Streamline-oriented grid generation for transport modelling in two-dimensional domains including wells

Flownets are useful tools for the visualization of groundwater flow fields. Using orthogonal flownets as grids for transport modeling is an effective way to control numerical dispersion, especially transverse to the direction of flow. Therefore tools for automatic generation of flownets may be seen both as postprocessors for groundwater flow simulations and preprocessors for contaminant transport models. Existing methods to generate streamline-oriented grids suffer from drawbacks such as the inability to include sources in the interior of the grid. In this paper, we introduce a new method for the generation of streamline-oriented grids which handles wells in the grid interior, and which produces orthogonal grids for anisotropic systems. Streamlines are generated from an accurate velocity field obtained from the solution of the mixed-hybrid finite element method for flow, while pseudopotentials, which are orthogonal to the streamlines, are obtained by a standard finite element solution of the pseudopotential equation. A comprehensive methodology for the generation of orthogonal grids, including the location of stagnation points and dividing streamlines, is introduced. The effectiveness of the method is illustrated by means of examples. A related paper presents a compatible formulation of the solution for reactive transport, while a second related paper gives a detailed quantitative assessment of the various forms of modelled mixing and their effect on the accuracy of simulations of the biodegradation of groundwater contaminants.

[1]  E. A. Sudicky,et al.  Simulation of biodegradable organic contaminants in groundwater: 2. Plume behavior in uniform and random flow fields , 1990 .

[2]  Jean E. Roberts,et al.  Mixed and hybrid finite element methods , 1987 .

[3]  Jean E. Roberts,et al.  A unified physical presentation of mixed, mixed-hybrid finite elements and standard finite difference approximations for the determination of velocities in waterflow problems , 1991 .

[4]  T. E. Short,et al.  An exact peak capturing and Oscillation‐Free Scheme to solve advection‐dispersion transport equations , 1992 .

[5]  C. Zheng.  Analysis of Particle Tracking Errors Associated with Spatial Discretization , 1994 .

[6]  Ilio Galligani,et al.  Mathematical Aspects of Finite Element Methods , 1977 .

[7]  G. Matanga,et al.  Stream functions in three‐dimensional groundwater flow , 1993 .

[8]  Emil O. Frind,et al.  Modeling of multicomponent transport with microbial transformation in groundwater: The Fuhrberg Case , 1990 .

[9]  L. Durlofsky.  Accuracy of mixed and control volume finite element approximations to Darcy velocity and related quantities , 1994 .

[10]  The Principal Direction Technique: A New Approach to Groundwater Contaminant Transport Modeling , 1982 .

[11]  P. Raviart,et al.  A mixed finite element method for 2-nd order elliptic problems , 1977 .

[12]  E. Sudicky,et al.  Simulation of biodegradable organic contaminants in groundwater. 1. Numerical formulation in principal directions. , 1990 .

[13]  Two‐dimensional modeling of advection‐dominated solute transport in groundwater by the matched artificial dispersivity method , 1991 .

[14]  George B. Matanga.  Pseudopotential functions in construction of flow nets for contaminant transport modeling , 1988 .

[15]  The Dual Formulation of Flow for Contaminant Transport Modeling: 2. The Borden Aquifer , 1985 .

[16]  Numerical generation of flow nets - The FLOWNS model. , 1990 .

[17]  Rainer Helmig,et al.  Numerical methods for reactive transport on rectangular and streamline-oriented grids , 1999 .

[18]  G. Pinder,et al.  Computational Methods in Subsurface Flow , 1983 .

[19]  W. Kinzelbach,et al.  Continuous Groundwater Velocity Fields and Path Lines in Linear, Bilinear, and Trilinear Finite Elements , 1992 .

[20]  E. A. Sudicky,et al.  Micro-scale modelling in the study of plume evolution in heterogeneous media , 1987 .

[21]  Graham E. Fogg,et al.  Automatic Generation of Flow Nets with Conventional Ground-Water Modeling Algorithmsa , 1985 .

[22]  Rainer Helmig,et al.  Numerical simulation of biodegradation controlled by transverse mixing , 1999 .

[23]  Clayton V. Deutsch,et al.  GSLIB: Geostatistical Software Library and User's Guide , 1993 .

[24]  Graham F. Carey,et al.  Parallel supercomputing: methods, algorithms and applications , 1989 .

[25]  G. Chavent,et al.  Application of the mixed hybrid finite element approximation in a groundwater flow model: Luxury or necessity? , 1994 .

[26]  Emil O. Frind,et al.  The Dual Formulation of Flow for Contaminant Transport Modeling: 1. Review of Theory and Accuracy Aspects , 1985 .

[27]  D. Arnold,et al.  Mixed and nonconforming finite element methods : implementation, postprocessing and error estimates , 1985 .

[28]  J. Bear.  Dynamics of Fluids in Porous Media , 1975 .

[29]  Emil O. Frind,et al.  Simulation of the Borden Plume using the alternating direction Galerkin Technique , 1987 .