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A method of alternating characteristics with application to advection-dominated environmental systems

Journal Article · · Computational Geosciences
 [1];  [2];  [2];  [3]
  1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Univ. of California, Berkeley, CA (United States)
  2. Univ. of California, Berkeley, CA (United States)
  3. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
+ Show Author Affiliations

We present a numerical method for solving a class of systems of partial differential equations (PDEs) that arises in modeling environmental processes undergoing advection and biogeochemical reactions. The salient feature of these PDEs is that all partial derivatives appear in linear expressions. As a result, the system can be viewed as a set of ordinary differential equations (ODEs), albeit each one along a different characteristic. The method then consists of alternating between equations and integrating each one step-wise along its own characteristic, thus creating a customized grid on which solutions are computed. Since the solutions of such PDEs are generally smoother along their characteristics, the method offers the potential of using larger time steps while maintaining accuracy and reducing numerical dispersion. The advantages in efficiency and accuracy of the proposed method are demonstrated in two illustrative examples that simulate depth-resolved reactive transport and soil carbon cycling.

Research Organization:
Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Biological and Environmental Research (BER) (SC-23)
Grant/Contract Number:
AC02-05CH11231
OSTI ID:
1477303
Journal Information:
Computational Geosciences, Journal Name: Computational Geosciences Journal Issue: 3 Vol. 22; ISSN 1420-0597
Publisher:
SpringerCopyright Statement
Country of Publication:
United States
Language:
English

References (41)

Explicitly representing soil microbial processes in Earth system models: Soil microbes in earth system models journal October 2015
Weighted Essentially Non-oscillatory Schemes journal November 1994
A Fully Conservative Second-Order Finite Difference Scheme for Incompressible Flow on Nonuniform Grids journal March 2002
Simulation of multiphase flows in porous media journal January 1991
Soil carbon sensitivity to temperature and carbon use efficiency compared across microbial-ecosystem models of varying complexity journal January 2014
Unbiased identification of nonlinear sorption characteristics by soil column breakthrough experiments journal March 2006
Reactive transport codes for subsurface environmental simulation journal September 2014
Uniformly high order accurate essentially non-oscillatory schemes, III journal August 1987
Efficient implementation of essentially non-oscillatory shock-capturing schemes journal August 1988
Compact finite difference schemes with spectral-like resolution journal November 1992
Convergence analysis of an approximation of miscible displacement in porous media by mixed finite elements and a modified method of characteristics journal December 1984
An introduction to finite element methods for transient advection problems journal March 1992
A summary of numerical methods for time-dependent advection-dominated partial differential equations journal March 2001
Coupling water flow and solute transport into a physically-based surface–subsurface hydrological model journal January 2011
A general simulator for reaction-based biogeochemical processes journal February 2006
GeoSysBRNS—A flexible multidimensional reactive transport model for simulating biogeochemical subsurface processes journal March 2010
Reactive transport modeling: An essential tool and a new research approach for the Earth sciences journal December 2005
Modeling reactive transport in sediments subject to bioturbation and compaction journal July 2005
High order Godunov mixed methods on tetrahedral meshes for density driven flow simulations in porous media journal September 2005
Analytical and variational numerical methods for unstable miscible displacement flows in porous media journal April 2017
Contribution of sorption, DOC transport and microbial interactions to the 14C age of a soil organic carbon profile: Insights from a calibrated process model journal September 2015
Finite Volume Methods for Hyperbolic Problems book January 2002
Catchment travel time distributions and water flow in soils: CATCHMENT TRAVEL TIMES journal July 2011
Surface micro-topography causes hot spots of biogeochemical activity in wetland systems: A virtual modeling experiment: MICRO-TOPOGRAPHY AND HOT SPOT FORMATION journal October 2012
The modeling of reactive solute transport with sorption to mobile and immobile sorbents: 1. Experimental evidence and model development journal June 1996
Numerical predictions of two-dimensional transient groundwater flow by the method of characteristics journal October 1976
A modified method of characteristics technique and mixed finite elements method for simulation of groundwater solute transport journal July 1989
Contaminant accumulation during transport through porous media journal January 1990
Soil-carbon response to warming dependent on microbial physiology journal April 2010
Upwind difference schemes for hyperbolic systems of conservation laws journal May 1982
A review of numerical methods for nonlinear partial differential equations journal January 2012
Carbon use efficiency of microbial communities: stoichiometry, methodology and modelling journal April 2013
Microbial models with data-driven parameters predict stronger soil carbon responses to climate change journal March 2015
Does dispersal control population densities in advection-dominated systems? A fresh look at critical assumptions and a direct test journal January 2010
Numerical Methods for Convection-Dominated Diffusion Problems Based on Combining the Method of Characteristics with Finite Element or Finite Difference Procedures journal October 1982
A Characteristics-Mixed Finite Element Method for Advection-Dominated Transport Problems journal April 1995
Finite-Element-Approximation of Solute Transport in Porous Media with General Adsorption Processes conference March 2012
Relation between Soil Order and Sorption of Dissolved Organic Carbon in Temperate Subsoils journal January 2012
Changes in soil organic carbon storage predicted by Earth system models during the 21st century journal January 2014
CLM4-BeTR, a generic biogeochemical transport and reaction module for CLM4: model development, evaluation, and application journal January 2013
Long residence times of rapidly decomposable soil organic matter: application of a multi-phase, multi-component, and vertically resolved model (BAMS1) to soil carbon dynamics journal January 2014

Figures / Tables (14)

Table 1(p. 13)table Table 1
Fig. 1(p. 20)figure Fig. 1
Fig. 2(p. 21)figure Fig. 2
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Fig. 11(p. 24)figure Fig. 11
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Fig. 13(p. 25)figure Fig. 13

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Related Subjects

54 ENVIRONMENTAL SCIENCES