Skip to main content
OSTI.GOVU.S. Department of Energy Office of Scientific and Technical Information
U.S. Department of Energy
Office of Scientific and Technical Information
 

Hyperbolic Reformulation Approach to Enable Efficient Simulation of Groundwater Flow and Reactive Transport

Journal Article · · Environmental Engineering Science (Online)
 [1];  [2];  [1];  [1]
  1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
  2. Centro Universitario de la Defensa, Zaragoza (Spain)
+ Show Author Affiliations

We apply Cattaneo's relaxation approach to the one-dimensional coupled Boussinesq groundwater flow and advection-diffusion-reaction equations, commonly used in engineering applications to simulate contaminant transport in the subsurface. The diffusion-type governing equations are reformulated as a hyperbolic system, augmented by an equation that can be interpreted as a momentum balance. The hyperbolization enables an efficient unified computation of the primary variable and its gradients, for example piezometric head and unit discharge in the Boussinesq equation. An augmented Roe scheme is used to solve the hyperbolic system. The hyperbolized system of equations is studied in a set of steady state and transient test cases with idealized geometry. These test cases confirm the equivalence of the hyperbolic system to its original formulation. The larger time step size of the hyperbolic equation is verified theoretically by means of a stability analysis and numerically in the test cases. Finally, a reach-scale application of flow and transport across a river meander is considered. This application case shows that the performance of the hyperbolic relaxation approach holds for more realistic groundwater flow and transport problems, relevant to water resources management.

Research Organization:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Organization:
USDOE Office of Energy Efficiency and Renewable Energy (EERE)
Grant/Contract Number:
AC02-05CH11231
OSTI ID:
1827667
Journal Information:
Environmental Engineering Science (Online), Journal Name: Environmental Engineering Science (Online) Journal Issue: 3 Vol. 38; ISSN 1557-9018
Publisher:
Mary Ann Liebert, Inc.Copyright Statement
Country of Publication:
United States
Language:
English

References (23)

Mixing effects on nitrogen and oxygen concentrations and the relationship to mean residence time in a hyporheic zone of a riffle-pool sequence: MIXING EFFECTS ON NITROGEN AND OXYGEN THE HYPORHEIC ZONE journal September 2015
The relaxation schemes for systems of conservation laws in arbitrary space dimensions journal January 1995
�ber die partiellen Differenzengleichungen der mathematischen Physik journal December 1928
Reactive transport codes for subsurface environmental simulation journal September 2014
A Well-Balanced Path-Integral f-Wave Method for Hyperbolic Problems with Source Terms journal August 2010
Approximate Riemann solvers, parameter vectors, and difference schemes journal October 1981
A weak formulation of roe's approximate riemann solver journal October 1992
An adaptive time step solution for raster-based storage cell modelling of floodplain inundation journal September 2005
A comprehensive explanation and exercise of the source terms in hyperbolic systems using Roe type solutions. Application to the 1D-2D shallow water equations journal December 2016
Expanding the role of reactive transport models in critical zone processes journal February 2017
Pollutant transport by shallow water equations on unstructured meshes: Hyperbolization of the model and numerical solution via a novel flux splitting scheme journal September 2016
Verification, conservation, stability and efficiency of a finite volume method for the 1D Richards equation journal February 2013
Finite Volume Methods for Hyperbolic Problems book January 2002
Streambed nitrogen cycling beyond the hyporheic zone: Flow controls on horizontal patterns and depth distribution of nitrate and dissolved oxygen in the upwelling groundwater of a lowland river: NITROGEN CYCLING BEYOND THE HYPORHEIC journal January 2013
Geochemical Exports to River From the Intrameander Hyporheic Zone Under Transient Hydrologic Conditions: East River Mountainous Watershed, Colorado journal October 2018
Depth‐ and Time‐Resolved Distributions of Snowmelt‐Driven Hillslope Subsurface Flow and Transport and Their Contributions to Surface Waters journal November 2019
Mitigating Climate Change at the Carbon Water Nexus: A Call to Action for the Environmental Engineering Community journal October 2016
Numerical methods for nonconservative hyperbolic systems: a theoretical framework. journal January 2006
Advection-Diffusion-Reaction Equations: Hyperbolization and High-Order ADER Discretizations journal January 2014
Diffusive Relaxation Schemes for Multiscale Discrete-Velocity Kinetic Equations journal December 1998
A Well-Balanced Scheme Using Non-Conservative Products Designed for Hyperbolic Systems of Conservation laws with Source Terms journal March 2001
Solutions for groundwater flow with sloping stream boundary: analytical, numerical and experimental models journal June 2017
LiDAR collection in August 2015 over the East River Watershed, Colorado, USA dataset January 2017

Similar Records

Hyperbolic reformulation of a 1D viscoelastic blood flow model and ADER finite volume schemes
Journal Article · Sun Jun 01 00:00:00 EDT 2014 · Journal of Computational Physics · OSTI ID:22314866
An investigation of the effect of diffusivity on the transport and spread of contaminants in groundwater systems
Conference · Tue Jul 01 00:00:00 EDT 1997 · OSTI ID:489031
Parallel-In-Time Integration for Hyperbolic Problems (Final Report)
Technical Report · Thu Apr 15 00:00:00 EDT 2021 · OSTI ID:1784601

Related Subjects

54 ENVIRONMENTAL SCIENCES
advection-diffusion-reaction equation
hyperbolic relaxation system
augmented Roe scheme
groundwater flow