What are the differences between Nodal data and Cell data or Voxels?

Simple comparisons of of nodal based vs Voxel (cell-based) would be:

• plume vs. plume_cell
• indicator_geology Smooth vs. Block (this is truly analogous since Block probabilities are kriged to the cells and Smooth is kriged to the nodes).

To appreciate the difference resulting from a plume operation, you merely need to “visualize” what is happening within a single EVS hexahedron (8 node) cell.  It helps if you grab a rectangular cardboard box (kleenex or amazon) and consider some cases by marking it up with colored markers.

 

FOR NODAL DATA (EVS Paradigm)

• Values are computed at all 8 nodes.  
  • Though a cell has 8 nodes, except at model faces, edges and corners, each node is shared with 7 other cells.
  • For a typical 100 x 100 x 100 node grid, there will be 99 x 99 x 99 cells.
    • For the above grid there are ~3% more nodes than cells.  
• When a plume is computed for Do > Tn (Data is greater than Threshold-n), a complex process ensues:
  • All cells where all of the cell’s nodes are < Tn are removed.
  • All cells where all of the cell’s nodes are > Tn remain.
  • For cells where some nodes > Tn and some are < Tn
    • All cell edges where the two edge nodes are < Tn are removed.
    • All cell edges where the two edge nodes are > Tn remain.
    • All cell edges where one edge node is < Tn and the other is > Tn are split.  
      
      • For the small domain of a single cell, linear interpolation across any edge to determine the location of the split is very accurate (sub-percentile) as compared with kriging values along the edge.  
      • At the split location a new node is created.
      • The edge node < Tn is removed.
    • The complexity of the subdivided cell can vary dramatically depending on the number of remaining nodes.
      • The minimum number of remaining nodes is 4 and the maximum is 16! (yes, much greater than what you start with).
      • New cells are created using the remaining and created (from splits) nodes.
      • There are 256 cases of how new cells are created from all permutations of which nodes remain.
        • All possible volumetric cell types can result from the subdivision, but all higher order cells can be cleanly subdivided into tetrahedrons.
          • This is why a hexahedral grid becomes Tetrahedrons after subsetting operations. 
        • The reason there are so many cases is that we take extreme care to eliminate internal volume faces that do not have a matching face to ensure that transparency of volumetric plumes is correct and lacks unwanted internal faces.
    • The accuracy of the splitting is the reason why nodal representations are far superior to cell-based representations.
      
      • Since splitting occurs along all three dimensions (x-y-z), and is sub-percentile accurate, the cell subdivision is at-least as good as a cell-based grid whose resolution is 100 times greater in X, Y & Z directions. 
      • NOTE: The reason why I insist that grids should have at least two cells between any samples that exhibit a high gradient is to enforce and maintain the subdivision accuracy.