--- /dev/null
+
+c---------------------------------------------------------------------
+c---------------------------------------------------------------------
+
+ subroutine verify(no_time_steps, class, verified)
+
+c---------------------------------------------------------------------
+c---------------------------------------------------------------------
+
+c---------------------------------------------------------------------
+c verification routine
+c---------------------------------------------------------------------
+
+ include 'header.h'
+ include 'mpinpb.h'
+
+ double precision xcrref(5),xceref(5),xcrdif(5),xcedif(5),
+ > epsilon, xce(5), xcr(5), dtref
+ integer m, no_time_steps
+ character class
+ logical verified
+
+c---------------------------------------------------------------------
+c tolerance level
+c---------------------------------------------------------------------
+ epsilon = 1.0d-08
+
+
+c---------------------------------------------------------------------
+c compute the error norm and the residual norm, and exit if not printing
+c---------------------------------------------------------------------
+ call error_norm(xce)
+ call copy_faces
+
+ call rhs_norm(xcr)
+
+ do m = 1, 5
+ xcr(m) = xcr(m) / dt
+ enddo
+
+ if (node .ne. 0) return
+
+ class = 'U'
+ verified = .true.
+
+ do m = 1,5
+ xcrref(m) = 1.0
+ xceref(m) = 1.0
+ end do
+
+c---------------------------------------------------------------------
+c reference data for 12X12X12 grids after 100 time steps, with DT = 1.50d-02
+c---------------------------------------------------------------------
+ if ( (grid_points(1) .eq. 12 ) .and.
+ > (grid_points(2) .eq. 12 ) .and.
+ > (grid_points(3) .eq. 12 ) .and.
+ > (no_time_steps .eq. 100 )) then
+
+ class = 'S'
+ dtref = 1.5d-2
+
+c---------------------------------------------------------------------
+c Reference values of RMS-norms of residual.
+c---------------------------------------------------------------------
+ xcrref(1) = 2.7470315451339479d-02
+ xcrref(2) = 1.0360746705285417d-02
+ xcrref(3) = 1.6235745065095532d-02
+ xcrref(4) = 1.5840557224455615d-02
+ xcrref(5) = 3.4849040609362460d-02
+
+c---------------------------------------------------------------------
+c Reference values of RMS-norms of solution error.
+c---------------------------------------------------------------------
+ xceref(1) = 2.7289258557377227d-05
+ xceref(2) = 1.0364446640837285d-05
+ xceref(3) = 1.6154798287166471d-05
+ xceref(4) = 1.5750704994480102d-05
+ xceref(5) = 3.4177666183390531d-05
+
+
+c---------------------------------------------------------------------
+c reference data for 36X36X36 grids after 400 time steps, with DT = 1.5d-03
+c---------------------------------------------------------------------
+ elseif ( (grid_points(1) .eq. 36) .and.
+ > (grid_points(2) .eq. 36) .and.
+ > (grid_points(3) .eq. 36) .and.
+ > (no_time_steps . eq. 400) ) then
+
+ class = 'W'
+ dtref = 1.5d-3
+
+c---------------------------------------------------------------------
+c Reference values of RMS-norms of residual.
+c---------------------------------------------------------------------
+ xcrref(1) = 0.1893253733584d-02
+ xcrref(2) = 0.1717075447775d-03
+ xcrref(3) = 0.2778153350936d-03
+ xcrref(4) = 0.2887475409984d-03
+ xcrref(5) = 0.3143611161242d-02
+
+c---------------------------------------------------------------------
+c Reference values of RMS-norms of solution error.
+c---------------------------------------------------------------------
+ xceref(1) = 0.7542088599534d-04
+ xceref(2) = 0.6512852253086d-05
+ xceref(3) = 0.1049092285688d-04
+ xceref(4) = 0.1128838671535d-04
+ xceref(5) = 0.1212845639773d-03
+
+c---------------------------------------------------------------------
+c reference data for 64X64X64 grids after 400 time steps, with DT = 1.5d-03
+c---------------------------------------------------------------------
+ elseif ( (grid_points(1) .eq. 64) .and.
+ > (grid_points(2) .eq. 64) .and.
+ > (grid_points(3) .eq. 64) .and.
+ > (no_time_steps . eq. 400) ) then
+
+ class = 'A'
+ dtref = 1.5d-3
+
+c---------------------------------------------------------------------
+c Reference values of RMS-norms of residual.
+c---------------------------------------------------------------------
+ xcrref(1) = 2.4799822399300195d0
+ xcrref(2) = 1.1276337964368832d0
+ xcrref(3) = 1.5028977888770491d0
+ xcrref(4) = 1.4217816211695179d0
+ xcrref(5) = 2.1292113035138280d0
+
+c---------------------------------------------------------------------
+c Reference values of RMS-norms of solution error.
+c---------------------------------------------------------------------
+ xceref(1) = 1.0900140297820550d-04
+ xceref(2) = 3.7343951769282091d-05
+ xceref(3) = 5.0092785406541633d-05
+ xceref(4) = 4.7671093939528255d-05
+ xceref(5) = 1.3621613399213001d-04
+
+c---------------------------------------------------------------------
+c reference data for 102X102X102 grids after 400 time steps,
+c with DT = 1.0d-03
+c---------------------------------------------------------------------
+ elseif ( (grid_points(1) .eq. 102) .and.
+ > (grid_points(2) .eq. 102) .and.
+ > (grid_points(3) .eq. 102) .and.
+ > (no_time_steps . eq. 400) ) then
+
+ class = 'B'
+ dtref = 1.0d-3
+
+c---------------------------------------------------------------------
+c Reference values of RMS-norms of residual.
+c---------------------------------------------------------------------
+ xcrref(1) = 0.6903293579998d+02
+ xcrref(2) = 0.3095134488084d+02
+ xcrref(3) = 0.4103336647017d+02
+ xcrref(4) = 0.3864769009604d+02
+ xcrref(5) = 0.5643482272596d+02
+
+c---------------------------------------------------------------------
+c Reference values of RMS-norms of solution error.
+c---------------------------------------------------------------------
+ xceref(1) = 0.9810006190188d-02
+ xceref(2) = 0.1022827905670d-02
+ xceref(3) = 0.1720597911692d-02
+ xceref(4) = 0.1694479428231d-02
+ xceref(5) = 0.1847456263981d-01
+
+c---------------------------------------------------------------------
+c reference data for 162X162X162 grids after 400 time steps,
+c with DT = 0.67d-03
+c---------------------------------------------------------------------
+ elseif ( (grid_points(1) .eq. 162) .and.
+ > (grid_points(2) .eq. 162) .and.
+ > (grid_points(3) .eq. 162) .and.
+ > (no_time_steps . eq. 400) ) then
+
+ class = 'C'
+ dtref = 0.67d-3
+
+c---------------------------------------------------------------------
+c Reference values of RMS-norms of residual.
+c---------------------------------------------------------------------
+ xcrref(1) = 0.5881691581829d+03
+ xcrref(2) = 0.2454417603569d+03
+ xcrref(3) = 0.3293829191851d+03
+ xcrref(4) = 0.3081924971891d+03
+ xcrref(5) = 0.4597223799176d+03
+
+c---------------------------------------------------------------------
+c Reference values of RMS-norms of solution error.
+c---------------------------------------------------------------------
+ xceref(1) = 0.2598120500183d+00
+ xceref(2) = 0.2590888922315d-01
+ xceref(3) = 0.5132886416320d-01
+ xceref(4) = 0.4806073419454d-01
+ xceref(5) = 0.5483377491301d+00
+
+c---------------------------------------------------------------------
+c reference data for 408X408X408 grids after 500 time steps,
+c with DT = 0.3d-03
+c---------------------------------------------------------------------
+ elseif ( (grid_points(1) .eq. 408) .and.
+ > (grid_points(2) .eq. 408) .and.
+ > (grid_points(3) .eq. 408) .and.
+ > (no_time_steps . eq. 500) ) then
+
+ class = 'D'
+ dtref = 0.30d-3
+
+c---------------------------------------------------------------------
+c Reference values of RMS-norms of residual.
+c---------------------------------------------------------------------
+ xcrref(1) = 0.1044696216887d+05
+ xcrref(2) = 0.3204427762578d+04
+ xcrref(3) = 0.4648680733032d+04
+ xcrref(4) = 0.4238923283697d+04
+ xcrref(5) = 0.7588412036136d+04
+
+c---------------------------------------------------------------------
+c Reference values of RMS-norms of solution error.
+c---------------------------------------------------------------------
+ xceref(1) = 0.5089471423669d+01
+ xceref(2) = 0.5323514855894d+00
+ xceref(3) = 0.1187051008971d+01
+ xceref(4) = 0.1083734951938d+01
+ xceref(5) = 0.1164108338568d+02
+
+c---------------------------------------------------------------------
+c reference data for 1020X1020X1020 grids after 500 time steps,
+c with DT = 0.1d-03
+c---------------------------------------------------------------------
+ elseif ( (grid_points(1) .eq. 1020) .and.
+ > (grid_points(2) .eq. 1020) .and.
+ > (grid_points(3) .eq. 1020) .and.
+ > (no_time_steps . eq. 500) ) then
+
+ class = 'E'
+ dtref = 0.10d-3
+
+c---------------------------------------------------------------------
+c Reference values of RMS-norms of residual.
+c---------------------------------------------------------------------
+ xcrref(1) = 0.6255387422609d+05
+ xcrref(2) = 0.1495317020012d+05
+ xcrref(3) = 0.2347595750586d+05
+ xcrref(4) = 0.2091099783534d+05
+ xcrref(5) = 0.4770412841218d+05
+
+c---------------------------------------------------------------------
+c Reference values of RMS-norms of solution error.
+c---------------------------------------------------------------------
+ xceref(1) = 0.6742735164909d+02
+ xceref(2) = 0.5390656036938d+01
+ xceref(3) = 0.1680647196477d+02
+ xceref(4) = 0.1536963126457d+02
+ xceref(5) = 0.1575330146156d+03
+
+ else
+ verified = .false.
+ endif
+
+c---------------------------------------------------------------------
+c verification test for residuals if gridsize is one of
+c the defined grid sizes above (class .ne. 'U')
+c---------------------------------------------------------------------
+
+c---------------------------------------------------------------------
+c Compute the difference of solution values and the known reference values.
+c---------------------------------------------------------------------
+ do m = 1, 5
+
+ xcrdif(m) = dabs((xcr(m)-xcrref(m))/xcrref(m))
+ xcedif(m) = dabs((xce(m)-xceref(m))/xceref(m))
+
+ enddo
+
+c---------------------------------------------------------------------
+c Output the comparison of computed results to known cases.
+c---------------------------------------------------------------------
+
+ if (class .ne. 'U') then
+ write(*, 1990) class
+ 1990 format(' Verification being performed for class ', a)
+ write (*,2000) epsilon
+ 2000 format(' accuracy setting for epsilon = ', E20.13)
+ verified = (dabs(dt-dtref) .le. epsilon)
+ if (.not.verified) then
+ class = 'U'
+ write (*,1000) dtref
+ 1000 format(' DT does not match the reference value of ',
+ > E15.8)
+ endif
+ else
+ write(*, 1995)
+ 1995 format(' Unknown class')
+ endif
+
+
+ if (class .ne. 'U') then
+ write (*,2001)
+ else
+ write (*, 2005)
+ endif
+
+ 2001 format(' Comparison of RMS-norms of residual')
+ 2005 format(' RMS-norms of residual')
+ do m = 1, 5
+ if (class .eq. 'U') then
+ write(*, 2015) m, xcr(m)
+ else if (xcrdif(m) .le. epsilon) then
+ write (*,2011) m,xcr(m),xcrref(m),xcrdif(m)
+ else
+ verified = .false.
+ write (*,2010) m,xcr(m),xcrref(m),xcrdif(m)
+ endif
+ enddo
+
+ if (class .ne. 'U') then
+ write (*,2002)
+ else
+ write (*,2006)
+ endif
+ 2002 format(' Comparison of RMS-norms of solution error')
+ 2006 format(' RMS-norms of solution error')
+
+ do m = 1, 5
+ if (class .eq. 'U') then
+ write(*, 2015) m, xce(m)
+ else if (xcedif(m) .le. epsilon) then
+ write (*,2011) m,xce(m),xceref(m),xcedif(m)
+ else
+ verified = .false.
+ write (*,2010) m,xce(m),xceref(m),xcedif(m)
+ endif
+ enddo
+
+ 2010 format(' FAILURE: ', i2, E20.13, E20.13, E20.13)
+ 2011 format(' ', i2, E20.13, E20.13, E20.13)
+ 2015 format(' ', i2, E20.13)
+
+ if (class .eq. 'U') then
+ write(*, 2022)
+ write(*, 2023)
+ 2022 format(' No reference values provided')
+ 2023 format(' No verification performed')
+ else if (verified) then
+ write(*, 2020)
+ 2020 format(' Verification Successful')
+ else
+ write(*, 2021)
+ 2021 format(' Verification failed')
+ endif
+
+ return
+
+
+ end
