[E = Eulerian; L = Lagrangian]
CAUTION: Assumption is that the node spacing (D x) equals D y in the E node when initially generated, which places constraints on nye and nxe for a given aspect ratio (ar) of the global E mesh, for a particular choice of pp. See Step 4 below.
Step 1. Choose number of process(or)s, pp
Step 2. Define L node in y direction. Choose nyl as defined below.
Let nyl = number of nodes in y direction in the global L node. Then ny is given by
ny = [(nyl-1)/pp] + 1
where ny = number of nodes in y direction in a horizontal Lagrangian slice (i.e. the part of the L node in each process)
ny must be an exact integer. If not, you must adjust nyl or pp.
CAUTION: User chooses nyl (number of L nodes in y direction in the global L node), and ny (number of L nodes in y direction for a L slice) is calculated from nyl and pp. This is equivalent to ny-1 "elements" because the nodes are distributed starting at the top boundary and ending at the bottom boundary. The bottom boundary of each L slice is equal to the top boundary of the next L slice, thereby duplicating the nodes on this boundary. Therefore, there are (ny-1)*pp "elements" in the global Lagrangian grid in the y direction, and (ny-1)*pp+1 separate rows of nodes, but some of these rows have double particles.
Example: Let nyl = 161 and pp = 8. Then ny = ((161-1)/8) + 1 = 21 . So there will be 161 rows of nodes in the global L node, and if elements are defined in the mesh, there will be 160 elements in the y direction of the global L mesh (if one is defined).
Step 3. Define an E node in the y direction. Choose nye, the number of nodes in the y direction for the E node.
CAUTION: Comparison of E node and the L particles: If nye = the number of nodes in y direction in the E node, and nyl = (ny-1)*pp+1 is the number of nodes in the y direction of the L node, then possible choices of ny and nye are as follows:
a) nye and nyl can only be equal for certain choices of ny, pp, and nye.
b) The user needs to consider these choices and the consequences for nxe and nxl, where nxe = the number of nodes in the x direction per processor (including overlap) in the E node and nxl = the global number of nodes in the x direction in the L grid.
c) Note that the size and aspect ratio of the L grid and the E node are usually not the same.
Example I: E and L have same resolution in y direction... choose nye = nyl = (ny-1)*pp + 1.
Example II: E and L nodes have no relationship in y. Choose whatever nye you like, but be aware of consequences when the L nodes are not related to the E mesh.
Example III: L has ky times the resolution of E. Choose nye = 1+ (nyl-1)/ky. Note: this must be an exact integer.
Step 4. Calculate nxe, the number of nodes in the x direction per process for the E node, including the overlap.
Define the size of the global E mesh, Ex units by Ey units. Then each E process will "hold" a piece of the global domain dimensioned Ex/pp by Ey. Therefore Ex should be chosen so that it is divisible into pp slices, such that (Ex/pp)/(nxe-3) = Dx, and that Dx = Dy where Dy = Ey/(nye-1). Rearranging,
nxe = [(Ex/pp) / (Ey/(nye-1))] + 3 [ this works for Ex = 8, ly = 1, pp = 8, nye = 51, which gives nxe = 53 ]
CAUTION: nxe must be an exact integer.
Step 5. Define nxl, the number of nodes in the global L node. Choose Lx, which is the size of the global L mesh in x.
REMEMBER: L node extends beyond E node to allow for inward advection. Choose Lx to create L mesh outside of E mesh.
Example I: E and L have same resolution in x direction. Given that Dx = Dy = Ey/(nye-1), then
nxl -1 = Lx/(Ey/(nye-1))
Rearranging,
nxl = Lx/(Ey/(nye-1)) + 1
nxl must be an exact integer.
Example II: E and L nodes have no relationship in x. Choose whatever nxl you like, but be aware of consequences when the L nodes are not related to the E mesh.
Example III: L has kx times the resolution of E. Choose
nxl = kx * [Lx/(Ey/(nye-1)) + 1]
nxl must be an exact integer.
Example IV: The resolution of the L mesh is the same in the x and y directions. Use Step 5, Example III and Step 3, Example III and set kx = ky.
NOTE: The relative positioning of the global L and E grids is defined in the input file Gnodes.i (where geometries are defined).
NOTE: If the resolution of the L node is to be equal in both the x and the y directions, kx = ky.