tapios
commented
2 years ago I think it's specific to conductivities: using the harmonic mean is the right thing to do for a series of resistors to flow, each with a fixed conductivity. This may be what they mean with "certain quadrature."
A paper describing the spatial discretization used by ParFlow notes that they use the harmonic mean of cell quantities when computing face quantities (for a particular field of interest, the hydraulic conductivity). They write, "For spatial discretization, we use a tensor product grid with Nx, Ny and Nz cells in the x,y, and z directions, respectively. We then apply cell-centered finite-differences over this mesh....We apply this spatial discretization method because it is locally conservative, and, in the linear case, is equivalent to the lowest order mixed finite element method with certain quadrature [27]. Thus, this method can be shown to be second-order in space if harmonic averaging is used for k(x) and kr(p)." Here, k = hydraulic conductivity functions. They also discuss using one-point upstream weighting to get face quantities.
Is something like this of wider interest to other teams? or will most only want the arithmetic mean (what is implemented now)?