From 96843600122f5a26d970c2fe9034418519e2f7db Mon Sep 17 00:00:00 2001 From: David Cicoria <46363078+DavidCico@users.noreply.github.com> Date: Tue, 15 Jan 2019 12:18:46 +0800 Subject: [PATCH] Add files via upload --- Documents/Program_presentation.pdf | Bin 0 -> 370495 bytes Documents/cavityflow.pdf | Bin 0 -> 547456 bytes Documents/ghia82.pdf | Bin 0 -> 1333628 bytes Documents/steps_recap.txt | 7 + Makefile | 78 ++++++++ boundary_conditions.f90 | 77 +++++++ calcul_2nd_membre.f90 | 30 +++ calcul_new_velocity.f90 | 87 ++++++++ calcul_pressure_field.f90 | 25 +++ coordinates.txt | 122 ++++++++++++ discretisation_centre.f90 | 39 ++++ discretisation_upwind.f90 | 103 ++++++++++ ensight_cavity.f90 | 252 +++++++++++++++++++++++ initial_conditions.f90 | 27 +++ main.f90 | 68 +++++++ matgen_cavity.f90 | 63 ++++++ mesh_creation.f90 | 25 +++ omega_boundary.txt | 11 + reading_data.f90 | 11 + solver.f90 | 310 +++++++++++++++++++++++++++++ timestep.f90 | 34 ++++ u_velocity.txt | 12 ++ v_velocity.txt | 12 ++ variables_module.f90 | 26 +++ velocities_output.f90 | 25 +++ 25 files changed, 1444 insertions(+) create mode 100644 Documents/Program_presentation.pdf create mode 100644 Documents/cavityflow.pdf create mode 100644 Documents/ghia82.pdf create mode 100644 Documents/steps_recap.txt create mode 100644 Makefile create mode 100644 boundary_conditions.f90 create mode 100644 calcul_2nd_membre.f90 create mode 100644 calcul_new_velocity.f90 create mode 100644 calcul_pressure_field.f90 create mode 100644 coordinates.txt create mode 100644 discretisation_centre.f90 create mode 100644 discretisation_upwind.f90 create mode 100644 ensight_cavity.f90 create mode 100644 initial_conditions.f90 create mode 100644 main.f90 create mode 100644 matgen_cavity.f90 create mode 100644 mesh_creation.f90 create mode 100644 omega_boundary.txt create mode 100644 reading_data.f90 create mode 100644 solver.f90 create mode 100644 timestep.f90 create mode 100644 u_velocity.txt create mode 100644 v_velocity.txt 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This is due to the conditions on u_tilde et v_tilde. + +(a,b,c,d) for calculations in x +(e,f,g,h) for calculations in y + diff --git a/Makefile b/Makefile new file mode 100644 index 0000000..7613b7d --- /dev/null +++ b/Makefile @@ -0,0 +1,78 @@ +# Makefile +# Nom du compilateur +FC = gfortran + +# Options de compilation: optimisation, debug etc... +OPT = -fdefault-real-8 -O3 +# nom de l'executable +EXE = NS_lid_driven_cavity +# Options de l'edition de lien.. +LINKOPT = + +# Defining the objects (OBJS) variables + +OBJS = \ + variables_module.o \ + main.o \ + reading_data.o \ + mesh_creation.o \ + initial_conditions.o \ + boundary_conditions.o \ + timestep.o \ + discretisation_upwind.o \ + discretisation_centre.o \ + calcul_2nd_membre.o \ + matgen_cavity.o \ + solver.o \ + calcul_pressure_field.o \ + calcul_new_velocity.o \ + velocities_output.o \ + ensight_cavity.o \ + + + +# Linking object files +exe : $(OBJS) + $(FC) $(LINKOPT) $(OBJS) -o $(EXE) + +%.o:%.f90 + $(FC) $(OPT) -c $< + +main.o : variables_module.o + +reading_data.o : variables_module.o + +mesh_creation.o: variables_module.o + +initial_conditions.o : variables_module.o + +boundary_conditions.o : variables_module.o + +timestep.o : variables_module.o + +discretisation_upwind.o : variables_module.o + +discretisation_centre.o : variables_module.o + +calcul_2nd_membre.o : variables_module.o + +calcul_pressure_field.o : variables_module.o + +calcul_new_velocity.o : variables_module.o + +velocities_output.o : variables_module.o + + + +# Removing object files +clean : + /bin/rm -f $(OBJS) $(EXE) *.mod + +cleanall : + /bin/rm -f $(OBJS) $(EXE) *.mod + /bin/rm -f *.scl + /bin/rm -f *.vec + +config : + if [ ! -d obj ] ; then mkdir obj ; fi + if [ ! -d run ] ; then mkdir run ; fi diff --git a/boundary_conditions.f90 b/boundary_conditions.f90 new file mode 100644 index 0000000..2fd01cf --- /dev/null +++ b/boundary_conditions.f90 @@ -0,0 +1,77 @@ +subroutine boundary_conditions() +use variables +implicit none + + +!---------------------------------------------------! +! Boundary conditions calculation ! +!---------------------------------------------------! + + +!!!!!!!!Velocity boundary conditions!!!!!!!! + +!Left vertical wall +do j=0,ny+1 + u(0,j) = 0 + v(0,j) = -v(1,j) + u1(0,j) = 0 + v1(0,j) = -v1(1,j) + u_star(0,j) = 0 + v_star(0,j) = -v_star(1,j) +end do + +!Right vertical wall +do j=0,ny+1 + u(nx,j) = 0 + v(nx+1,j) = -v(nx,j) + u1(nx,j) = 0 + v1(nx+1,j) = -v1(nx,j) + u_star(nx,j) = 0 + v_star(nx+1,j) = -v_star(nx,j) +end do + +!Bottom horizontal wall +do i=0,nx+1 + u(i,0) = -u(i,1) + v(i,0) = 0 + u1(i,0) = -u1(i,1) + v1(i,0) = 0 + u_star(i,0) = -u_star(i,1) + v_star(i,0) = 0 +end do + +!Top horizontal wall +do i=0,nx+1 + u(i,ny+1) = 2-u(i,ny) + v(i,ny) = 0 + u1(i,ny+1) = 2-u1(i,ny) + v1(i,ny) = 0 + u_star(i,ny+1) = 2-u_star(i,ny) + v_star(i,ny) = 0 +end do + + +!!!!!!!Pressure boundary conditions!!!!!!! + +!Left vertical wall +do j=0,ny+1 + p(0,j)=p(1,j) +end do + +!Right vertical wall +do j=0,ny+1 + p(nx+1,j)=p(nx,j) +end do + + +!Bottom horizontal wall +do i=0,nx+1 + p(i,0)=p(i,1) +end do + +!Top horizontal wall +do i=0,nx+1 + p(i,ny+1)=p(i,ny) +end do + +end subroutine boundary_conditions diff --git a/calcul_2nd_membre.f90 b/calcul_2nd_membre.f90 new file mode 100644 index 0000000..2aef8e0 --- /dev/null +++ b/calcul_2nd_membre.f90 @@ -0,0 +1,30 @@ +subroutine calcul_2nd_membre() ! Calculate the second membre of equation AX=B +use variables +implicit none + + + do j=1,ny + do i=1,nx + div(i,j)= ddt*(ddx*(u_star(i,j)-u_star(i-1,j))+ddy*(v_star(i,j)-v_star(i,j-1))) + enddo + enddo + + sum=0.0 + do j=1,ny + do i=1,nx + sum=sum+div(i,j) + enddo + enddo + + sum=sum/float(nx*ny) + k=1 + do j=1,ny + do i=1,nx + div(i,j)=div(i,j)-sum + div1(k)=-div(i,j) + x1(k)=0. + k=k+1 + enddo + enddo + +end subroutine calcul_2nd_membre diff --git a/calcul_new_velocity.f90 b/calcul_new_velocity.f90 new file mode 100644 index 0000000..6478eb2 --- /dev/null +++ b/calcul_new_velocity.f90 @@ -0,0 +1,87 @@ +subroutine calcul_new_velocity() +use variables +implicit none + + +!-------------------------------------------------! +! Calculation of velocity field at t = dt*n+1 ! +!-------------------------------------------------! + +!!! In x direction !!! + +do j=1,ny + do i=1,nx-1 +u1(i,j) = u_star(i,j) - dt*ddx*(p(i+1,j)-p(i,j)) + end do +end do + +!!! In y direction !!! + +do j=1,ny-1 + do i =1,nx +v1(i,j) = v_star(i,j) - dt*ddy*(p(i,j+1)-p(i,j)) + end do +end do + + + + +!------------------------------------------------------------------------------------------! +! Centering variables to get matrix (1:nx,1:ny) for Paraview ! +!------------------------------------------------------------------------------------------! + + +do j=1,ny + do i=1,nx +uc(i,j) = 0.5*(u1(i,j)+u1(i-1,j)) +vc(i,j) = 0.5*(v1(i,j)+v1(i,j-1)) + end do +end do + + + +!---------------------------------------------------! +! Rotational calculus (corners + centering) ! +!---------------------------------------------------! + + +!!! Corner boundary conditions (variable w) !!! + +w(1,1)=0 +w(nx,1)=0 +w(1,ny)=0 +w(nx,ny)=0 + +!!! General calculation !!! + +do j=2,ny + do i=2,nx +w(i,j) = ddx*(v1(i+1,j)-v1(i,j))-ddy*(u1(i,j+1)-u1(i,j)) + end do +end do + +!!! Top and bottom wall computation !!! + +do i=2,nx-1 + w(i,1) = ddx*(v1(i+1,1)-v1(i,1))-ddy*(u1(i,2)-u1(i,1)) + w(i,ny) = ddx*(v1(i+1,ny)-v1(i,ny))-ddy*(u1(i,ny+1)-u1(i,j)) +end do + +!!! Left and right wall computation !!! + +do j=2,ny-1 + w(1,j) = ddx*(v1(2,j)-v1(1,j))-ddy*(u1(1,j+1)-u1(1,j)) + w(nx,j) = ddx*(v1(nx+1,j)-v1(nx,j))-ddy*(u1(nx,j+1)-u1(nx,j)) +end do + +!!! Centered rotational (at the center of mesh cells) !!! + +do j=2,ny + do i=2,nx +rot(i,j) = 0.25*(w(i,j)+w(i-1,j)+w(i,j-1)+w(i-1,j-1)) + end do +end do + +end subroutine calcul_new_velocity + + diff --git a/calcul_pressure_field.f90 b/calcul_pressure_field.f90 new file mode 100644 index 0000000..d592d5c --- /dev/null +++ b/calcul_pressure_field.f90 @@ -0,0 +1,25 @@ +subroutine calcul_pressure_field() +use variables +implicit none + +!-------------------------------------------------! +! Update pressure field ! +!-------------------------------------------------! + + k=1 + do j=1,ny + do i=1,nx + pre(i,j)=x1(k) + k=k+1 + enddo + enddo + + + do j=1,ny + do i=1,nx + p(i,j) = pre(i,j) + end do + end do + + +end subroutine calcul_pressure_field diff --git a/coordinates.txt b/coordinates.txt new file mode 100644 index 0000000..25cb9e5 --- /dev/null +++ b/coordinates.txt @@ -0,0 +1,122 @@ + 11 11 + 0.045 0.045 + 0.045 0.136 + 0.045 0.227 + 0.045 0.318 + 0.045 0.409 + 0.045 0.500 + 0.045 0.591 + 0.045 0.682 + 0.045 0.773 + 0.045 0.864 + 0.045 0.955 + 0.136 0.045 + 0.136 0.136 + 0.136 0.227 + 0.136 0.318 + 0.136 0.409 + 0.136 0.500 + 0.136 0.591 + 0.136 0.682 + 0.136 0.773 + 0.136 0.864 + 0.136 0.955 + 0.227 0.045 + 0.227 0.136 + 0.227 0.227 + 0.227 0.318 + 0.227 0.409 + 0.227 0.500 + 0.227 0.591 + 0.227 0.682 + 0.227 0.773 + 0.227 0.864 + 0.227 0.955 + 0.318 0.045 + 0.318 0.136 + 0.318 0.227 + 0.318 0.318 + 0.318 0.409 + 0.318 0.500 + 0.318 0.591 + 0.318 0.682 + 0.318 0.773 + 0.318 0.864 + 0.318 0.955 + 0.409 0.045 + 0.409 0.136 + 0.409 0.227 + 0.409 0.318 + 0.409 0.409 + 0.409 0.500 + 0.409 0.591 + 0.409 0.682 + 0.409 0.773 + 0.409 0.864 + 0.409 0.955 + 0.500 0.045 + 0.500 0.136 + 0.500 0.227 + 0.500 0.318 + 0.500 0.409 + 0.500 0.500 + 0.500 0.591 + 0.500 0.682 + 0.500 0.773 + 0.500 0.864 + 0.500 0.955 + 0.591 0.045 + 0.591 0.136 + 0.591 0.227 + 0.591 0.318 + 0.591 0.409 + 0.591 0.500 + 0.591 0.591 + 0.591 0.682 + 0.591 0.773 + 0.591 0.864 + 0.591 0.955 + 0.682 0.045 + 0.682 0.136 + 0.682 0.227 + 0.682 0.318 + 0.682 0.409 + 0.682 0.500 + 0.682 0.591 + 0.682 0.682 + 0.682 0.773 + 0.682 0.864 + 0.682 0.955 + 0.773 0.045 + 0.773 0.136 + 0.773 0.227 + 0.773 0.318 + 0.773 0.409 + 0.773 0.500 + 0.773 0.591 + 0.773 0.682 + 0.773 0.773 + 0.773 0.864 + 0.773 0.955 + 0.864 0.045 + 0.864 0.136 + 0.864 0.227 + 0.864 0.318 + 0.864 0.409 + 0.864 0.500 + 0.864 0.591 + 0.864 0.682 + 0.864 0.773 + 0.864 0.864 + 0.864 0.955 + 0.955 0.045 + 0.955 0.136 + 0.955 0.227 + 0.955 0.318 + 0.955 0.409 + 0.955 0.500 + 0.955 0.591 + 0.955 0.682 + 0.955 0.773 + 0.955 0.864 + 0.955 0.955 diff --git a/discretisation_centre.f90 b/discretisation_centre.f90 new file mode 100644 index 0000000..a433f00 --- /dev/null +++ b/discretisation_centre.f90 @@ -0,0 +1,39 @@ +subroutine discretisation_intermediary_velocity_centre() +use variables +implicit none + +!!! u_star calculation (x component) !!! + +do j=1,ny + do i=1,nx-1 + +u_tilde_x1=0.5*(u(i,j)+u(i+1,j)) !1 for +(i or j) +u_tilde_x2=0.5*(u(i-1,j)+u(i,j)) !2 for -(i or j) +v_tilde_x1=0.5*(v(i,j)+v(i+1,j)) +v_tilde_x2=0.5*(v(i,j-1)+v(i+1,j-1)) + +u_star(i,j) = u(i,j)-dt*ddx*0.5*(u_tilde_x1*(u(i,j)+u(i+1,j))-u_tilde_x2*(u(i,j)+u(i-1,j))) & + -dt*ddy*0.5*(v_tilde_x1*(u(i,j)+u(i,j+1))-v_tilde_x2*(u(i,j)+u(i,j-1))) & + +nu*dt*(ddx**2)*(u(i+1,j)-2*u(i,j)+u(i-1,j))+nu*dt*(ddy**2)*(u(i,j+1)-2*u(i,j)+u(i,j-1)) + + end do +end do + +!!! v_star calculation (y component) !!! + +do j=1,ny-1 + do i=1,nx + +u_tilde_y1=0.5*(u(i,j)+u(i,j+1)) +u_tilde_y2=0.5*(u(i-1,j)+u(i-1,j+1)) +v_tilde_y1=0.5*(v(i,j)+v(i,j+1)) +v_tilde_y2=0.5*(v(i,j-1)+v(i,j)) + +v_star(i,j) = v(i,j)-dt*ddx*0.5*(u_tilde_y1*(v(i,j)+v(i+1,j))-u_tilde_y2*(v(i,j)+v(i-1,j))) & + -dt*ddy*0.5*(v_tilde_y1*(v(i,j)+v(i,j+1))-v_tilde_y2*(v(i,j)+v(i,j-1))) & + +nu*dt*(ddx**2)*(v(i+1,j)-2*v(i,j)+v(i-1,j))+nu*dt*(ddy**2)*(v(i,j+1)-2*v(i,j)+v(i,j-1)) + + end do +end do + +end subroutine discretisation_intermediary_velocity_centre diff --git a/discretisation_upwind.f90 b/discretisation_upwind.f90 new file mode 100644 index 0000000..4445ad5 --- /dev/null +++ b/discretisation_upwind.f90 @@ -0,0 +1,103 @@ +subroutine discretisation_intermediary_velocity_upwind() +use variables +implicit none + + +!!! u_star calculation (x component) !!! + +do j=1,ny + do i=1,nx-1 + +u_tilde_x1=0.5*(u(i,j)+u(i+1,j)) !1 for +(i or j) +u_tilde_x2=0.5*(u(i-1,j)+u(i,j)) !2 for -(i or j) +v_tilde_x1=0.5*(v(i,j)+v(i+1,j)) +v_tilde_x2=0.5*(v(i,j-1)+v(i+1,j-1)) + +if (u_tilde_x1 >= 0) then + + a=u(i,j) + else + a=u(i+1,j) +end if + + +if (u_tilde_x2 >= 0) then + + b=u(i-1,j) + else + b=u(i,j) +end if + + +if (v_tilde_x1 >= 0) then + + c=u(i,j) + else + c=u(i,j+1) +end if + + +if (v_tilde_x2 >= 0) then + + d=u(i,j-1) + else + d=u(i,j) +end if + + +u_star(i,j) = u(i,j)-dt*ddx*(u_tilde_x1*a-u_tilde_x2*b)-dt*ddy*(v_tilde_x1*c-v_tilde_x2*d) & + +nu*dt*(ddx**2)*(u(i+1,j)-2*u(i,j)+u(i-1,j))+nu*dt*(ddy**2)*(u(i,j+1)-2*u(i,j)+u(i,j-1)) + + end do +end do + + +!!! v_star calculation (y component) !!! + +do j=1,ny-1 + do i=1,nx + +u_tilde_y1=0.5*(u(i,j)+u(i,j+1)) +u_tilde_y2=0.5*(u(i-1,j)+u(i-1,j+1)) +v_tilde_y1=0.5*(v(i,j)+v(i,j+1)) +v_tilde_y2=0.5*(v(i,j-1)+v(i,j)) + +if (u_tilde_y1 >= 0) then + + e=v(i,j) + else + e=v(i+1,j) +end if + + +if (u_tilde_y2 >= 0) then + + f=v(i-1,j) + else + f=v(i,j) +end if + + +if (v_tilde_y1 >= 0) then + + g=v(i,j) + else + g=v(i,j+1) +end if + + +if (v_tilde_y2 >= 0) then + + h=v(i,j-1) + else + h=v(i,j) +end if + + +v_star(i,j) = v(i,j)-dt*ddx*(u_tilde_y1*e-u_tilde_y2*f)-dt*ddy*(v_tilde_y1*g-v_tilde_y2*h) & + +nu*dt*(ddx**2)*(v(i+1,j)-2*v(i,j)+v(i-1,j))+nu*dt*(ddy**2)*(v(i,j+1)-2*v(i,j)+v(i,j-1)) + + end do +end do + +end subroutine discretisation_intermediary_velocity_upwind diff --git a/ensight_cavity.f90 b/ensight_cavity.f90 new file mode 100644 index 0000000..3ac6402 --- /dev/null +++ b/ensight_cavity.f90 @@ -0,0 +1,252 @@ +SUBROUTINE write_result_ensight(xEnsight,yEnsight,u,v,omega,press,nx,ny,nz,istep,isto,nstep) + +!-------------------------------------------------! +! Subroutine to write results in Ensight format ! +!-------------------------------------------------! + + implicit none + + real*8, dimension(nx,ny), intent(in) :: u,v,omega,press + real*8, dimension(3,nx,ny,nz) :: velocity + real*8, dimension(1,nx,ny,nz) :: scalar + integer, parameter :: iskip = 1 + integer, parameter :: nbVar = 3 + integer :: nbImages,ntini + character(len=80) :: caseName,speedName,omegaName,presName + character(len=80), dimension(nbVar) :: varName + integer, dimension(nbVar) :: varType + real*8, dimension(nx) :: xEnsight + real*8, dimension(ny) :: yEnsight + real*8, dimension(1 ) :: zEnsight + integer :: i,j,imin,imax,jmin,jmax,kmin,kmax,istep_rep + integer :: nx,ny,nz,istep,isto,nstep + + write(caseName,'(A)') 'EnsightOutput' + write(varName(1),'(A)') 'velocity' + varType(1) = 2 + write(varName(2),'(A)') 'omega' + varType(2) = 1 + write(varName(3),'(A)') 'press' + varType(3) = 1 + nbImages = nstep/isto + + zEnsight=0. + + kmin = 1 + kmax = 1 + jmin = 1 + jmax = ny + imin = 1 + imax = nx + if (nstep/isto .eq. 1) then + write(speedName,'(A)') 'velocity' + write(omegaName,'(A)') 'omega' + write(presName,'(A)') 'press' + else + write(speedName,'(A,I6.6)') 'velocity',istep + write(omegaName,'(A,I6.6)') 'omega',istep + write(presName,'(A,I6.6)') 'press',istep + end if + call EnsightCase(nbVar,varName,caseName,VarType,istep,nstep,isto) + call WriteRectEnsightGeo(imin,imax,jmin,jmax,kmin,kmax,xEnsight,yEnsight,zEnsight,caseName) + + + do j=1,ny + do i=1,nx + + velocity(1,i,j,1) = u(i,j) + velocity(2,i,j,1) = v(i,j) + velocity(3,i,j,1) = 0. + enddo + enddo + + + call WriteEnsightVar(3,nx,ny,nz,velocity,speedName,imin,imax,jmin,jmax,kmin,kmax) + do j=1,ny + do i=1,nx + scalar(1,i,j,1)=omega(i,j) + enddo + enddo + + call WriteEnsightVar(1,nx,ny,nz,scalar,omegaName ,imin,imax,jmin,jmax,jmin,kmax) + do j=1,ny + do i=1,nx + scalar(1,i,j,1)=press(i,j) + enddo + enddo + call WriteEnsightVar(1,nx,ny,nz,scalar,presName ,imin,imax,jmin,jmax,kmin,kmax) + + + + +END SUBROUTINE write_result_ensight + +! +! ****************************************************************************** +! subrout WriteRectEnsightGeo +! ****************************************************************************** +! +! writes mesh data in Ensight's ascii format for rectilinear geometry +! +! n1,n2,n3....: number of nodes in the x1,x2,x3 direction +! x1,x2,x3....: coordinates +! + subroutine WriteRectEnsightGeo(imin,imax,jmin,jmax,kmin,kmax,x1,x2,x3,FileName) + implicit none + + INTEGER,INTENT(IN)::imin,imax,jmin,jmax,kmin,kmax + REAL*8,DIMENSION(imax),INTENT(IN)::x1 + REAL*8,DIMENSION(jmax),INTENT(IN)::x2 + REAL*8,DIMENSION(1 ),INTENT(IN)::x3 + CHARACTER(LEN=80) ,INTENT(IN)::FileName + + character(LEN=80)::binary_form + character(LEN=80)::file_description1,file_description2 + character(LEN=80)::node_id,element_id + character(LEN=80)::part,description_part,blocck + + integer::FileUnit,i,j,k,npart,isize,jsize,ksize + integer::reclength + + FileUnit = 40 + + binary_form ='C Binary' + file_description1='Ensight Model Geometry File Created by ' + file_description2='WriteRectEnsightGeo Routine' + node_id ='node id off' + element_id ='element id off' + part ='part' + npart =1 + description_part ='Sortie Ensight' + blocck ='block rectilinear' + isize=(imax-imin+1) + jsize=(jmax-jmin+1) + ksize=(kmax-kmin+1) + + reclength=80*8+4*(4+isize+jsize+ksize) + + open (unit=FileUnit,file=trim(FileName)//'.geo',form='UNFORMATTED',access="direct",recl=reclength,status='replace') + write(unit=FileUnit,rec=1) binary_form & + ,file_description1 & + ,file_description2 & + ,node_id & + ,element_id & + ,part,npart & + ,description_part & + ,blocck & + ,isize,jsize,ksize & + ,(real(sngl(x1(i)),4),i=imin,imax) & + ,(real(sngl(x2(j)),4),j=jmin,jmax) & + ,(real(sngl(x3(k)),4),k=kmin,kmax) + + close(FileUnit) + + end subroutine +! +! ****************************************************************************** +! +! WriteEnsightSca writes result data in Ensight's format +! +! m1,m2,m3....: size of the variable in the x1,x2,x3 direction +! ndv.........: number of dimension of the variable (1=>scalar 3=>vector) +! var.........: data to be written +! Varname.....: word used to build filenames +! imin,imax...: range of writting data in the x1 direction +! jmin,jmax...: range of writting data in the x2 direction +! kmin,kmax...: range of writting data in the x3 direction +! +! ****************************************************************************** + subroutine WriteEnsightVar(ndv,nx,ny,nz,var,VarName,imin,imax,jmin,jmax,kmin,kmax) + + implicit none + + INTEGER ,INTENT(IN)::ndv,nx,ny,nz + REAL*8,DIMENSION(ndv,nx,ny,nz),INTENT(IN)::var + CHARACTER*80,INTENT(IN)::Varname + + character(len=80):: VarFileName + character(len=80):: part,blocck + integer::FileUnit,i,j,k,ii,npart,m,descripteur,tailleDoublePrecision,tailleCharacter,tailleInteger,tailleReel + integer :: type_carre,type_cube,imin,imax,jmin,jmax,kmin,kmax,reclength + + + FileUnit = 41 + part ='part' + npart=1 + blocck='block rectilinear' + + + if (ndv.eq.1)VarFileName = trim(Varname)//'.scl' + if (ndv.eq.3)VarFileName = trim(Varname)//'.vec' + + reclength=80*3+4*(1+(imax-imin+1)*(jmax-jmin+1)*(kmax-kmin+1)*ndv) + + open (unit=FileUnit,file=VarFileName,form='UNFORMATTED',access="direct",recl=reclength) + + + + write(unit=FileUnit,rec=1) VarFileName & + ,part,npart,blocck & + ,((((real(sngl(var(m,i,j,k)),4) & + ,i=imin,imax) & + ,j=jmin,jmax) & + ,k=kmin,kmax) & + ,m=1,ndv) + + close(FileUnit) + + end subroutine +! +! ****************************************************************************** +! EnsightCase helps to write a Ensight's case file +! +! VarName.....: Name of the variable +! GeoName.....: Name of the geometrie +! VarType.....: 1 => Scalar 3 => Vector +! ntini.......: filename start number +! nstop.......: filename end number +! nprint......: filename increment +! +! nfile.......: number of result files (time steps) +! + subroutine EnsightCase(nbVar,VarName,GeoName,VarType,istep,nstep,isto) + implicit none + + INTEGER,INTENT(IN)::nbVar,nstep,isto,istep + INTEGER, DIMENSION(nbVar),INTENT(IN)::VarType + CHARACTER(LEN=80),DIMENSION(nbVar),INTENT(IN)::Varname + CHARACTER(LEN=80),INTENT(IN)::GeoName + integer::FileUnit,i,j,nfile + + nfile=nstep/isto + + FileUnit = 40 + open(FileUnit,file=trim(GeoName)//'.case',status='replace') + + write(FileUnit,10) trim(GeoName)//'.geo' + 10 format('FORMAT' ,/ ,'type: ensight gold',//,'GEOMETRY' ,/ ,'model: ',A ,//,'VARIABLE') + + do i=1,nbVar + if (nfile.eq.1) then + if(VarType(i).eq.1) write(FileUnit,15)trim(Varname(i)),trim(Varname(i))//'.scl' + if(VarType(i).eq.2) write(FileUnit,25)trim(Varname(i)),trim(Varname(i))//'.vec' + else + if(VarType(i).eq.1) write(FileUnit,15)trim(Varname(i)),trim(Varname(i))//'******.scl' + if(VarType(i).eq.2) write(FileUnit,25)trim(Varname(i)),trim(Varname(i))//'******.vec' + endif + enddo + + if (nfile.gt.1) then + write(FileUnit,45) nfile,isto,isto + write(FileUnit,'(i5)') (j*isto,j=1,nfile) + endif + + close(FileUnit) + + 15 format('scalar per node: ',A,' ', A) + 25 format('vector per node: ',A,' ', A) + + 45 format(/,'TIME ' ,/,'time set: 1 ' ,/,'number of steps:' ,i4 ,/, & + 'filename start number:',i10/,'filename increment:' ,i4/,'time values: ') + + end subroutine diff --git a/initial_conditions.f90 b/initial_conditions.f90 new file mode 100644 index 0000000..3336821 --- /dev/null +++ b/initial_conditions.f90 @@ -0,0 +1,27 @@ +subroutine initial_conditions() +use variables +implicit none + +!---------------------------------------------------! +! Initial conditions calculation ! +!---------------------------------------------------! + + +do j=0,ny+1 + do i=0,nx+1 + + u(i,j) = 0 + v(i,j) = 0 + u1(i,j) = 0 + v1(i,j) = 0 + p(i,j) = 0 + u_star(i,j) = 0 + v_star(i,j) = 0 + + end do +end do + +end subroutine initial_conditions + + + diff --git a/main.f90 b/main.f90 new file mode 100644 index 0000000..40955f1 --- /dev/null +++ b/main.f90 @@ -0,0 +1,68 @@ +program NS_lid_driven_cavity + use variables + implicit none + + call reading_data() ! reading some data for mesh creation and calculation + call mesh_creation() ! creating the mesh for the simulation + call inital_conditions() ! initializing conditions + call boundary_conditions() ! boundary conditions of the domain + + write(*,*) 'Choice of numerical scheme: 1-Upwind; 2-Centred' + read(*,*) Q + + !!! Parameters for the simulation + zeta=1.e-8 ! zeta and itmax for solving pressure matrix in ICCG2 subroutines + itmax=300 + time = 0. ! initialize time of simulation + nstep = 20000 ! number of timesteps for the simulation + isto = 200 ! data stored every 'isto' steps + + do istep=1,nstep ! main loop on the timesteps + + if (Q == 1) then !Upwind scheme + + call timestep() + call discretisation_intermediary_velocity_upwind() + + else if (Q == 2) then !Centred scheme + + call timestep() + call discretisation_intermediary_velocity_centre() + + end if + + call calcul_2nd_membre() ! Calculate the second membre of equation AX=B + call matgen_cavity(coef,jcoef,nx,ny,ndim,mdim,dx,dy) ! Generate coefficients of matrix A + call ICCG2(coef,jcoef,L,Ldiag,div1,x1,ndim,mdim,zeta,p_s,r_s,r2_s,q_s,s_s,itmax) ! CONJUGUATE GRADIENT + PRECONDITIONED LU for solving X field (pressure here) + call calcul_pressure_field() ! update the pressure field + call calcul_new_velocity() ! update velocity field + calculate rotational 'omega' + + !! loops to update the main u and v velocity fields + do j=1,ny + do i=1,nx-1 + u(i,j) = u1(i,j) + enddo + enddo + + do j=1,ny-1 + do i=1,nx + v(i,j) = v1(i,j) + enddo + enddo + + time = time + dt ! update in time --> time = time + timestep + write(*,*) 'time = ',time ! write the time of simulation + + call boundary_conditions() ! recall boundary conditions to update them + + if (mod(istep,isto)==0) then ! write results in ensight format if isto = istep + + call write_result_ensight(xx,yy,uc,vc,rot,pre,nx,ny,nz,istep,isto,nstep) + + end if + + end do + + call velocities_output() ! write velocity and omega on lines at final stage + +end program NS_lid_driven_cavity diff --git a/matgen_cavity.f90 b/matgen_cavity.f90 new file mode 100644 index 0000000..63d23d0 --- /dev/null +++ b/matgen_cavity.f90 @@ -0,0 +1,63 @@ + subroutine matgen_cavity(coef,jcoef,nx,ny,ndim,mdim,dx,dy) + implicit none + + integer :: nx,ny,i,j,k,mdim,ndim + integer ,dimension(1:mdim) :: jcoef + + + real*8 ,dimension(1:ndim,1:mdim)::coef + real*8 :: dx,dy,aa,bb + + k=1 + do j=1,ny + do i=1,nx + coef(k,1) =2./dx/dx+2./dy/dy + coef(k,2) =-1./dx/dx + coef(k,3) =-1./dy/dy + k=k+1 + enddo + enddo + + k=1 + do j=1,ny + do i=1,nx + if(i.eq.1)then + aa=-1./dx/dx + elseif(i.eq.nx)then + aa=-1./dx/dx + else + aa=0.0 + endif + + if(j.eq.1)then + bb=-1./dy/dy + elseif(j.eq.ny)then + bb=-1./dy/dy + else + bb=0.0 + endif + + coef(k,1)=coef(k,1)+aa+bb + k=k+1 + enddo + enddo + + k=1 + do j=1,ny + do i=1,nx + if(i.eq.nx)then + coef(k,2)=0.0 + endif + if(j.eq.ny)then + coef(k,3)=0.0 + endif + k=k+1 + enddo + enddo + + jcoef(1)=0 + jcoef(2)=1 + jcoef(3)=nx + + return + end diff --git a/mesh_creation.f90 b/mesh_creation.f90 new file mode 100644 index 0000000..609d1fe --- /dev/null +++ b/mesh_creation.f90 @@ -0,0 +1,25 @@ +subroutine mesh_creation() +use variables +implicit none + + do i=1,nx + xx(i)=(i-0.5)*dx + enddo + + do j=1,ny + yy(j)=(j-0.5)*dy + enddo + +!Results are stored in the file 'coordinates.txt' + + open (7,file='coordinates.txt') + write(7,'(2I6)') nx,ny + do i=1,nx + do j=1,ny + write (7,'(F6.3,a,F6.3)') xx(i),' ', yy(j) + enddo + enddo + close(7) + + +end subroutine mesh_creation diff --git a/omega_boundary.txt b/omega_boundary.txt new file mode 100644 index 0000000..4adc75e --- /dev/null +++ b/omega_boundary.txt @@ -0,0 +1,11 @@ + omega_boundary +* +* +* +* +* +* +* +* +* +* diff --git a/reading_data.f90 b/reading_data.f90 new file mode 100644 index 0000000..46eda57 --- /dev/null +++ b/reading_data.f90 @@ -0,0 +1,11 @@ +subroutine reading_data() +use variables +implicit none + +dx = 1./float(nx) +dy = 1./float(ny) +ddx = 1./dx +ddy = 1./dy +nu1 = 1./nu + +end subroutine reading_data diff --git a/solver.f90 b/solver.f90 new file mode 100644 index 0000000..2f66927 --- /dev/null +++ b/solver.f90 @@ -0,0 +1,310 @@ +SUBROUTINE ICCG2(coef,jcoef,L,Ldiag,b,x,n,m,eps,p,r,r2,q,s,itmax) + +!-----------------------------------------------------------------------! +! ! +! CONJUGUATE GRADIENT + PRECONDITIONED LU FILL-IN 2 ! +! ! +! ATTENTION : coef, jcoef et b are modified in this routine ! +! --------- ! +! ! +!-----------------------------------------------------------------------! + + implicit none + +!---------------------------------------------------! +! VARIABLES IN CALL ! +!---------------------------------------------------! + + integer, intent(in) :: n,m,itmax + real*8, intent(in) :: eps + + integer, dimension(m), intent(inout) :: jcoef + real*8, dimension(n,m), intent (inout) :: coef + + integer, dimension(5), intent(inout) :: Ldiag + real*8, dimension(n,5), intent (inout) :: L + + real*8, dimension(n), intent (inout) :: b,x + real*8, dimension(n), intent(inout) :: p,r,r2,q,s + +!---------------------------------------------------! +! LOCAL VARIABLES ! +!---------------------------------------------------! + + real*8 :: alpha,beta,nu,mu,norm0,norm,sum,scal,norm1,norm2 + integer :: i,j,col + + + + write(6,*) 'itmax=',itmax +!-----------------------------------------------------------! +! PRECONDITIONING MATRIX CALCULUS + SCALING ! +!-----------------------------------------------------------! + do i=1,3; Ldiag(i)=jcoef(i); end do + Ldiag(4)=Ldiag(3)-1 + Ldiag(5)=Ldiag(3)-2 + + L=0. + + do i=1,n + + L(i,1)=coef(i,1) + do j=2,5 + col=Ldiag(j) + if (col1) then + L(i,4)=-L(i-1,3)*L(i-1,2)*s(i-1) + L(i,5)=-L(i-1,4)*L(i-1,2)*s(i-1) + end if + + end do + + do i=1,n; L(i,1)=sqrt(s(i)); end do + + do j=1,3 + col=Ldiag(j) + do i=1,n-col + coef(i,j)=coef(i,j)*L(i,1)*L(i+col,1) + end do + end do + + do i=1,n + + L(i,2)=coef(i,2) + do j=4,5 + col=Ldiag(j) + if (col1) then + L(i,4)=-L(i-1,3)*L(i-1,2) + L(i,5)=-L(i-1,4)*L(i-1,2) + end if + + end do + + norm0=norm2(b,n) + + do i=1,n; s(i)=1./s(i); end do + + do i=1,n; b(i)=b(i)*L(i,1); end do + +!---------------------------------------------------! +! CONJUGUATE GRADIENT ! +!---------------------------------------------------! + + call matmul_ell(p,coef,jcoef,x,n,m) + do i=1,n; r(i)=b(i)-p(i); end do + + call resLU_ell5(r2,L,Ldiag,r,n) + + p=r2 + nu=scal(r,r2,n) + + norm=0. + do i=1,n; norm=norm+r(i)*r(i)*s(i); end do + norm=sqrt(norm)/norm0 + + j=0 + + do while (norm>eps.and.j.lt.itmax) + j=j+1 + + call matmul_ell(q,coef,jcoef,p,n,m) + + alpha=nu/scal(p,q,n) + + do i=1,n; x(i)=x(i)+alpha*p(i); end do + do i=1,n; r(i)=r(i)-alpha*q(i); end do + + call resLU_ell5(r2,L,Ldiag,r,n) + + mu=scal(r,r2,n) + + beta=mu/nu + + do i=1,n; p(i)=r2(i)+beta*p(i); end do + + nu=mu + + norm=0. + do i=1,n; norm=norm+r(i)*r(i)*s(i); end do + norm=sqrt(norm)/norm0 + + end do + +!---------------------------------------------------! +! SOLUTION SCALING ! +!---------------------------------------------------! + + do i=1,n; x(i)=x(i)*L(i,1); end do + + if(j.ge.itmax) then + print*, 'non convergence apres =', j,norm + else + print*, ' Nombre It�rations ICCG2 ( Fill-In 2 ) =', j + endif + return + +END SUBROUTINE ICCG2 + + + + + +SUBROUTINE resLU_ell5(x,L,Ldiag,y,n) + + implicit none + + integer, intent(in) :: n + real*8, dimension(n,5), intent (in) :: L + integer, dimension(5), intent(in) :: Ldiag + real*8, dimension(n), intent(in) :: y + real*8, dimension(n), intent(out) :: x + + integer :: i,j,col1,col2,col3,col4,col5,col6 + + col1=Ldiag(2) + col2=Ldiag(5) + col3=Ldiag(4) + col4=Ldiag(3) + + do i=1,col1 + x(i)=y(i) + end do + + do i=col1+1,col2 + x(i)=y(i)-L(i-col1,2)*x(i-col1) + end do + + do i=col2+1,col3 + x(i)=y(i)-L(i-col1,2)*x(i-col1)-L(i-col2,5)*x(i-col2) + end do + + do i=col3+1,col4 + x(i)=y(i)-L(i-col1,2)*x(i-col1)-L(i-col2,5)*x(i-col2)& + -L(i-col3,4)*x(i-col3) + end do + + do i=col4+1,n + x(i)=y(i)-L(i-col1,2)*x(i-col1)-L(i-col2,5)*x(i-col2)& + -L(i-col3,4)*x(i-col3)-L(i-col4,3)*x(i-col4) + end do + + do i=n-col1,n-col2+1,-1 + x(i)=x(i)-L(i,2)*x(i+col1) + end do + + do i=n-col2,n-col3+1,-1 + x(i)=x(i)-L(i,2)*x(i+col1)-L(i,5)*x(i+col2) + end do + + do i=n-col3,n-col4+1,-1 + x(i)=x(i)-L(i,2)*x(i+col1)-L(i,5)*x(i+col2)-L(i,4)*x(i+col3) + end do + + do i=n-col4,1,-1 + x(i)=x(i)-L(i,2)*x(i+col1)-L(i,5)*x(i+col2)-L(i,4)*x(i+col3)& + -L(i,3)*x(i+col4) + end do + + return + +END SUBROUTINE resLU_ell5 + + + + + +SUBROUTINE matmul_ell(x,coef,jcoef,y,n,m) + + implicit none + + integer, intent(in) :: n,m + real*8, dimension(n,m), intent (in) :: coef + integer, dimension(m), intent(in) :: jcoef + real*8, dimension(n), intent(in) :: y + real*8, dimension(n), intent(out) :: x + + integer :: i,j,col + + do i=1,n + x(i)=coef(i,1)*y(i) + end do + + do j=2,m + col=jcoef(j) + do i=1,n-col + x(i)=x(i)+coef(i,j)*y(i+col) + x(i+col)=x(i+col)+coef(i,j)*y(i) + end do + end do + + return + +END SUBROUTINE matmul_ell + + +FUNCTION scal(x,y,n) result(res) + + implicit none + + integer, intent(in) :: n + real*8, dimension(n), intent(in) :: x,y + + integer :: i + + real*8 :: res + + res=0. + do i=1,n; res=res+x(i)*y(i); end do + +END FUNCTION + + +FUNCTION norm1(x,n) result(res) + + implicit none + + integer, intent(in) :: n + real*8, dimension(n), intent(in) :: x + + integer :: i + + real*8 :: res + + res=0. + do i=1,n; res=res+x(i)*x(i); end do + +END FUNCTION + + +FUNCTION norm2(x,n) result(res) + + implicit none + + integer, intent(in) :: n + real*8, dimension(n), intent(in) :: x + + integer :: i + + real*8 :: res + + res=0. + do i=1,n; res=res+x(i)*x(i); end do + res=sqrt(res) + +END FUNCTION diff --git a/timestep.f90 b/timestep.f90 new file mode 100644 index 0000000..0e1b643 --- /dev/null +++ b/timestep.f90 @@ -0,0 +1,34 @@ +subroutine timestep() +use variables +implicit none + +do j = 0,ny+1 + do i = 0,nx+1 + + abs_u(i,j)=abs(u(i,j)) + abs_v(i,j)=abs(v(i,j)) + + end do +end do + +max_x = 1./maxval(abs_u) +max_y = 1./maxval(abs_v) + +if (Q == 1) then ! Timestep for Upwind scheme + +min_u = min(dx*max_x,dx**2*0.5*nu1) +min_v = min(dy*max_y,dy**2*0.5*nu1) + +else if (Q == 2) then ! Timestep for Centered scheme + +min_u = min(nu*(max_x)**2,(dx)**2*0.5*nu1) +min_v = min(nu*(max_y)**2,(dy)**2*0.5*nu1) + +end if + +dt = min(min_u,min_v,dt2) + +ddt = 1./dt + + +end subroutine timestep diff --git a/u_velocity.txt b/u_velocity.txt new file mode 100644 index 0000000..4cf427d --- /dev/null +++ b/u_velocity.txt @@ -0,0 +1,12 @@ + u_vertical_line +* +* +* +* +* +* +* +* +* +* +* diff --git a/v_velocity.txt b/v_velocity.txt new file mode 100644 index 0000000..97ee439 --- /dev/null +++ b/v_velocity.txt @@ -0,0 +1,12 @@ + v_horizontal_line +* +* +* +* +* +* +* +* +* +* +* diff --git a/variables_module.f90 b/variables_module.f90 new file mode 100644 index 0000000..4102f49 --- /dev/null +++ b/variables_module.f90 @@ -0,0 +1,26 @@ +MODULE variables +implicit none + +!This module gathers all structures and variable declarations. +!The different variables no need to be redefined and can this file can just be called in the subroutines. + +integer ,parameter :: nx=11,ny=11,nz=1 +real*8 ,parameter :: nu = 1e-02, dt2 = 1e-04 + + +integer :: k, i, j, itmax, isto, istep, nstep, Q +integer ,parameter :: ndim = nx*ny,mdim=3 +integer, dimension(1:mdim):: jcoef +integer, dimension(1:5):: Ldiag +real*8 :: max_x, max_y, min_u, min_v, u_tilde_x1, u_tilde_x2, u_tilde_y1, u_tilde_y2, v_tilde_x1, v_tilde_x2, v_tilde_y1, v_tilde_y2 +real*8 :: zeta, time, dt, dx, dy, ddx, ddt, ddy, nu1, a, b, c, d, e, f, g, h, sum ! a=u(i+1/2,j); b=u(i-1/2,j); c=u(i,j+1/2); d=u(i,j-1/2); e=v(i+1/2,j); f=v(i-1/2,j); g=v(i,j+1/2); h=v(i,j-1/2) +real*8, dimension(0:nx+1,0:ny+1) :: p,u,v,u1,v1,u_star,v_star,abs_u,abs_v +real*8 ,dimension(1:nx,1:ny):: div,uc,vc,rot,w,pre +real*8 ,dimension(1:ndim,1:mdim) :: coef +real*8 ,dimension(1:ndim) :: div1,p_s,r_s,r2_s +real*8 ,dimension(1:ndim) :: q_s,s_s,x1 +real*8 ,dimension(1:ndim,1:5)::L +real, dimension (1:nx) :: xx +real, dimension (1:ny) :: yy + +end module diff --git a/velocities_output.f90 b/velocities_output.f90 new file mode 100644 index 0000000..c470633 --- /dev/null +++ b/velocities_output.f90 @@ -0,0 +1,25 @@ +subroutine velocities_output() +use variables + + open (9,file='u_velocity.txt') + write(9,*) 'u_vertical_line' + do j=1,ny + write (9,'(F1.5)') u((nx-1)/2,j) + enddo + close(9) + + open (10,file='v_velocity.txt') + write(10,*) 'v_horizontal_line' + do i=1,nx + write (10,'(F1.5)') v(i,(ny-1)/2) + enddo + close(10) + + open (11,file='omega_boundary.txt') + write(11,*) 'omega_boundary' + do i=2,nx + write (11,'(F1.5)') rot(i,ny) + enddo + close(11) + +end subroutine velocities_output