3D Advection-diffusion Equation Research Articles

Digital Simulations for Three-dimensional Nonlinear Advection-diffusion Equations Using Quasi-variable Meshes High-resolution Implicit Compact Scheme

A two-level implicit compact formulation with quasi-variable meshes is reported for solving three-dimensions second-order nonlinear parabolic partial differential equations. The new nineteen-point compact scheme exhibit fourth and second-order accuracy in space and time on a variable mesh steps and uniformly spaced mesh points. We have also developed an operator-splitting technique to implement the alternating direction implicit (ADI) scheme for computing the 3D advection-diffusion equation. Thomas algorithm computes each tri-diagonal matrix that arises from ADI steps in minimal computing time. The operator-splitting form is unconditionally stable. The improved accuracy is achieved at a lower cost of computation and storage because the spatial mesh parameters tune the mesh location according to solution values' behavior. The new method is successfully applied to the Navier-Stokes equation, advection-diffusion equation, and Burger's equation for the computational illustrations that corroborate the order, accuracies, and robustness of the new high-order implicit compact scheme. The main highlight of the present work lies in obtaining a fourth-order scheme on a quasi-variable mesh network, and its superiority over the comparable uniform meshes high-order compact scheme.

Digital Simulations for Three-dimensional Nonlinear Advection-diffusion Equations Using Quasi-variable Meshes High-resolution Implicit Compact Scheme

A two-level implicit compact formulation with quasi-variable meshes is reported for solving three-dimensions second-order nonlinear parabolic partial differential equations. The new nineteen-point compact scheme exhibit fourth and second-order accuracy in space and time on a variable mesh steps and uniformly spaced mesh points. We have also developed an operator-splitting technique to implement the alternating direction implicit (ADI) scheme for computing the 3D advection-diffusion equation. Thomas algorithm computes each tri-diagonal matrix that arises from ADI steps in minimal computing time. The operator-splitting form is unconditionally stable. The improved accuracy is achieved at a lower cost of computation and storage because the spatial mesh parameters tune the mesh location according to solution values' behavior. The new method is successfully applied to the Navier-Stokes equation, advection-diffusion equation, and Burger's equation for the computational illustrations that corroborate the order, accuracies, and robustness of the new high-order implicit compact scheme. The main highlight of the present work lies in obtaining a fourth-order scheme on a quasi-variable mesh network, and its superiority over the comparable uniform meshes high-order compact scheme.

Taylor dispersion in Poiseuille flow in three-dimensional tubes of varying diameter.

Diffusion of particles carried by Poiseuille flow of the surrounding solvent in a three-dimensional (3D) tube of varying diameter is considered. We revisit our mapping technique [F. Slanina and P. Kalinay, Phys. Rev. E 100, 032606 (2019)2470-004510.1103/PhysRevE.100.032606], projecting the corresponding 3D advection-diffusion equation onto the longitudinal coordinate and generating an effective one-dimensional modified Fick-Jacobs (or Smoluchowski) equation. A different scaling of the transverse forces by a small auxiliary parameter ε is used here. It results in a recurrence scheme enabling us to derive the corrections of the effective diffusion coefficient and the averaged driving force up to higher orders in ε. The new scaling also preserves symmetries of the stationary solution in any order of ε. Finally we show that Reguera-Rubí's formula, widely applied for description of diffusion in corrugated tubes, can be systematically corrected by the strength of the flow Q; we give here the first two terms in the form of closed analytic formulas.

Estimating airborne particulate emissions using a finite-volume forward solver coupled with a Bayesian inversion approach

We propose a numerical algorithm for solving the atmospheric dispersion problem with elevated point sources and ground-level deposition. The problem is modelled by the 3D advection-diffusion equation with delta-distribution source terms, as well as height-dependent advection speed and diffusion coefficients. We construct a finite volume scheme using a splitting approach in which the Clawpack software package is used as the advection solver and an implicit time discretization is proposed for the diffusion terms. The algorithm is then applied to an actual industrial scenario involving emissions of airborne particulates from a zinc smelter using actual wind measurements. We also address various practical considerations such as choosing appropriate methods for regularizing noisy wind data and quantifying sensitivity of the model to parameter uncertainty. Afterwards, we use the algorithm within a Bayesian framework for estimating emission rates of zinc from multiple sources over the industrial site. We compare our finite volume solver with a Gaussian plume solver within the Bayesian framework and demonstrate that the finite volume solver results in tighter uncertainty bounds on the estimated emission rates.

An efficient quasi-3D particle tracking-based approach for transport through fractures with application to dynamic dispersion calculation

The quantitative study of transport through fractured media has continued for many decades, but has often been constrained by observational and computational challenges. Here, we developed an efficient quasi-3D random walk particle tracking (RWPT) algorithm to simulate solute transport through natural fractures based on a 2D flow field generated from the modified local cubic law (MLCL). As a reference, we also modeled the actual breakthrough curves (BTCs) through direct simulations with the 3D advection–diffusion equation (ADE) and Navier–Stokes equations. The RWPT algorithm along with the MLCL accurately reproduced the actual BTCs calculated with the 3D ADE. The BTCs exhibited non-Fickian behavior, including early arrival and long tails. Using the spatial information of particle trajectories, we further analyzed the dynamic dispersion process through moment analysis. From this, asymptotic time scales were determined for solute dispersion to distinguish non-Fickian from Fickian regimes. This analysis illustrates the advantage and benefit of using an efficient combination of flow modeling and RWPT.

A Global Atmospheric Contaminant Transport Model Based on 3D Advection-Diffusion Equation

To study the global air pollution concentration and evaluate the impact of regional pollution on whole earth, a global atmospheric contaminant transport model is established based on 3D advection-diffusion equation, which captures the processes of advection by wind and turbulent diffusion during atmospheric dispersion. The Eulerian finite difference method is employed for numerical solution of the proposed model. Then one-year aerosol transport on global scale is simulated using the proposed model, and the simulation results are verified against the real remote sensing data of NASA. It turns out that the simulated values of aerosol concentration are strongly correlated with the real values and the correlation coefficient is above 0.8 for sample point. Furthermore, the proposed model is used for predicting the next-year global atmospheric contaminant concentration by simulation. Compared with the related models on atmospheric contaminant transport, we propose a model in this paper with three appealing features: three-dimensional (3D), global scale, and targeted for aerosol transport simulation. In this paper, we present the global 3D atmospheric contaminant transport model and simulate the transport of aerosol around the world. This proposed model uses 3D space coordinates which can fully address the spread of pollutants in space. In this mode, the wind speed and turbulent diffusivity are considered. Furthermore, a comprehensive term is introduced into the model to take into account the factors of emission source, chemical conversion, dry deposition and wet scavenging. The parameters in the model are variables changing over time and space. For simulation purposes, the horizontal resolution of the model is 45 oo × , and the vertical direction is divided into 11 layers. We first simulate the aerosol diffusion in the world in one year. It turns out that the simulated global aerosol concentration distribution is consistent with the real aerosol concentration distribution. Actually, the simulated value has strong correlation with the real data, and the correlation coefficient is above 0.8 for sample point. We also predict the global aerosol concentration over next year. Hence, the proposed model in this paper can be a useful tool for predicting the global aerosol concentration. If we combine this model with more precise chemical patterns, the accuracy of the model can be improved and the proposed model can be further extended to study other atmospheric contaminants. The rest of paper is organized as follows. Section II introduces the proposed global atmospheric contaminant transport model based on 3D advection-diffusion equation. Numerical solution of the proposed model is given in Section III. Section IV presents and discusses the simulation results. Finally, conclusions are drawn in Section V.

Modeling Methanol Crossover by Diffusion and Electro‐Osmosis in a Flowing Electrolyte Direct Methanol Fuel Cell

AbstractA CFD model is created to analyze methanol transport in a flowing electrolyte direct methanol fuel cell (FE‐DMFC) by solving the 3D advection‐diffusion equation, with consideration of electro‐osmosis. The average methanol flux at the anode and cathode surfaces is simulated and compared to equivalent direct methanol fuel cells. Methanol crossover is defined as methanol flux at the cathode surface, and the results reveal that methanol crossover can be drastically reduced by the flowing electrolyte. The performance of the FE‐DMFC at peak power current density is evaluated, and diffusion is shown to be the dominant contribution, although electro‐osmosis increases with current density. The power consumption of the electrolyte pump is shown to be negligible compared to the cell power output. This indicates that thin electrolyte channels with high flow rates could further improve the efficiency.