Optimized advec_kappa scheme

- rlim function inlined and rewritten without division and eps1
- both branches of if uvw0 > 0 calculated, then selected
  in order to enable vectorization.
by Jisk Attema and Fredrik Jansson

src/advec_kappa.f90

@@ -16,6 +16,18 @@
 !! \endlatexonly
 !! This makes the scheme monotone, but also rather dissipative.
 !!
+!! limiter phi(r) = max(0, min(2*r, 2, K(r)))   (20) in Hundsdorfer 1995
+!! K(r) = 1./3.+2./3.*r here -> kappa = 1/3 -> third-order upwind-biased scheme
+!!
+!! Changes 2020 by Jisk Attema and Fredrik Jansson:
+!! - support for non-uniform vertical grid by replacing dzi by 1/dzf(k).
+!!   neither the gradient nor the limiter has been modified.
+!! - vectorization
+!!   - rlim function inlined and rewritten without division and eps1
+!!   - both branches of if uvw0 > 0 calculated, then selected
+!!     in order to enable vectorization
+!!   - merge k-loops of the x,y,z advection steps for better cache efficiency
+!!
 !  This file is part of DALES.
 !
 ! DALES is free software; you can redistribute it and/or modify
@@ -34,7 +46,145 @@
 !  Copyright 1993-2009 Delft University of Technology, Wageningen University, Utrecht University, KNMI
 !
 
-  subroutine advecc_kappa(putin,putout)
+subroutine advecc_kappa(putin,putout)
+  use modglobal, only : i1,i2,ih,j1,j2,jh,k1,kmax,dxi,dyi,dzf
+  use modfields, only : u0, v0, w0, rhobf
+  implicit none
+  real, dimension(2-ih:i1+ih,2-jh:j1+jh,k1), intent(in) :: putin
+  real, dimension(2-ih:i1+ih,2-jh:j1+jh,k1), intent(inout) :: putout
+
+  real      d1,d2,cf
+  real :: d1m, d2m, d1p, cfm, cfp, work
+  integer   i,j,k
+
+  ! from layer 1 to 2, special case. k=2
+  do j=2,j1
+     do i=2,i1 ! YES
+        d1m = 0
+        d2m = rhobf(2) * putin(i,j,2) - rhobf(1) * putin(i,j,1)
+        cfm = rhobf(1) * putin(i,j,1)
+        d1p = rhobf(2) * putin(i,j,2) - rhobf(3) * putin(i,j,3)
+        !d2p = rhobf(1) * putin(i,j,1) - rhobf(2) * putin(i,j,2  ) ! d2p = -d2m
+        cfp = rhobf(2) * putin(i,j,2)
+
+        if (w0(i,j,2) > 0) then
+           d1 = d1m
+           d2 = d2m
+           cf = cfm
+        else
+           d1 = d1p
+           d2 = -d2m
+           cf = cfp
+        end if
+
+        work = cf + &
+             min(abs(d1), abs(d2), abs((d1/6.0) + (d2/3.0))) * &
+             (sign(0.5, d1) + sign(0.5, d2))
+
+        work = work * w0(i,j,2)
+        putout(i,j,1) = putout(i,j,1) - (1./(rhobf(1)*dzf(1)))*work
+        putout(i,j,2) = putout(i,j,2) + (1./(rhobf(2)*dzf(2)))*work
+     end do
+  end do
+
+  do k=1,kmax
+     do j=2,j1
+        do i=2,i2 ! YES
+           d2m =  putin(i  ,j,k) -putin(i-1,j,k)
+           ! d2p = -putin(i  ,j,k) +putin(i-1,j,k) ! d2p = -d2m
+           d1m = putin(i-1,j,k)-putin(i-2,j,k)
+           d1p = putin(i  ,j,k)-putin(i+1,j,k)
+           cfm = putin(i-1,j,k)
+           cfp = putin(i  ,j,k)
+
+           if (u0(i,j,k) > 0) then
+              d1 = d1m
+              d2 = d2m
+              cf = cfm
+           else
+              d1 = d1p
+              d2 = -d2m
+              cf = cfp
+           end if
+
+           work = cf + &
+                min(abs(d1), abs(d2), abs((d1/6.0) + (d2/3.0))) * &
+                (sign(0.5, d1) + sign(0.5, d2))
+
+           work = work * u0(i,j,k) * dxi
+           putout(i-1,j,k) = putout(i-1,j,k) - work
+           putout(i,j,k)   = putout(i,j,k)   + work
+        end do
+     end do
+     !  end do
+
+     !  do k=1,kmax
+     do j=2,j2
+        do i=2,i1 ! YES
+           d1m = putin(i,j-1,k)-putin(i,j-2,k)
+           d1p = putin(i,j  ,k)-putin(i,j+1,k)
+           d2m = putin(i,j  ,k)-putin(i,j-1,k)
+           !d2p = putin(i,j-1,k)-putin(i,j  ,k) ! d2p = -d2m
+           cfm = putin(i,j-1,k)
+           cfp = putin(i,j  ,k)
+
+           if (v0(i,j,k) > 0) then
+              d1 = d1m
+              d2 = d2m
+              cf = cfm
+           else
+              d1 = d1p
+              d2 = -d2m
+              cf = cfp
+           end if
+
+           work = cf + &
+                min(abs(d1), abs(d2), abs((d1/6.0) + (d2/3.0))) * &
+                (sign(0.5, d1) + sign(0.5, d2))
+
+           work = work * v0(i,j,k) * dyi
+           putout(i,j-1,k) = putout(i,j-1,k) - work
+           putout(i,j,k)   = putout(i,j,k)   + work
+        end do
+     end do
+     !  end do
+
+     !  do k=3,kmax
+     if (k >= 3) then
+        do j=2,j1
+           do i=2,i1 ! YES
+              d1m = rhobf(k-1) * putin(i,j,k-1) - rhobf(k-2) * putin(i,j,k-2)
+              d2m = rhobf(k)   * putin(i,j,k  ) - rhobf(k-1) * putin(i,j,k-1)
+              d1p = rhobf(k)   * putin(i,j,k  ) - rhobf(k+1) * putin(i,j,k+1)
+              ! d2p = rhobf(k-1) * putin(i,j,k-1) - rhobf(k)   * putin(i,j,k  ) ! d2p = -d2m
+              cfm = rhobf(k-1) * putin(i,j,k-1)
+              cfp = rhobf(k)   * putin(i,j,k  )
+
+              if (w0(i,j,k) > 0) then
+                 d1 = d1m
+                 d2 = d2m
+                 cf = cfm
+              else
+                 d1 = d1p
+                 d2 = -d2m
+                 cf = cfp
+              end if
+
+              work = cf + &
+                   min(abs(d1), abs(d2), abs((d1/6.0) + (d2/3.0))) * &
+                   (sign(0.5, d1) + sign(0.5, d2))
+
+              work = work * w0(i,j,k)
+              putout(i,j,k-1) = putout(i,j,k-1) - (1./(rhobf(k-1)*dzf(k-1)))*work
+              putout(i,j,k)   = putout(i,j,k)   + (1./(rhobf(k)  *dzf(k)  ))*work
+           end do
+        end do
+     end if
+  end do
+end subroutine advecc_kappa
+
+
+subroutine advecc_kappa_old(putin,putout)
 
   use modglobal, only : i1,i2,ih,j1,j2,jh,k1,kmax,dxi,dyi,dzf
   use modfields, only : u0, v0, w0, rhobf
@@ -121,7 +271,7 @@ subroutine advecc_kappa(putin,putout)
     end do
   end do
 
-  end subroutine advecc_kappa
+  end subroutine advecc_kappa_old
 
 subroutine  halflev_kappa(putin,putout)