rayleigh taylor不稳定性流动cfd分析fortran代码

以下是一个简单的Fortran代码，可用于处理Rayleigh-Taylor不稳定性流动的CFD分析：

PROGRAM Rayleigh_Taylor
IMPLICIT NONE
INTEGER, PARAMETER :: Nx = 100, Ny = 100, Nt = 1000
REAL, PARAMETER :: dx = 0.1, dy = 0.1, dt = 0.01
REAL, PARAMETER :: g = 9.81, rho1 = 1.0, rho2 = 2.0, sigma = 0.1
REAL, DIMENSION(0:Nx+1, 0:Ny+1) :: u, v, p, rho, x, y
INTEGER :: i, j, k
REAL :: t

! Initialize variables
x = (/ (i-1)*dx, i=0:Nx+1 /)
y = (/ (j-1)*dy, j=0:Ny+1 /)
rho(:,:) = rho1
rho(:,Ny/2+1:) = rho2
u = 0.0
v = 0.0
p = 0.0

! Main time loop
DO k = 1, Nt
    t = k*dt
    CALL UpdateVelocity(u,v,rho,p,dx,dy,dt,Nx,Ny,g,sigma)
    CALL UpdatePressure(p,u,v,rho,dx,dy,Nx,Ny)
    CALL UpdateDensity(rho,u,v,dx,dy,dt,Nx,Ny)
    IF (MOD(k,100) == 0) THEN
        WRITE(*,*) 'Time:', t
        DO j = 1, Ny
            DO i = 1, Nx
                WRITE(*,*) x(i), y(j), u(i,j), v(i,j), p(i,j), rho(i,j)
            END DO
        END DO
    END IF
END DO

END PROGRAM

SUBROUTINE UpdateVelocity(u,v,rho,p,dx,dy,dt,Nx,Ny,g,sigma)
IMPLICIT NONE
REAL, INTENT(INOUT) :: u(Nx+2,Ny+2), v(Nx+2,Ny+2), rho(Nx+2,Ny+2), p(Nx+2,Ny+2)
REAL, INTENT(IN) :: dx, dy, dt, g, sigma
INTEGER, INTENT(IN) :: Nx, Ny
INTEGER :: i, j
REAL, DIMENSION(1:3,1:3) :: du, dv, dp
REAL :: rho_avg, rho_diff

DO j = 2, Ny+1
    DO i = 2, Nx+1
        rho_avg = 0.25*(rho(i-1,j) + rho(i+1,j) + rho(i,j-1) + rho(i,j+1))
        rho_diff = 0.5*(rho(i,j+1) - rho(i,j-1))
        du = (u(i+1:i+3,j) - 3.0*u(i:i+2,j) + u(i-1:i+1,j))/dx
        dv = (v(i+1:i+3,j) - 3.0*v(i:i+2,j) + v(i-1:i+1,j))/dx
        dp = (p(i+1:i+3,j) - 3.0*p(i:i+2,j) + p(i-1:i+1,j))/dx
        u(i,j) = u(i,j) + dt*(-dp/rho_avg + g*rho_diff + sigma*du(2,2))
        u(i,j) = u(i,j) + dt*(-dp/rho_avg + g*rho_diff + sigma*dv(2,2))
    END DO
END DO

END SUBROUTINE

SUBROUTINE UpdatePressure(p,u,v,rho,dx,dy,Nx,Ny)
IMPLICIT NONE
REAL, INTENT(INOUT) :: p(Nx+2,Ny+2), u(Nx+2,Ny+2), v(Nx+2,Ny+2), rho(Nx+2,Ny+2)
REAL, INTENT(IN) :: dx, dy
INTEGER, INTENT(IN) :: Nx, Ny
INTEGER :: i, j
REAL :: rho_avg
DO j = 2, Ny+1
    DO i = 2, Nx+1
        rho_avg = 0.25*(rho(i-1,j) + rho(i+1,j) + rho(i,j-1) + rho(i,j+1))
        p(i,j) = p(i,j) - 0.5*dt*rho_avg*((u(i+1,j) - u(i-1,j))/(2.0*dx) &
            + (v(i,j+1) - v(i,j-1))/(2.0*dy))
    END DO
END DO
END SUBROUTINE

SUBROUTINE UpdateDensity(rho,u,v,dx,dy,dt,Nx,Ny)
IMPLICIT NONE
REAL, INTENT(INOUT) :: rho(Nx+2,Ny+2), u(Nx+2,Ny+2), v(Nx+2,Ny+2)
REAL, INTENT(IN) :: dx, dy, dt
INTEGER, INTENT(IN) :: Nx, Ny
INTEGER :: i, j
DO j = 2, Ny+1
    DO i = 2, Nx+1
        rho(i,j) = rho(i,j) - dt*((rho(i,j)*(u(i+1,j) - u(i-1,j))/(2.0*dx) &
            + rho(i,j)*(v(i,j+1) - v(i,j-1))/(2.0*dy)))
    END DO
END DO
END SUBROUTINE

请注意，这只是一个简单的示例代码，可能需要进行修改和优化以满足您的具体要求。此外，您还需要提供适当的边界条件，例如，您可以使用周期性边界条件或壁面条件，具体取决于您的应用场景。