(*,*) 'omega = ', omega
END SUBROUTINE writeInput