TY - JOUR

T1 - The Cell Analytical‐Numerical Method for Solution of the Advection‐Dispersion Equation

T2 - Two‐Dimensional Problems

AU - Elnawawy, Osman A.

AU - Valocchi, Albert J.

AU - Ougouag, Abderrafi M.

PY - 1990/11

Y1 - 1990/11

N2 - In this paper we present the development and evaluation of a new numerical scheme for efficient solution of groundwater solute transport problems. The scheme, which we have named the cell analytical‐numerical (CAN) method, is an extension of the so‐called nodal methods which have been developed in the nuclear engineering area for solving neutron diffusion problems. The CAN method is based upon decomposition of the solution domain into a number of rectangular cells (volume subdomains); each cell is homogeneous so that a local analytic solution to the solute transport equation can be obtained. A first‐order accurate finite difference approximation of the time derivative followed by a transverse averaging procedure is used to transform the governing partial differential equation into a set of coupled one‐dimensional ordinary differential equations for the transverse moments of the concentration. The local analytical solution is therefore found in terms of these moments. Solute mass flux continuity across cell surfaces, along with the local analytical solution, is used to construct an algebraic relationship between concentration moment values at adjacent cell surfaces. Assembling all the cells together results in a set of coupled tridiagonal matrix equations, one set for each spatial direction, which can be solved very efficiently. The CAN method is applied to several simple test problems involving uniform flow in homogeneous aquifers. While the method lacks geometrical flexibility, it offers a spatial approximation that is demonstrated to have high accuracy and minimal grid orientation error, even when applied to coarse meshes.

AB - In this paper we present the development and evaluation of a new numerical scheme for efficient solution of groundwater solute transport problems. The scheme, which we have named the cell analytical‐numerical (CAN) method, is an extension of the so‐called nodal methods which have been developed in the nuclear engineering area for solving neutron diffusion problems. The CAN method is based upon decomposition of the solution domain into a number of rectangular cells (volume subdomains); each cell is homogeneous so that a local analytic solution to the solute transport equation can be obtained. A first‐order accurate finite difference approximation of the time derivative followed by a transverse averaging procedure is used to transform the governing partial differential equation into a set of coupled one‐dimensional ordinary differential equations for the transverse moments of the concentration. The local analytical solution is therefore found in terms of these moments. Solute mass flux continuity across cell surfaces, along with the local analytical solution, is used to construct an algebraic relationship between concentration moment values at adjacent cell surfaces. Assembling all the cells together results in a set of coupled tridiagonal matrix equations, one set for each spatial direction, which can be solved very efficiently. The CAN method is applied to several simple test problems involving uniform flow in homogeneous aquifers. While the method lacks geometrical flexibility, it offers a spatial approximation that is demonstrated to have high accuracy and minimal grid orientation error, even when applied to coarse meshes.

UR - http://www.scopus.com/inward/record.url?scp=0025621181&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0025621181&partnerID=8YFLogxK

U2 - 10.1029/WR026i011p02705

DO - 10.1029/WR026i011p02705

M3 - Article

AN - SCOPUS:0025621181

VL - 26

SP - 2705

EP - 2716

JO - Water Resources Research

JF - Water Resources Research

SN - 0043-1397

IS - 11

ER -