Fast Transport Simulation with an Adaptive Grid Refinement

Abstract

One of the main difficulties in transport modeling and calibration is the extraordinarily long computing times necessary for simulation runs. Improved execution time is a prerequisite for calibration in transport modeling. In this paper we investigate the problem of code acceleration using an adaptive grid refinement, neglecting subdomains, and devising a method by which the Courant condition can be ignored while maintaining accurate solutions. Grid refinement is based on dividing selected cells into regular subcells and including the balance equations of subcells in the equation system. The connection of coarse and refined cells satisfies the mass balance with an interpolation scheme that is implicitly included in the equation system. The refined subdomain can move with the average transport velocity of the subdomain. Very small time steps are required on a fine or a refined grid, because of the combined effect of the Courant and Peclet conditions. Therefore, we have developed a special upwind technique in small grid cells with high velocities (velocity suppression). We have neglected grid subdomains with very small concentration gradients (zero suppression). The resulting software, MODCALIF, is a three-dimensional, modularly constructed FORTRAN code. For convenience, the package names used by the well-known MODFLOW and MT3D computer programs are adopted, and the same input file structure and format is used, but the program presented here is separate and independent. Also, MODCALIF includes algorithms for variable density modeling and model calibration. The method is tested by comparison with an analytical solution, and illustrated by means of a two-dimensional theoretical example and three-dimensional simulations of the variable-density Cape Cod and SALTPOOL experiments. Crossing from fine to coarse grid produces numerical dispersion when the whole subdomain of interest is refined; however, we show that accurate solutions can be obtained using a fraction of the execution time required by uniformly fine-grid solutions.

MODFLOW-2005, the U.S. Geological Survey modular ground-water model - documentation of shared node local grid refinement (LGR) and the boundary flow and head (BFH) package

“…Thus, the stencil for the coefficient matrix is always consistent with the standard stencil of the original model. This is different from other two-way coupled local grid refinement methods where equations for the irregular connections across the interface of the parent and child grids are directly embedded into a single coefficient matrix, thus altering the conventional stencil (for example, Wasserman, 1987;Ewing and others, 1991;Edwards, 1999;Schaars and Kamps, 2001;Haefner and Boy, 2003). For MODFLOW, the coefficient matrix is formulated symmetrically and all non-zero terms are located on the matrix diagonal and six off diagonals (McDonald and Harbaugh, 1988, p. 12-2 -12-4).…”

“…Various forms of one-dimensional Darcy-based interpolation have been developed and used by others (Wasserman, 1987;Schaars and Kamps, 2001;Haefner and Boy, 2003). For confined flow, they all produce the same interpolated heads, and these heads are consistent with the flow of the parent grid.…”

MODFLOW–LGR—Documentation of ghost node local grid refinement (LGR2) for multiple areas and the boundary flow and head (BFH2) package

“…Thus, the stencil for the coefficient matrix is always consistent with the standard stencil of the original model. This is different from other two-way coupled local grid-refinement methods, in which equations for the irregular connections across the interface of the parent and child grids are directly embedded into a single coefficient matrix, thus altering the conventional stencil (for example, Wasserman, 1987;Ewing and others, 1991;Edwards, 1999;Schaars and Kamps, 2001;Haefner and Boy, 2003). For MODFLOW, the coefficient matrix is formulated symmetrically and all non-zero terms are located on the matrix diagonal and six off diagonals (McDonald and Harbaugh, 1988, p. 12-2-12-4).…”

“…is the flow between adjacent parent cells K p is the hydraulic conductivity of the parent cell, A p is the cross-sectional area of the parent cell perpendicular to flow, L p→g is the distance between parent node and ghost node. Various forms of one-dimensional Darcy-based interpolation have been developed and used by others (Wasserman, 1987;Schaars and Kamps, 2001;Haefner and Boy, 2003). For confined flow, they all produce the same interpolated heads, and these heads are consistent with the flow of the parent grid.…”

Hybrid analytical and finite element numerical modeling of mass and heat transport in fractured rocks with matrix diffusion

“…Solving this problem requires a very fine discretization near the fracture-matrix interface [9,17]. Such mesh refinement significantly increases computational requirements, and may require consideration of grid adaptation algorithms; for example, see Kaiser et al [18] and Haefner and Boy [19].…”