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|
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#include "ctrparam.h" |
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|
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! ============================================================ |
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! |
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! PDADV.F: Subroutines of Modified Bott advection scheme |
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! |
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! ------------------------------------------------------------ |
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! |
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! Author: Chien Wang |
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! MIT Joint Program on Science and Policy |
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! of Global Change |
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! |
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! ---------------------------------------------------------- |
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! |
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! Revision History: |
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! |
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! When Who What |
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! ---- ---------- ------- |
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! 080200 Chien Wang repack based on CliChem3 & add cpp |
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! |
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! ========================================================== |
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|
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C ************************************** |
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C ************************************** |
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SUBROUTINE pdadv1(C,W4,W2,W1,N) |
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C ************************************** |
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C ************************************** |
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C |
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C ****************************************************************** |
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C |
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C This is a subroutine for the first part of Bott's advection scheme. |
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C |
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C Andreas Bott 1989: A Positive Definite Advection scheme obtained |
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C by Nonlinear Renormalization of the advective fluxes |
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C Mon. Wea. Rev. 117 1006-15 |
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C |
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C Fourth Order: with coefficients from Mon. Wea. Rev. 117 2633-36 |
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C |
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C Input: C=U*DT/DX[N+1] Output: W4[3:N1,5],W2[2;3;n1;n,3] and |
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C W1[1;2;n;n+1,2] |
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C On the Staggered Grid: C(i')----Q(i)----C(i'+1) |
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C |
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C ****************************************************************** |
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|
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PARAMETER ( C0=1.0/1920.0,C1=1.0/384.00,C2=1.0/384.0 |
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& , C3=1.0/768.00,C4=1.0/3840.0,EP=1.0E-15 ) |
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c parameter (cc0=1.,cc1=1./16.,cc2=1./48.) |
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parameter (cc0=-1./24.,cc1=1./16.,cc2=1./48.) |
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c parameter (cc0=-1./24.,cc1=1./16.,cc2=1./16.) |
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|
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DIMENSION C(N+1),W4(N,5),W2(N,3),W1(4,2) |
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|
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! ----------------------------------------------------------- |
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|
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#if ( defined CPL_CHEM ) |
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|
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n1=n-1 |
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n2=n-2 |
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n3=n-3 |
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|
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do 1 i=1,n |
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do 2 j=1,5 |
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w4(i,j)=0.0 |
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2 continue |
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do 3 j=1,3 |
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w2(i,j)=0.0 |
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3 continue |
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1 continue |
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|
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C |
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C GET THE COEFFICIENTS DEPENDENT ON C ONLY |
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C |
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w1(1,1)=abs(c(1)) |
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w1(1,2)=0.0 |
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w1(2,1)=abs(c(2)) |
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w1(2,2)=2.0*w1(2,1)*(1.-w1(2,1)) |
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w1(3,1)=abs(c(n)) |
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w1(3,2)=2.0*w1(3,1)*(1.-w1(3,1)) |
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w1(4,1)=abs(c(n+1)) |
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w1(4,2)=0.0 |
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|
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rr1=abs(c(2)) |
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rr2=1.-(rr1+rr1) |
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r1=rr2**2 |
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r2=r1*rr2 |
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w2(2,1)=rr1*cc0 |
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w2(2,2)=(1.-r1)*cc1 |
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w2(2,3)=(1.-r2)*cc2 |
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|
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rr1=abs(c(3)) |
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rr2=1.-(rr1+rr1) |
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r1=rr2**2 |
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r2=r1*rr2 |
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w2(3,1)=rr1*cc0 |
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w2(3,2)=(1.-r1)*cc1 |
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w2(3,3)=(1.-r2)*cc2 |
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|
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rr1=abs(c(4)) |
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rr2=1.-(rr1+rr1) |
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r1=rr2**2 |
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r2=r1*rr2 |
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w2(4,1)=rr1*cc0 |
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w2(4,2)=(1.-r1)*cc1 |
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w2(4,3)=(1.-r2)*cc2 |
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|
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rr1=abs(c(n2)) |
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rr2=1.-(rr1+rr1) |
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r1=rr2**2 |
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r2=r1*rr2 |
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w2(n2,1)=rr1*cc0 |
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w2(n2,2)=(1.-r1)*cc1 |
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w2(n2,3)=(1.-r2)*cc2 |
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|
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rr1=abs(c(n1)) |
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rr2=1.-(rr1+rr1) |
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r1=rr2**2 |
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r2=r1*rr2 |
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w2(n1,1)=rr1*cc0 |
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w2(n1,2)=(1.-r1)*cc1 |
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w2(n1,3)=(1.-r2)*cc2 |
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|
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rr1=abs(c(n)) |
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rr2=1.-(rr1+rr1) |
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r1=rr2**2 |
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r2=r1*rr2 |
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w2(n,1)=rr1*cc0 |
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w2(n,2)=(1.-r1)*cc1 |
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w2(n,3)=(1.-r2)*cc2 |
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|
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DO 100 I = 3 ,N1 |
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|
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rr1 = ABS( C(I) ) |
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rr2 = 1.0 - (rr1+rr1) |
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R1 = Rr2*Rr2 |
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R2 = R1*Rr2 |
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R3 = R2*Rr2 |
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R4 = R3*Rr2 |
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|
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W4(I,1) = rr1 *C0 |
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W4(I,2) = (1.0-R1)*C1 |
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W4(I,3) = (1.0-R2)*C2 |
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W4(I,4) = (1.0-R3)*C3 |
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W4(I,5) = (1.0-R4)*C4 |
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|
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100 CONTINUE |
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C |
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|
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#endif |
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|
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return |
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end |
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|
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|
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C ************************************** |
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C ************************************** |
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SUBROUTINE pdadv2(C,Q,W4,W2,W1,ww,ww2,N,NOOS) |
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C ************************************** |
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C ************************************** |
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C |
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C ************************************************************* |
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C |
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C This is a subroutine for the second part of Bott's advection |
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C scheme. |
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C |
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C Andreas Bott 1989: A Positive Definite Advection scheme obtained |
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C by Nonlinear Renormalization of the advective fluxes |
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C Mon. Wea. Rev. 117 1006-15 |
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C |
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C Fourth Order: with coefficients from Mon. Wea. Rev. 117 2633-36 |
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C |
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C Input: C=U*DT/DX[N+1] & Q[N] Output: Q[2 N-1] |
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C On the Staggered Grid: C(i')----Q(i)----C(i'+1) |
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C |
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C NOSS = 1: Perform non-oscillatory option |
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C |
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PARAMETER ( C0=1.0/1920.0,C1=1.0/384.00,C2=1.0/384.0 |
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& , C3=1.0/768.00,C4=1.0/3840.0,EP=1.0E-15 ) |
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c parameter ( cc0=1.,cc1=1./16.,cc2=1./24.) |
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parameter ( cc0=-1./24.,cc1=1./16.,cc2=1./24.) |
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c parameter ( cc0=-1./24.,cc1=1./16.,cc2=1./16.) |
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|
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DIMENSION C(N+1),Q(N),W4(n,5),w2(n,3),w1(4,2), |
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& ww(n+1,5),ww2(n+1,5) |
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C |
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|
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! -------------------------------------------------------- |
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|
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#if ( defined CPL_CHEM ) |
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|
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N1 = N-1 |
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N2 = N-2 |
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N3 = N-3 |
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|
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do 1 i=1,(n+1)*5 |
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ww (i,1)=0.0 |
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ww2(i,1)=0.0 |
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1 continue |
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|
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C |
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C FOR ANY POSITIVE-DEFINITE Q ADVECTION |
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C |
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C 1. First order scheme for i=2 and n: |
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|
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a0=q(1) |
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a1=q(2)-q(1) |
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ww(1,1)=a0 |
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ww(1,2)=a0*w1(1,1) |
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ww(2,3)=a0*w1(2,1)+a1*w1(2,2) |
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|
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a0=q(n) |
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a1=q(n)-q(n1) |
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ww(n,1)=a0 |
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ww(n,2)=a0*w1(3,1)-a1*w1(3,2) |
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ww(n+1,3)=a0*w1(4,1) |
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|
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C 2. Second order scheme for i=2,3,n1,n: |
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|
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ww2(1,1)=ww(1,1) |
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ww2(1,2)=ww(1,2) |
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ww2(2,3)=ww(2,3) |
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|
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a0=q(3)-26.*q(2)+q(1) |
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a1=q(3)-q(1) |
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a2=q(3)-2.*q(2)+q(1) |
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ww2(2,1)=cc0*a0+cc2*a2 |
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ww2(2,2)=a0*w2(2,1)-a1*w2(2,2)+a2*w2(2,3) |
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ww2(3,3)=a0*w2(3,1)+a1*w2(3,2)+a2*w2(3,3) |
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|
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a0=q(4)-26.*q(3)+q(2) |
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a1=q(4)-q(2) |
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a2=q(4)-2.*q(3)+q(2) |
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ww2(3,1)=cc0*a0+cc2*a2 |
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ww2(3,2)=a0*w2(3,1)-a1*w2(3,2)+a2*w2(3,3) |
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ww2(4,3)=a0*w2(4,1)+a1*w2(4,2)+a2*w2(4,3) |
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|
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a0=q(n1)-26.*q(n2)+q(n3) |
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a1=q(n1)-q(n3) |
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a2=q(n1)-2.0*q(n2)+q(n3) |
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ww2(n2,1)=cc0*a0+cc2*a2 |
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ww2(n2,2)=a0*w2(n2,1)-a1*w2(n2,2)+a2*w2(n2,3) |
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ww2(n1,3)=a0*w2(n1,1)+a1*w2(n1,2)+a2*w2(n1,3) |
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|
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a0=q(n)-26.*q(n1)+q(n2) |
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a1=q(n)-q(n2) |
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a2=q(n)-2.*q(n1)+q(n2) |
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ww2(n1,1)=cc0*a0+cc2*a2 |
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ww2(n1,2)=a0*w2(n1,1)-a1*w2(n1,2)+a2*w2(n1,3) |
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ww2(n,3) =a0*w2( n,1)+a1*w2( n,2)+a2*w2( n,3) |
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|
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ww2(n,1) =ww(n,1) |
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ww2(n,2) =ww(n,2) |
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ww2(n+1,3)=ww(n+1,3) |
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|
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C 3. Fourth order scheme for i=3,n1: |
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|
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ww(2,1)=ww2(2,1) |
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ww(2,2)=ww2(2,2) |
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ww(3,3)=ww2(3,3) |
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|
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ww(n1,1)=ww2(n1,1) |
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ww(n1,2)=ww2(n1,2) |
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ww(n, 3)=ww2(n, 3) |
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|
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DO 200 I = 3 ,N2 |
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QL2 = Q(I-2) |
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QL1 = Q(I-1) |
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Q00 = Q(I) |
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QR1 = Q(I+1) |
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QR2 = Q(I+2) |
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QP1 = QR1+QL1 |
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QP2 = QR2+QL2 |
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QM1 = QR1-QL1 |
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QM2 = QR2-QL2 |
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C COEFFICIENTS: AREA PRESERVING FLUX FORM |
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A0 = 9.0*QP2 - 116.0*QP1 + 2134.0*Q00 |
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A1 =-5.0*QM2 + 34.0*QM1 |
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A2 = -QP2 + 12.0*QP1 - 22.0*Q00 |
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A3 = QM2 - 2.0*QM1 |
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A4 = QP2 - 4.0*QP1 + 6.0*Q00 |
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C INTEGRALS: FOR THE USE OF IN/OUT FLUX OF THE GRID |
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ww(I,1) = C0*(A0+10.0*A2+A4) |
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c ww(I,1) = Q00 |
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ww(I,2) = A0*W4(I,1)-A1*W4(I,2)+A2*W4(I,3) |
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& - A3*W4(I,4)+A4*W4(I,5) |
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ww(I+1,3) = A0*W4(I+1,1)+A1*W4(I+1,2)+A2*W4(I+1,3) |
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& +A3*W4(I+1,4)+A4*W4(I+1,5) |
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200 CONTINUE |
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C |
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C RESTRICT THE INTEGRALS TO PRESERVE THE SIGN |
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C |
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I = 1 |
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IF( C(I).GT.0.0 ) THEN |
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ww(I,2) = 0.0 |
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ELSE IF( C(I).LT.0.0 ) THEN |
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ww(I,2) = max( 0.0 , ww(I,2) ) |
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ENDIF |
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DO 210 I = 2 ,N |
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IF( C(I).GT.0.0 ) THEN |
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ww(I,2) = 0.0 |
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ww(I,3) = max( 0.0 , ww(I,3) ) |
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ww2(i,2)= 0.0 |
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ww2(i,3)= max( 0.0, ww2(i,3)) |
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ELSE IF( C(I).LT.0.0 ) THEN |
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ww(I,2) = max( 0.0 , ww(I,2) ) |
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ww(I,3) = 0.0 |
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ww2(i,2)= max( 0.0, ww2(i,2) ) |
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ww2(i,3)= 0.0 |
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ENDIF |
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210 CONTINUE |
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I = N+1 |
| 312 |
IF( C(I).GT.0.0 ) THEN |
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ww(I,3) = max( 0.0 , ww(I,3) ) |
| 314 |
ELSE IF( C(I).LT.0.0 ) THEN |
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ww(I,3) = 0.0 |
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ENDIF |
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DO 220 I = 1 ,N |
| 318 |
ww(I,1) = max( ww(I,2)+ww(I+1,3)+EP , ww(I,1) ) |
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ww2(i,1) = max(ww2(i,2)+ww2(i+1,3)+ep,ww2(i,1)) |
| 320 |
220 CONTINUE |
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C |
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C GET THE WEIGHTING FACTOR |
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C |
| 324 |
DO 230 I = 1 ,N |
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ww(I,1) = Q(I) / ww(I,1) |
| 326 |
ww2(i,1) = q(i) /ww2(i,1) |
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230 CONTINUE |
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C <= ww(I,2) |
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C GET THE IN/OUT FLUX OF THE GRID I --- I+1/2 |
| 330 |
C ww(I,3) => |
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DO 250 I = 1 ,N+1 |
| 332 |
if(i.ne.n+1) ww(I,2) = ww(I,2)*ww(I,1) |
| 333 |
if(i.ne.1) ww(I,3) = ww(I,3)*ww(I-1,1) |
| 334 |
if(i.ne.n+1) ww2(i,2) = ww2(i,2)*ww2(i,1) |
| 335 |
if(i.ne.1) ww2(i,3) = ww2(i,3)*ww2(i-1,1) |
| 336 |
250 CONTINUE |
| 337 |
C |
| 338 |
IF( NOOS.NE.1 ) THEN |
| 339 |
C COMPUTE THE TOTAL ADVECTION TENDENCY |
| 340 |
|
| 341 |
c DO 300 I = 2 ,N1 |
| 342 |
q(2) =ww2(3,2)-ww2(3,3)-ww2(2,2) +ww2(2,3) |
| 343 |
q(n1)=ww2(n,2)-ww2(n,3)-ww2(n1,2)+ww2(n1,3) |
| 344 |
DO 300 I = 3 ,N2 |
| 345 |
c q(i) = ww(i+1,2)-ww(i+1,3)-ww(i,2)+ww(i,3) !tendency |
| 346 |
q(i) = ww(i+1,2)-ww(i+1,3)-ww(i,2)+ww(i,3)+q(i) !value |
| 347 |
300 CONTINUE |
| 348 |
C |
| 349 |
ELSE |
| 350 |
C |
| 351 |
C NON-OSCILLATORY OPTION: FCT LIMITER |
| 352 |
C P.K.Smolarkiewicz & W.W.Grabowski, 1990: The multidimensional |
| 353 |
C positive definite advection transport algorithm: Nonoscillatory |
| 354 |
C option, J. Comput. Phys., 86, 355-375 |
| 355 |
C |
| 356 |
C GET THE DONOR-CELL FLUXES (Low-order) |
| 357 |
|
| 358 |
DO 400 I = 2 ,N |
| 359 |
IF( C(I).GT.0.0 ) THEN |
| 360 |
ww(I,1) = Q(I-1) |
| 361 |
ELSE |
| 362 |
ww(I,1) =-Q(I) |
| 363 |
ENDIF |
| 364 |
400 CONTINUE |
| 365 |
|
| 366 |
c ww(1,1)=max(-q(1)*c(1),0.0) |
| 367 |
ww(1,1)=abs(q(1)*c(1)) |
| 368 |
if(c(1).gt.0.0)then |
| 369 |
ww(1,4)=0.0 |
| 370 |
ww(1,5)=ww(1,1) |
| 371 |
else |
| 372 |
ww(1,4)=ww(1,1) |
| 373 |
ww(1,5)=0.0 |
| 374 |
endif |
| 375 |
|
| 376 |
DO 405 I = 2 ,N |
| 377 |
ww(I,1) = ww(I,1) * C(I) |
| 378 |
ww(I,4) = 0.0 |
| 379 |
ww(I,5) = 0.0 |
| 380 |
405 CONTINUE |
| 381 |
|
| 382 |
c ww(n+1,1)=max(q(n)*c(n+1),0.0) |
| 383 |
ww(n+1,1)=abs(q(n)*c(n+1)) |
| 384 |
if(c(n+1).gt.0.0)then |
| 385 |
ww(n+1,4)=0.0 |
| 386 |
ww(n+1,5)=ww(n+1,1) |
| 387 |
else |
| 388 |
ww(n+1,4)=ww(n+1,1) |
| 389 |
ww(n+1,5)=0.0 |
| 390 |
endif |
| 391 |
|
| 392 |
DO 410 I = 2 ,N |
| 393 |
IF( C(I).GT.0.0 ) THEN |
| 394 |
ww(I,5)= ww(I,1) |
| 395 |
ELSE |
| 396 |
ww(I,4) = ww(I,1) |
| 397 |
ENDIF |
| 398 |
410 CONTINUE |
| 399 |
|
| 400 |
DO 415 I = 1 ,N |
| 401 |
ww(I,1) = ww(I+1,4) - ww(I+1,5) - ww(I,4) + ww(I,5) |
| 402 |
415 CONTINUE |
| 403 |
|
| 404 |
DO 420 I = 1 ,N |
| 405 |
ww(I,1) = ww(I,1) + Q(I) |
| 406 |
c ww(I,1) = ww(I,1) |
| 407 |
420 CONTINUE |
| 408 |
|
| 409 |
C GET THE A-FLUX = F(High-order)-F(Low-order) |
| 410 |
DO 430 I = 1 ,N |
| 411 |
ww(I,4) = ww(I,2) - ww(I,4) |
| 412 |
ww(I,5) = ww(I,3) - ww(I,5) |
| 413 |
430 CONTINUE |
| 414 |
DO 435 I = 1 ,N |
| 415 |
ww(I,2) = max( 0.0,ww(I,4) ) - min(0.0, ww(I,5) ) |
| 416 |
ww(I,3) = max( 0.0,ww(I,5) ) - min(0.0, ww(I,4) ) |
| 417 |
435 CONTINUE |
| 418 |
|
| 419 |
ww(1,4)=min(ww(1,1),ww(2,1),q(1),q(2)) |
| 420 |
ww(1,5)=max(ww(1,1),ww(2,1),q(1),q(2)) |
| 421 |
DO 440 I = 2 ,N1 |
| 422 |
J = I-1 |
| 423 |
K = I+1 |
| 424 |
ww(I,4) = min(ww(J,1),ww(I,1),ww(K,1),Q(J),Q(I),Q(K)) |
| 425 |
ww(I,5) = max(ww(J,1),ww(I,1),ww(K,1),Q(J),Q(I),Q(K)) |
| 426 |
440 CONTINUE |
| 427 |
ww(n,4)=min(ww(n1,1),ww(n,1),q(n1),q(n)) |
| 428 |
ww(n,5)=max(ww(n1,1),ww(n,1),q(n1),q(n)) |
| 429 |
|
| 430 |
DO 450 I = 1 ,N |
| 431 |
ww(I,4) =(ww(I,1)-ww(I,4)) / (ww(I,2)+ww(I+1,3)+EP) |
| 432 |
ww(I,5) =(ww(I,5)-ww(I,1)) / (ww(I,3)+ww(I+1,2)+EP) |
| 433 |
Q(I) = ww(I,01) |
| 434 |
450 CONTINUE |
| 435 |
|
| 436 |
DO 460 I = 2 ,N |
| 437 |
ww(I,1) = min( 1.0,ww(I-1,5),ww(I,4) ) |
| 438 |
460 CONTINUE |
| 439 |
DO 465 I = 2 ,N |
| 440 |
ww(I,2) = ww(I,2) * ww(I,1) |
| 441 |
465 CONTINUE |
| 442 |
DO 470 I = 2 ,N |
| 443 |
ww(I,1) = min( 1.0,ww(I-1,4),ww(I,5) ) |
| 444 |
470 CONTINUE |
| 445 |
DO 475 I = 2 ,N |
| 446 |
ww(I,3) = ww(I,3) * ww(I,1) |
| 447 |
475 CONTINUE |
| 448 |
C COMPUTE THE HIGH-ORDER ADVECTION TENDENCY |
| 449 |
DO 500 I = 2 ,N1 |
| 450 |
ww(I,1) = ww(I+1,2)-ww(I+1,3)-ww(I,2)+ww(I,3) |
| 451 |
500 CONTINUE |
| 452 |
C |
| 453 |
C COMPUTE THE TOTAL ADVECTION TENDENCY |
| 454 |
C |
| 455 |
DO 600 I = 2 ,N1 |
| 456 |
c q(i) = ww(i,1) !tendency |
| 457 |
q(i) = ww(i,1)+q(i) !value |
| 458 |
600 CONTINUE |
| 459 |
|
| 460 |
ENDIF |
| 461 |
|
| 462 |
#endif |
| 463 |
|
| 464 |
RETURN |
| 465 |
END |
| 466 |
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