fix(prt): avoid fpes, patch centroid calculation (#2119)

Fix several related issues that can occur with the generalized tracking method on vertex grids.

1. The polygon centroid formula used when dividing cells into subcells can fail due to floating (im)precision when the vertex coordinates are all large and near to one another, i.e. big grids with really small cells. One option is to do a point-in-polygon check on the result of the centroid calculation and use a simple geometric mean if it fails, but the check is not cheap. Another option is to always use the geo mean instead of the polygon centroid — to guarantee that this is safe we will need to check that the cell vertices don't "wrap around" or contain duplicates I think. In the meantime this PR aims for an 80/20 solution and uses the geometric mean if the cell has 3 vertices, otherwise the full formula. This avoids the error in the common case that the very small cell is a triangle.

2. The tracking routine could encounter floating point exceptions due to a failure to terminate particles in subcells with no exit face.

3. Avoid floating point exceptions due to log of a negative number in the subroutine to calculate travel time to exit. This is done by taking the absolute value of the argument to `log`. Is this safe? I think so because the direction of travel is determined elsewhere.

src/Solution/ParticleTracker/MethodCellTernary.f90

@@ -1,6 +1,6 @@
 module MethodCellTernaryModule
 
-  use KindModule, only: DP, I4B
+  use KindModule, only: DP, I4B, LGP
   use ErrorUtilModule, only: pstop
   use MethodModule
   use MethodSubcellPoolModule
@@ -9,7 +9,8 @@ module MethodCellTernaryModule
   use SubcellTriModule, only: SubcellTriType, create_subcell_tri
   use ParticleModule
   use GeomUtilModule, only: area
-  use ConstantsModule, only: DZERO, DONE, DTWO
+  use ConstantsModule, only: DZERO, DONE, DTWO, DSIX
+  use GeomUtilModule, only: point_in_polygon
   implicit none
 
   private
@@ -86,6 +87,7 @@ subroutine load_mct(this, particle, next_level, submethod)
     type is (SubcellTriType)
       call this%load_subcell(particle, subcell)
     end select
+
     call method_subcell_tern%init( &
       fmi=this%fmi, &
       cell=this%cell, &
@@ -137,6 +139,7 @@ subroutine pass_mct(this, particle)
       ! Subcell top (cell top)
       inface = this%nverts + 3
     end select
+
     if (inface .eq. -1) then
       particle%iboundary(2) = 0
     else if (inface .eq. 0) then
@@ -356,6 +359,8 @@ subroutine vertvelo(this)
     real(DP), allocatable, dimension(:) :: vm0y
     real(DP), allocatable, dimension(:) :: vm1x
     real(DP), allocatable, dimension(:) :: vm1y
+    ! real(DP), allocatable, dimension(:, :) :: poly
+    integer(I4B) :: nvert
 
     select type (cell => this%cell)
     type is (CellPolyType)
@@ -393,14 +398,30 @@ subroutine vertvelo(this)
       unextx = -wk2 / le
       unexty = wk1 / le
 
-      ! Cell area
-      areacell = area(this%xvert, this%yvert)
-
       ! Cell centroid (in general, this is NOT the average of the vertex coordinates)
-      sixa = areacell * 6.d0
+      areacell = area(this%xvert, this%yvert)
+      sixa = areacell * DSIX
       wk1 = -(this%xvert * this%yvertnext - this%xvertnext * this%yvert)
-      this%xctr = sum((this%xvert + this%xvertnext) * wk1) / sixa
-      this%yctr = sum((this%yvert + this%yvertnext) * wk1) / sixa
+      nvert = size(this%xvert)
+      if (nvert == 3) then
+        this%xctr = sum(this%xvert) / 3.0_DP
+        this%yctr = sum(this%yvert) / 3.0_DP
+      else
+        this%xctr = sum((this%xvert + this%xvertnext) * wk1) / sixa
+        this%yctr = sum((this%yvert + this%yvertnext) * wk1) / sixa
+      end if
+
+      ! TODO: do we need to check if center is in polygon?
+      ! only if using the centroid method which misbehaves
+      !
+      ! allocate(poly(2, nvert))
+      ! poly(1,:) = this%xvert
+      ! poly(2,:) = this%yvert
+      ! if (.not. point_in_polygon(this%xctr, this%yctr, poly)) then
+      !   print *, "error -- centroid not in cell ", this%cell%defn%icell, this%xctr, this%yctr
+      !   call pstop(1)
+      ! end if
+      ! deallocate(poly)
 
       ! Subcell areas
       do i = 1, this%nverts

src/Solution/ParticleTracker/MethodSubcellTernary.f90

@@ -11,6 +11,7 @@ module MethodSubcellTernaryModule
   use TernarySolveTrack, only: traverse_triangle, step_analytical, canonical
   use PrtFmiModule, only: PrtFmiType
   use BaseDisModule, only: DisBaseType
+  use MathUtilModule, only: is_close
   implicit none
 
   private
@@ -30,9 +31,9 @@ module MethodSubcellTernaryModule
 
   !> @brief Create a new ternary subcell tracking method.
   subroutine create_method_subcell_ternary(method)
-    ! -- dummy
+    ! dummy
     type(MethodSubcellTernaryType), pointer :: method
-    ! -- local
+    ! local
     type(SubcellTriType), pointer :: subcell
 
     allocate (method)
@@ -218,14 +219,19 @@ subroutine track_subcell(this, subcell, particle, tmax)
       ! Exit through lateral subcell face
       exitFace = itrifaceexit
       dtexit = dtexitxy
-    else if (dtexitz < dtexitxy) then
+    else if (dtexitz < dtexitxy .and. dtexitz >= 0.0_DP) then
       ! Exit through top or bottom
       if (itopbotexit == -1) then
         exitFace = 4
       else
         exitFace = 5
       end if
       dtexit = dtexitz
+    else
+      particle%istatus = 9
+      particle%advancing = .false.
+      call this%save(particle, reason=3)
+      return
     end if
     texit = particle%ttrack + dtexit
     t0 = particle%ttrack
@@ -257,17 +263,17 @@ subroutine track_subcell(this, subcell, particle, tmax)
     ! (local, unscaled) and other properties. The particle may at this
     ! point lie on a boundary of the subcell or may still be within it.
     if (texit .gt. tmax) then
-      ! -- The computed exit time is greater than the maximum time, so set
-      ! -- final time for particle trajectory equal to maximum time.
+      ! The computed exit time is greater than the maximum time, so set
+      ! final time for particle trajectory equal to maximum time.
       t = tmax
       dt = t - t0
       exitFace = 0
       particle%istatus = 1
       particle%advancing = .false.
       reason = 2 ! timestep end
     else
-      ! -- The computed exit time is less than or equal to the maximum time,
-      ! -- so set final time for particle trajectory equal to exit time.
+      ! The computed exit time is less than or equal to the maximum time,
+      ! so set final time for particle trajectory equal to exit time.
       t = texit
       dt = dtexit
       reason = 1 ! (sub)cell transition
@@ -280,6 +286,7 @@ subroutine track_subcell(this, subcell, particle, tmax)
     particle%z = z
     particle%ttrack = t
     particle%iboundary(3) = exitFace
+
     call this%save(particle, reason=reason)
   end subroutine track_subcell
 
@@ -417,7 +424,7 @@ subroutine calculate_dt(v1, v2, dx, xL, v, dvdx, &
     end if
 
     ! Compute travel time to exit face. Return with status = 0
-    dt = log(vr) / dvdx
+    dt = log(abs(vr)) / dvdx
     status = 0
   end subroutine calculate_dt
 
@@ -481,13 +488,13 @@ subroutine calculate_xyz_position(dt, rxx, rxy, ryx, ryy, sxx, sxy, syy, &
     else
       ! otherwise calculate z.
       if (izstatus .eq. 2) then
-        ! -- vz uniformly zero
+        ! vz uniformly zero
         z = zi
       else if (izstatus .eq. 1) then
-        ! -- vz uniform, nonzero
+        ! vz uniform, nonzero
         z = zi + vzi * dt
       else
-        ! -- vz nonuniform
+        ! vz nonuniform
         z = zbot + (vzi * dexp(az * dt) - vzbot) / az
       end if
     end if

src/Solution/ParticleTracker/Particle.f90

@@ -89,7 +89,6 @@ module ParticleModule
     ! state
     integer(I4B), dimension(:, :), pointer, public, contiguous :: idomain !< array of indices for domains in the tracking domain hierarchy
     integer(I4B), dimension(:, :), pointer, public, contiguous :: iboundary !< array of indices for tracking domain boundaries
-    integer(I4B), dimension(:), pointer, public, contiguous :: icp !< previous cell number (reduced)
     integer(I4B), dimension(:), pointer, public, contiguous :: icu !< cell number (user)
     integer(I4B), dimension(:), pointer, public, contiguous :: ilay !< layer
     integer(I4B), dimension(:), pointer, public, contiguous :: izone !< current zone number
@@ -133,7 +132,6 @@ subroutine allocate_particle_store(this, np, mempath)
     call mem_allocate(this%irpt, np, 'PLIRPT', mempath)
     call mem_allocate(this%iprp, np, 'PLIPRP', mempath)
     call mem_allocate(this%name, LENBOUNDNAME, np, 'PLNAME', mempath)
-    call mem_allocate(this%icp, np, 'PLICP', mempath)
     call mem_allocate(this%icu, np, 'PLICU', mempath)
     call mem_allocate(this%ilay, np, 'PLILAY', mempath)
     call mem_allocate(this%izone, np, 'PLIZONE', mempath)
@@ -165,7 +163,6 @@ subroutine deallocate (this, mempath)
     call mem_deallocate(this%iprp, 'PLIPRP', mempath)
     call mem_deallocate(this%irpt, 'PLIRPT', mempath)
     call mem_deallocate(this%name, 'PLNAME', mempath)
-    call mem_deallocate(this%icp, 'PLICP', mempath)
     call mem_deallocate(this%icu, 'PLICU', mempath)
     call mem_deallocate(this%ilay, 'PLILAY', mempath)
     call mem_deallocate(this%izone, 'PLIZONE', mempath)
@@ -200,7 +197,6 @@ subroutine resize(this, np, mempath)
     call mem_reallocate(this%iprp, np, 'PLIPRP', mempath)
     call mem_reallocate(this%irpt, np, 'PLIRPT', mempath)
     call mem_reallocate(this%name, LENBOUNDNAME, np, 'PLNAME', mempath)
-    call mem_reallocate(this%icp, np, 'PLICP', mempath)
     call mem_reallocate(this%icu, np, 'PLICU', mempath)
     call mem_reallocate(this%ilay, np, 'PLILAY', mempath)
     call mem_reallocate(this%izone, np, 'PLIZONE', mempath)
@@ -244,7 +240,7 @@ subroutine load_particle(this, store, imdl, iprp, ip)
     this%istopweaksink = store%istopweaksink(ip)
     this%istopzone = store%istopzone(ip)
     this%idrymeth = store%idrymeth(ip)
-    this%icp = store%icp(ip)
+    this%icp = 0
     this%icu = store%icu(ip)
     this%ilay = store%ilay(ip)
     this%izone = store%izone(ip)
@@ -281,7 +277,6 @@ subroutine save_particle(this, particle, ip)
     this%istopweaksink(ip) = particle%istopweaksink
     this%istopzone(ip) = particle%istopzone
     this%idrymeth(ip) = particle%idrymeth
-    this%icp(ip) = particle%icp
     this%icu(ip) = particle%icu
     this%ilay(ip) = particle%ilay
     this%izone(ip) = particle%izone