The Experts below are selected from a list of 74232 Experts worldwide ranked by ideXlab platform
David A Benson - One of the best experts on this subject based on the ideXlab platform.
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connecting the dots semi analytical and random walk numerical solutions of the diffusion Reaction Equation with stochastic initial conditions
Journal of Computational Physics, 2014Co-Authors: Amir Paster, Diogo Bolster, David A BensonAbstract:We study a system with bimolecular irreversible kinetic Reaction A+B->@A where the underlying transport of reactants is governed by diffusion, and the local Reaction term is given by the law of mass action. We consider the case where the initial concentrations are given in terms of an average and a white noise perturbation. Our goal is to solve the diffusion-Reaction Equation which governs the system, and we tackle it with both analytical and numerical approaches. To obtain an analytical solution, we develop the Equations of moments and solve them approximately. To obtain a numerical solution, we develop a grid-less Monte Carlo particle tracking approach, where diffusion is modeled by a random walk of the particles, and Reaction is modeled by annihilation of particles. The probability of annihilation is derived analytically from the particles' co-location probability. We rigorously derive the relationship between the initial number of particles in the system and the amplitude of white noise represented by that number. This enables us to compare the particle simulations and the approximate analytical solution and offer an explanation of the late time discrepancies.
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Particle tracking and the diffusion‐Reaction Equation
Water Resources Research, 2013Co-Authors: Amir Paster, Diogo Bolster, David A BensonAbstract:[1] Particle tracking algorithms are very useful methods to model conservative transport in surface and subsurface hydrological systems. Recently, a novel ad hoc particle-based method was proposed to account for multicomponent reactive transport by Benson and Meerschaert (2008). This one-dimensional particle method has been shown to match theoretical predictions, but, to date, there has been no rigorous demonstration that the particle method actually matches the governing Equations for chemical transport. We generalize this particle method to two-dimensional and three-dimensional systems and rigorously demonstrate that this particle method converges to the diffusion-Reaction Equation at the limit of infinitely small time step. We also investigate the numerical error associated with the method.
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particle tracking and the diffusion Reaction Equation
Water Resources Research, 2013Co-Authors: Amir Paster, Diogo Bolster, David A BensonAbstract:[1] Particle tracking algorithms are very useful methods to model conservative transport in surface and subsurface hydrological systems. Recently, a novel ad hoc particle-based method was proposed to account for multicomponent reactive transport by Benson and Meerschaert (2008). This one-dimensional particle method has been shown to match theoretical predictions, but, to date, there has been no rigorous demonstration that the particle method actually matches the governing Equations for chemical transport. We generalize this particle method to two-dimensional and three-dimensional systems and rigorously demonstrate that this particle method converges to the diffusion-Reaction Equation at the limit of infinitely small time step. We also investigate the numerical error associated with the method.
Diogo Bolster - One of the best experts on this subject based on the ideXlab platform.
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connecting the dots semi analytical and random walk numerical solutions of the diffusion Reaction Equation with stochastic initial conditions
Journal of Computational Physics, 2014Co-Authors: Amir Paster, Diogo Bolster, David A BensonAbstract:We study a system with bimolecular irreversible kinetic Reaction A+B->@A where the underlying transport of reactants is governed by diffusion, and the local Reaction term is given by the law of mass action. We consider the case where the initial concentrations are given in terms of an average and a white noise perturbation. Our goal is to solve the diffusion-Reaction Equation which governs the system, and we tackle it with both analytical and numerical approaches. To obtain an analytical solution, we develop the Equations of moments and solve them approximately. To obtain a numerical solution, we develop a grid-less Monte Carlo particle tracking approach, where diffusion is modeled by a random walk of the particles, and Reaction is modeled by annihilation of particles. The probability of annihilation is derived analytically from the particles' co-location probability. We rigorously derive the relationship between the initial number of particles in the system and the amplitude of white noise represented by that number. This enables us to compare the particle simulations and the approximate analytical solution and offer an explanation of the late time discrepancies.
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Particle tracking and the diffusion‐Reaction Equation
Water Resources Research, 2013Co-Authors: Amir Paster, Diogo Bolster, David A BensonAbstract:[1] Particle tracking algorithms are very useful methods to model conservative transport in surface and subsurface hydrological systems. Recently, a novel ad hoc particle-based method was proposed to account for multicomponent reactive transport by Benson and Meerschaert (2008). This one-dimensional particle method has been shown to match theoretical predictions, but, to date, there has been no rigorous demonstration that the particle method actually matches the governing Equations for chemical transport. We generalize this particle method to two-dimensional and three-dimensional systems and rigorously demonstrate that this particle method converges to the diffusion-Reaction Equation at the limit of infinitely small time step. We also investigate the numerical error associated with the method.
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particle tracking and the diffusion Reaction Equation
Water Resources Research, 2013Co-Authors: Amir Paster, Diogo Bolster, David A BensonAbstract:[1] Particle tracking algorithms are very useful methods to model conservative transport in surface and subsurface hydrological systems. Recently, a novel ad hoc particle-based method was proposed to account for multicomponent reactive transport by Benson and Meerschaert (2008). This one-dimensional particle method has been shown to match theoretical predictions, but, to date, there has been no rigorous demonstration that the particle method actually matches the governing Equations for chemical transport. We generalize this particle method to two-dimensional and three-dimensional systems and rigorously demonstrate that this particle method converges to the diffusion-Reaction Equation at the limit of infinitely small time step. We also investigate the numerical error associated with the method.
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Effect of spatial concentration fluctuations on effective kinetics in diffusion-Reaction systems
Water Resources Research, 2012Co-Authors: Alexandre Tartakovsky, Pietro De Anna, Tanguy Le Borgne, A. Balter, Diogo BolsterAbstract:The effect of spatial concentration fluctuations on the Reaction of two solutes, A þ B* C, is considered. In the absence of fluctuations, the concentration of solutes decays as Adet ¼ Bdet t 1. Contrary to this, experimental and numerical studies suggest that concentrations decay significantly slower. Existing theory suggests a t d/4 scaling in the asymptotic regime (d is the dimensionality of the problem). Here we study the effect of fluctuations using the classical diffusion-Reaction Equation with random initial conditions. Initial concentrations of the reactants are treated as correlated random fields.We use the method of moment Equations to solve the resulting stochastic diffusion-Reaction Equation and obtain a solution for the average concentrations that deviates from t 1 to t d/4 behavior at characteristic transition time t . We also derive analytical expressions for t as a function of Damköhler number and the coefficient of variation of the initial concentration.
Mingrong Cui - One of the best experts on this subject based on the ideXlab platform.
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compact exponential scheme for the time fractional convection diffusion Reaction Equation with variable coefficients
Journal of Computational Physics, 2015Co-Authors: Mingrong CuiAbstract:High-order compact exponential finite difference scheme for solving the time fractional convection-diffusion Reaction Equation with variable coefficients is considered in this paper. The convection, diffusion and Reaction coefficients can depend on both the spatial and temporal variables. We begin with the one dimensional problem, and after transforming the original Equation to one with diffusion coefficient unity, the new Equation is discretized by a compact exponential finite difference scheme, with a high-order approximation for the Caputo time derivative. We prove the solvability of this fully discrete implicit scheme, and analyze its local truncation error. For the fractional Equation with constant coefficients, we use Fourier method to prove the stability and utilize matrix analysis as a tool for the error estimate. Then we discuss the two dimensional problem, give the compact ADI scheme with the restriction that besides the time variable, the convection coefficients can only depend on the corresponding spatial variables, respectively. Numerical results are provided to verify the accuracy and efficiency of the proposed algorithm. The time fractional convection-diffusion-Reaction Equation is numerically solved.Compact exponential scheme for the variable coefficients Equation is given.Fourier method and matrix analysis are used for the analysis.The compact exponential ADI scheme is given for the two dimensional problem.High accuracy and good efficiency of the proposed algorithm is demonstrated.
Amir Paster - One of the best experts on this subject based on the ideXlab platform.
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connecting the dots semi analytical and random walk numerical solutions of the diffusion Reaction Equation with stochastic initial conditions
Journal of Computational Physics, 2014Co-Authors: Amir Paster, Diogo Bolster, David A BensonAbstract:We study a system with bimolecular irreversible kinetic Reaction A+B->@A where the underlying transport of reactants is governed by diffusion, and the local Reaction term is given by the law of mass action. We consider the case where the initial concentrations are given in terms of an average and a white noise perturbation. Our goal is to solve the diffusion-Reaction Equation which governs the system, and we tackle it with both analytical and numerical approaches. To obtain an analytical solution, we develop the Equations of moments and solve them approximately. To obtain a numerical solution, we develop a grid-less Monte Carlo particle tracking approach, where diffusion is modeled by a random walk of the particles, and Reaction is modeled by annihilation of particles. The probability of annihilation is derived analytically from the particles' co-location probability. We rigorously derive the relationship between the initial number of particles in the system and the amplitude of white noise represented by that number. This enables us to compare the particle simulations and the approximate analytical solution and offer an explanation of the late time discrepancies.
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Particle tracking and the diffusion‐Reaction Equation
Water Resources Research, 2013Co-Authors: Amir Paster, Diogo Bolster, David A BensonAbstract:[1] Particle tracking algorithms are very useful methods to model conservative transport in surface and subsurface hydrological systems. Recently, a novel ad hoc particle-based method was proposed to account for multicomponent reactive transport by Benson and Meerschaert (2008). This one-dimensional particle method has been shown to match theoretical predictions, but, to date, there has been no rigorous demonstration that the particle method actually matches the governing Equations for chemical transport. We generalize this particle method to two-dimensional and three-dimensional systems and rigorously demonstrate that this particle method converges to the diffusion-Reaction Equation at the limit of infinitely small time step. We also investigate the numerical error associated with the method.
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particle tracking and the diffusion Reaction Equation
Water Resources Research, 2013Co-Authors: Amir Paster, Diogo Bolster, David A BensonAbstract:[1] Particle tracking algorithms are very useful methods to model conservative transport in surface and subsurface hydrological systems. Recently, a novel ad hoc particle-based method was proposed to account for multicomponent reactive transport by Benson and Meerschaert (2008). This one-dimensional particle method has been shown to match theoretical predictions, but, to date, there has been no rigorous demonstration that the particle method actually matches the governing Equations for chemical transport. We generalize this particle method to two-dimensional and three-dimensional systems and rigorously demonstrate that this particle method converges to the diffusion-Reaction Equation at the limit of infinitely small time step. We also investigate the numerical error associated with the method.
Ramon Codina - One of the best experts on this subject based on the ideXlab platform.
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analysis of a stabilized finite element approximation of the transient convection diffusion Reaction Equation using orthogonal subscales
Computing and Visualization in Science, 2002Co-Authors: Ramon Codina, Jordi BlascoAbstract:In this paper we analyze a stabilized finite element method to solve the transient convection-diffusion-Reaction Equation based on the decomposition of the unknowns into resolvable and subgrid scales. We start from the time-discrete form of the problem and obtain an evolution Equation for both components of the decomposition. A closed-form expression is proposed for the subscales which, when inserted into the Equation for the resolvable scale, leads to the stabilized formulation that we analyze. Optimal error estimates in space are provided for the first order, backward Euler time integration.
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comparison of some finite element methods for solving the diffusion convection Reaction Equation
Computer Methods in Applied Mechanics and Engineering, 1998Co-Authors: Ramon CodinaAbstract:Abstract In this paper we describe several finite element methods for solving the diffusion-convection-Reaction Equation. None of them is new, although the presentation is non-standard in an effort to emphasize the similarities and differences between them. In particular, it is shown that the classical SUPG method is very similar to an explicit version of the Characteristic-Galerkin method, whereas the Taylor-Galerkin method has a stabilization effect similar to a sub-grid scale model, which is in turn related to the introduction of bubble functions.
