Numerical solutions of reactive transport equations

2011 ◽  
pp. 155-170
Keyword(s):  
Reactive Transport ◽  
Numerical Solutions ◽  
Transport Equations

Interactions of cell volume, membrane potential, and membrane transport parameters

1980 ◽  
Vol 238 (5) ◽  
pp. C196-C206 ◽  
Author(s):  
E. Jakobsson
Keyword(s):  
Membrane Potential ◽  
Cell Volume ◽  
Membrane Transport ◽  
Numerical Solutions ◽  
Transport Equations ◽  
Time Varying ◽  
Transport Parameters ◽  
Animal Cells ◽  
Analytic Expressions ◽  
Solute Species

Equations have been written and solved that describe for animal cells the relationships among membrane transport, cell volume, membrane potential, and distribution of permeant solute. The essential system consists of n + 2 equations, where n is the number of permeant solute species. The n of the equations are the n transport equations for the permeant species, one for each species. The other two equations are statements of 1) the condition for bulk electroneutrality inside the cell and 2) the condition for isotonicity between the interior and exterior of the cell. Numerical solutions have been obtained in both the steady-state and time-varying cases for transport equations that are physically and phenomenologically reasonable. In addition to numerical solutions analytic expressions are presented that show the ranges of membrane parameters essential for volume regulation; for values of membrane parameters beyond explicitly defined bounds, the equations do not have real, positive solutions for cell volume.

Simulation on Short-Gap Streamer Discharge in Gases Using the Lattice Boltzmann Method

2017 ◽  
Vol 14 (1) ◽  
pp. 505-510
Author(s):  
Nan Wang ◽  
Qingquan Lei ◽  
Xuan Wang
Keyword(s):  
Numerical Simulation ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Numerical Solutions ◽  
Transport Equations ◽  
Physical Parameters ◽  
Streamer Discharge ◽  
Microscopic Mechanism ◽  
Discharge Simulation ◽  
Boltzmann Method

Streamer discharge is an important aspect of gap discharge in gases, but experimental method alone cannot delineate the microscopic mechanism of streamer discharge and all physical parameters of the discharge channel. Numerical simulation provides an important method for theoretical study of streamer discharge. To solve the particle transport equations in streamer discharge simulation, we applied the lattice Boltzmann method to the design of a solution model which requires a smaller calculation load. Furthermore, we provided the 1.5-dimensional streamer discharge simulation model based on the D1Q3 model as well as the numerical solutions to electron transport and positive ion transport equations. Using this model, numerical simulation was performed on two types of streamer development processes in N2 gas between the plate electrodes under atmospheric pressure. The simulation results were then compared against the results in the previous reports, and the feasibility of using the lattice Boltzmann method for streamer discharge simulation was demonstrated.

scholarly journals A similarity solution for reaction front propagation in a fracture–matrix system

2016 ◽  
Vol 374 (2078) ◽  
pp. 20150424 ◽  
Author(s):  
Harihar Rajaram ◽  
Masoud Arshadi
Keyword(s):  
Similarity Solution ◽  
Reaction Front ◽  
Reactive Transport ◽  
Numerical Solutions ◽  
Broad Class ◽  
Front Propagation ◽  
Similarity Solutions ◽  
Rock Matrix ◽  
Similarity Variable ◽  
Diffusion Limitations

We propose a new composite similarity variable, based on which a similarity solution is derived for reaction front propagation in fracture–matrix systems. The similarity solution neglects diffusion/dispersion within the fracture and assumes the existence of a sharp reaction front in the rock matrix. The reaction front location in the rock matrix is shown to follow a linear decrease with distance along the fracture. The reaction front propagation along the fracture is shown to scale like diffusion (i.e. as the square root of time). The similarity solution using the composite similarity variable appears to be applicable to a broad class of reactive transport problems involving mineral reactions in fracture–matrix systems. It also reproduces the solutions for non-reactive solute and heat transport when diffusion/dispersion/conduction are neglected in the fracture. We compared our similarity solution against numerical simulations for nonlinear reactive transport of an aqueous species with a mineral in the rock matrix. The similarity solutions agree very well with the numerical solutions, especially at later times when diffusion limitations are more pronounced. This article is part of the themed issue ‘Energy and the subsurface’.

scholarly journals Using Parallel Genetic Algorithms for Estimating Model Parameters in Complex Reactive Transport Problems

Processes ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 640 ◽  
Author(s):  
Jagadish Torlapati ◽  
T. Prabhakar Clement
Keyword(s):  
Genetic Algorithm ◽  
Reactive Transport ◽  
Numerical Solutions ◽  
Optimization Method ◽  
Water Quality Modeling ◽  
Model Parameters ◽  
Initial Population ◽  
Desktop Computer ◽  
Linear Speedup ◽  
Transport Problems

In this study, we present the details of an optimization method for parameter estimation of one-dimensional groundwater reactive transport problems using a parallel genetic algorithm (PGA). The performance of the PGA was tested with two problems that had published analytical solutions and two problems with published numerical solutions. The optimization model was provided with the published experimental results and reasonable bounds for the unknown kinetic reaction parameters as inputs. Benchmarking results indicate that the PGA estimated parameters that are close to the published parameters and it also predicted the observed trends well for all four problems. Also, OpenMP FORTRAN parallel constructs were used to demonstrate the speedup of the code on an Intel quad-core desktop computer. The parallel code showed a linear speedup with an increasing number of processors. Furthermore, the performance of the underlying optimization algorithm was tested to evaluate its sensitivity to the various genetic algorithm (GA) parameters, including initial population size, number of generations, and parameter bounds. The PGA used in this study is generic and can be easily scaled to higher-order water quality modeling problems involving real-world applications.

Surface Photovoltage Study of Indium Phosphide Nanowire Networks

2011 ◽  
Vol 1350 ◽  
Author(s):  
Andrew J. Lohn ◽  
Jin-Woo Han ◽  
Nobuhiko P. Kobayashi
Keyword(s):  
Thin Film ◽  
Indium Phosphide ◽  
Numerical Solutions ◽  
Three Dimensional ◽  
Transport Equations ◽  
Surface Photovoltage ◽  
Nanowire Network ◽  
Nanowire Networks

ABSTRACTSurface photovoltage of three-dimensional networks composed of fused indium phosphide (InP) nanowires is discussed. Particular emphasis is given to the dependence of surface photovoltage on the chopping frequency of light that excites the nanowire network as observed in regions which are laterally separated from the excitation. The nanowire network is modeled as a thin film to simplify numerical solutions to transport equations which aids in the interpretation of diffusion and drift of photo-generated carriers within the nanowire network.

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