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283 lines (211 loc) · 10.9 KB
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PROGRAM Solution
IMPLICIT NONE
INTEGER, PARAMETER :: realkind = 8 ! 4: single precision, 8: double precision
REAL(KIND=realkind), PARAMETER :: pi = 3.14159265358979323846264338327950288419716939937510_realkind
REAL(KIND=realkind) :: Q_v, Q_i, Q_2i, D_v, D_i, v_I, v_2i, v_D, v_N, K_iv, r_iv, k_gb, a_0, Omega, b_v
REAL(KIND=realkind) :: f_1, f_2, d_N, P_sl, z_vN, z_iN, z_vL, z_iL
INTEGER :: n_time_step, i_time_step
INTEGER :: n_write_step, i_write_step, i_write
REAL(KIND=realkind) :: dt, dt_half, dt_sixth
REAL(KIND=realkind) :: C_v_factor1, C_v_factor2
REAL(KIND=realkind) :: C_i_factor1, C_i_factor2, C_i_factor3
REAL(KIND=realkind) :: C_2i_factor1, C_2i_factor2, C_2i_factor3
REAL(KIND=realkind) :: rho_N_factor1, rho_N_factor2
REAL(KIND=realkind) :: C_J_factor1, C_J_factor2, C_J_factor3, C_J_factor4
REAL(KIND=realkind) :: d_J_factor1, d_J_factor2, d_J_factor3, d_J_factor4
REAL(KIND=realkind) :: k1_C_v, k2_C_v, k3_C_v, k4_C_v
REAL(KIND=realkind) :: k1_C_i, k2_C_i, k3_C_i, k4_C_i
REAL(KIND=realkind) :: k1_C_2i, k2_C_2i, k3_C_2i, k4_C_2i
REAL(KIND=realkind) :: k1_rho_N, k2_rho_N, k3_rho_N, k4_rho_N
REAL(KIND=realkind) :: k1_C_J, k2_C_J, k3_C_J, k4_C_J
REAL(KIND=realkind) :: k1_d_J, k2_d_J, k3_d_J, k4_d_J
REAL(KIND=realkind) :: t
REAL(KIND=realkind) :: C_v, C_i, C_2i, rho_N, C_J, d_J
REAL(KIND=realkind) :: C_v_ini, C_i_ini, C_2i_ini, rho_N_ini, C_J_ini, d_J_ini
REAL(KIND=realkind) :: C_v_tmp, C_i_tmp, C_2i_tmp, rho_N_tmp, C_J_tmp, d_J_tmp
!!!=== CONSTANTS ===============================================================================================================
Q_v = 1.0_realkind
Q_i = 1.0_realkind
Q_2i = 1.0_realkind
D_v = 1.0_realkind
D_i = 1.0_realkind
v_I = 1.0_realkind
v_2i = 1.0_realkind
v_D = 1.0_realkind
v_N = 1.0_realkind
K_iv = 1.0_realkind
r_iv = 1.0_realkind
k_gb = 1.0_realkind
a_0 = 1.0_realkind
Omega = 1.0_realkind
b_v = 1.0_realkind
f_1 = 1.0_realkind
f_2 = 1.0_realkind
d_N = 1.0_realkind
P_sl = 1.0_realkind
z_vN = 1.0_realkind
z_iN = 1.0_realkind
z_vL = 1.0_realkind
z_iL = 1.0_realkind
C_v_ini = 1.0_realkind
C_i_ini = 1.0_realkind
C_2i_ini = 1.0_realkind
rho_N_ini = 1.0_realkind
C_J_ini = 1.0_realkind
d_J_ini = 1.0_realkind
t = 0.0_realkind ! initial time
dt = 1.0E-3_realkind ! time increment
n_time_step = 3000 ! maximum number of time steps
n_write_step = 10 ! write results after every 'n_write_step' time steps
!!!=== INITIALIZATION ==========================================================================================================
dt_half = dt / 2
dt_sixth = dt / 6
C_v_factor1 = k_gb ** 2 * D_v
C_v_factor2 = 4 * pi * a_0 ** 2 * D_v / Omega
C_i_factor1 = k_gb ** 2 * D_i
C_i_factor2 = 16 * pi * r_iv * D_i
C_i_factor3 = 4 * pi * a_0 ** 2 * D_v / Omega
C_2i_factor1 = 8 * pi * r_iv * D_i / Omega ** 2
C_2i_factor2 = 4 * pi * r_iv * D_i / Omega
C_2i_factor3 = pi * v_2i / b_v
rho_N_factor1 = f_1 * ABS(v_D) * pi / d_N
rho_N_factor2 = f_2 * ABS(v_N) / d_N
C_J_factor1 = pi * v_I / (2 * a_0)
C_J_factor2 = 4 * v_I / d_N ** 2
C_J_factor3 = 8 * v_I
C_J_factor4 = f_1 * ABS(v_D) / d_N
d_J_factor1 = 2 * a_0
d_J_factor2 = pi * v_2i / (2 * a_0)
d_J_factor3 = 4 * v_I / (P_sl * d_N ** 2)
d_J_factor4 = 8 * v_I
C_v = C_v_ini
C_i = C_i_ini
C_2i = C_2i_ini
rho_N = rho_N_ini
C_J = C_J_ini
d_J = d_J_ini
i_write_step = 0
i_write = 1
! 123456 23456789 23456789012345678901234 23 23456789012345678901234 23456789012345678901234 23456789012345678901234 23456789012345678901234 23456789012345678901234 23456789012345678901234
WRITE(*, "(A)") "#...i step time C_v C_i C_2i&
& rho_N C_I d_J"
WRITE(*, "(I6,I9,ES24.15E3,3x,6ES24.15E3)") i_write, 0, t, C_v, C_i, C_2i, rho_N, C_J, d_J
!!!=== CALCULATIONS ============================================================================================================
DO i_time_step = 1, n_time_step
k1_C_v = Eqn_C_v (C_v, C_i, C_2i, rho_N, C_J, d_J)
k1_C_i = Eqn_C_i (C_v, C_i, C_2i, rho_N, C_J, d_J)
k1_C_2i = Eqn_C_2i (C_v, C_i, C_2i, rho_N, C_J, d_J)
k1_rho_N = Eqn_rho_N(C_v, C_i, C_2i, rho_N, C_J, d_J)
k1_C_J = Eqn_C_J (C_v, C_i, C_2i, rho_N, C_J, d_J)
k1_d_J = Eqn_d_J (C_v, C_i, C_2i, rho_N, C_J, d_J)
C_v_tmp = C_v + dt_half * k1_C_v
C_i_tmp = C_i + dt_half * k1_C_i
C_2i_tmp = C_2i + dt_half * k1_C_2i
rho_N_tmp = rho_N + dt_half * k1_rho_N
C_J_tmp = C_J + dt_half * k1_C_J
d_J_tmp = d_J + dt_half * k1_d_J
k2_C_v = Eqn_C_v (C_v_tmp, C_i_tmp, C_2i_tmp, rho_N_tmp, C_J_tmp, d_J_tmp)
k2_C_i = Eqn_C_i (C_v_tmp, C_i_tmp, C_2i_tmp, rho_N_tmp, C_J_tmp, d_J_tmp)
k2_C_2i = Eqn_C_2i (C_v_tmp, C_i_tmp, C_2i_tmp, rho_N_tmp, C_J_tmp, d_J_tmp)
k2_rho_N = Eqn_rho_N(C_v_tmp, C_i_tmp, C_2i_tmp, rho_N_tmp, C_J_tmp, d_J_tmp)
k2_C_J = Eqn_C_J (C_v_tmp, C_i_tmp, C_2i_tmp, rho_N_tmp, C_J_tmp, d_J_tmp)
k2_d_J = Eqn_d_J (C_v_tmp, C_i_tmp, C_2i_tmp, rho_N_tmp, C_J_tmp, d_J_tmp)
C_v_tmp = C_v + dt_half * k2_C_v
C_i_tmp = C_i + dt_half * k2_C_i
C_2i_tmp = C_2i + dt_half * k2_C_2i
rho_N_tmp = rho_N + dt_half * k2_rho_N
C_J_tmp = C_J + dt_half * k2_C_J
d_J_tmp = d_J + dt_half * k2_d_J
k3_C_v = Eqn_C_v (C_v_tmp, C_i_tmp, C_2i_tmp, rho_N_tmp, C_J_tmp, d_J_tmp)
k3_C_i = Eqn_C_i (C_v_tmp, C_i_tmp, C_2i_tmp, rho_N_tmp, C_J_tmp, d_J_tmp)
k3_C_2i = Eqn_C_2i (C_v_tmp, C_i_tmp, C_2i_tmp, rho_N_tmp, C_J_tmp, d_J_tmp)
k3_rho_N = Eqn_rho_N(C_v_tmp, C_i_tmp, C_2i_tmp, rho_N_tmp, C_J_tmp, d_J_tmp)
k3_C_J = Eqn_C_J (C_v_tmp, C_i_tmp, C_2i_tmp, rho_N_tmp, C_J_tmp, d_J_tmp)
k3_d_J = Eqn_d_J (C_v_tmp, C_i_tmp, C_2i_tmp, rho_N_tmp, C_J_tmp, d_J_tmp)
C_v_tmp = C_v + dt * k3_C_v
C_i_tmp = C_i + dt * k3_C_i
C_2i_tmp = C_2i + dt * k3_C_2i
rho_N_tmp = rho_N + dt * k3_rho_N
C_J_tmp = C_J + dt * k3_C_J
d_J_tmp = d_J + dt * k3_d_J
k4_C_v = Eqn_C_v (C_v_tmp, C_i_tmp, C_2i_tmp, rho_N_tmp, C_J_tmp, d_J_tmp)
k4_C_i = Eqn_C_i (C_v_tmp, C_i_tmp, C_2i_tmp, rho_N_tmp, C_J_tmp, d_J_tmp)
k4_C_2i = Eqn_C_2i (C_v_tmp, C_i_tmp, C_2i_tmp, rho_N_tmp, C_J_tmp, d_J_tmp)
k4_rho_N = Eqn_rho_N(C_v_tmp, C_i_tmp, C_2i_tmp, rho_N_tmp, C_J_tmp, d_J_tmp)
k4_C_J = Eqn_C_J (C_v_tmp, C_i_tmp, C_2i_tmp, rho_N_tmp, C_J_tmp, d_J_tmp)
k4_d_J = Eqn_d_J (C_v_tmp, C_i_tmp, C_2i_tmp, rho_N_tmp, C_J_tmp, d_J_tmp)
t = t + dt
C_v = C_v + (k1_C_v + 2 * (k2_C_v + k3_C_v ) + k4_C_v ) * dt_sixth
C_i = C_i + (k1_C_i + 2 * (k2_C_i + k3_C_i ) + k4_C_i ) * dt_sixth
C_2i = C_2i + (k1_C_2i + 2 * (k2_C_2i + k3_C_2i ) + k4_C_2i ) * dt_sixth
rho_N = rho_N + (k1_rho_N + 2 * (k2_rho_N + k3_rho_N) + k4_rho_N) * dt_sixth
C_J = C_J + (k1_C_J + 2 * (k2_C_J + k3_C_J ) + k4_C_J ) * dt_sixth
d_J = d_J + (k1_d_J + 2 * (k2_d_J + k3_d_J ) + k4_d_J ) * dt_sixth
IF (n_write_step > 0) THEN
i_write_step = i_write_step + 1
IF (i_write_step == n_write_step) THEN
i_write = i_write + 1
WRITE(*, "(I6,I9,ES24.15E3,3x,6ES24.15E3)") i_write, i_time_step, t, C_v, C_i, C_2i, rho_N, C_J, d_J
i_write_step = 0
END IF
END IF
END DO
IF ((n_write_step <= 0) .OR. (i_write_step > 0)) THEN
i_write = i_write + 1
WRITE(*, "(I6,I9,ES24.15E3,3x,6ES24.15E3)") i_write, n_time_step, t, C_v, C_i, C_2i, rho_N, C_J, d_J
END IF
CONTAINS
!!!#################################################################################################################################
REAL(KIND=realkind) FUNCTION K_vN(x)
REAL(KIND=realkind), INTENT(IN) :: x
K_vN = z_vN * x
END FUNCTION K_vN
!!!#################################################################################################################################
REAL(KIND=realkind) FUNCTION K_iN(x)
REAL(KIND=realkind), INTENT(IN) :: x
K_iN = z_iN * x
END FUNCTION K_iN
!!!#################################################################################################################################
REAL(KIND=realkind) FUNCTION K_vL(x)
REAL(KIND=realkind), INTENT(IN) :: x
K_vL = z_vL * x
END FUNCTION K_vL
!!!#################################################################################################################################
REAL(KIND=realkind) FUNCTION K_iL(x)
REAL(KIND=realkind), INTENT(IN) :: x
K_iL = z_iL * x
END FUNCTION K_iL
!!!#################################################################################################################################
REAL(KIND=realkind) FUNCTION Eqn_C_v(C_v, C_i, C_2i, rho_N, C_J, d_J)
REAL(KIND=realkind), INTENT(IN) :: C_v, C_i, C_2i, rho_N, C_J, d_J
Eqn_C_v = Q_v - (K_iv * C_i + K_vN(rho_N) * D_v + K_vL(pi * C_J * d_J) * D_v + C_v_factor1 + C_v_factor2 * C_2i) * C_v
END FUNCTION Eqn_C_v
!!!#################################################################################################################################
REAL(KIND=realkind) FUNCTION Eqn_C_i(C_v, C_i, C_2i, rho_N, C_J, d_J)
REAL(KIND=realkind), INTENT(IN) :: C_v, C_i, C_2i, rho_N, C_J, d_J
Eqn_C_i = Q_i - (K_iv * C_v + K_iN(rho_N) * D_i + K_iL(pi * C_J * d_J) * D_i + C_i_factor1 + C_i_factor2 * C_i) * C_i &
+ C_i_factor3 * C_v * C_2i
!
END FUNCTION Eqn_C_i
!!!#################################################################################################################################
REAL(KIND=realkind) FUNCTION Eqn_C_2i(C_v, C_i, C_2i, rho_N, C_J, d_J)
REAL(KIND=realkind), INTENT(IN) :: C_v, C_i, C_2i, rho_N, C_J, d_J
Eqn_C_2i = Q_2i + C_2i_factor1 * C_i ** 2 - (C_2i_factor2 * C_v + C_2i_factor3) * C_2i
END FUNCTION Eqn_C_2i
!!!#################################################################################################################################
REAL(KIND=realkind) FUNCTION Eqn_rho_N(C_v, C_i, C_2i, rho_N, C_J, d_J)
REAL(KIND=realkind), INTENT(IN) :: C_v, C_i, C_2i, rho_N, C_J, d_J
Eqn_rho_N = rho_N_factor1 * d_J * C_J - rho_N_factor2 * rho_N
END FUNCTION Eqn_rho_N
!!!#################################################################################################################################
REAL(KIND=realkind) FUNCTION Eqn_C_J(C_v, C_i, C_2i, rho_N, C_J, d_J)
REAL(KIND=realkind), INTENT(IN) :: C_v, C_i, C_2i, rho_N, C_J, d_J
Eqn_C_J = C_J_factor1 * C_2i - ((C_J_factor2 + C_J_factor3 * d_J * C_J) * d_J + C_J_factor4) * C_J
END FUNCTION Eqn_C_J
!!!#################################################################################################################################
REAL(KIND=realkind) FUNCTION Eqn_d_J(C_v, C_i, C_2i, rho_N, C_J, d_J)
REAL(KIND=realkind), INTENT(IN) :: C_v, C_i, C_2i, rho_N, C_J, d_J
Eqn_d_J = v_I - (d_J - d_J_factor1) * d_J_factor2 * C_2i / C_J - ((d_N - d_J) * d_J_factor3 + d_J_factor4 * d_J ** 2 * C_J) * d_J
END FUNCTION Eqn_d_J
!!!#################################################################################################################################
END PROGRAM Solution