ORCID Profile
0000-0002-6462-9540
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Publisher: Springer Science and Business Media LLC
Date: 27-10-2012
Publisher: Elsevier BV
Date: 02-2018
Publisher: University of Queensland Library
Date: 2019
Publisher: Elsevier BV
Date: 09-2017
Publisher: Springer Science and Business Media LLC
Date: 14-03-2014
Publisher: Elsevier BV
Date: 2018
Publisher: Hindawi Limited
Date: 19-02-2020
DOI: 10.1002/ER.5243
Publisher: Royal Society of Chemistry (RSC)
Date: 2014
DOI: 10.1039/C4RA03146F
Publisher: Elsevier BV
Date: 10-2019
Publisher: AIP Publishing
Date: 03-2022
DOI: 10.1063/5.0084789
Abstract: The advection–diffusion equation (ADE) describes many important processes in hydrogeology, mechanics, geology, and biology. The equations model the transport of a passive scalar quantity in a flow. In this paper, we have developed a new approach to solve incompressible advection–diffusion equations (ADEs) with variable convective terms, which are essential to study species transport in various flow scenarios. We first reinterpret advection diffusion equations on a microscopic level and obtain stochastic differential equations governing the behavior of in idual particles of the species transported by the flow. Then, simplified versions of ADEs are derived to approximate the original ADEs governing concentration evolution of species. The approximation is effectively a linearization of the spatially varying coefficient of the advective term. These simplified equations are solved analytically using the Fourier transform. We have validated this new method by comparing our results to solutions obtained from the canonical stochastic s ling method and the finite element method. This mesh-free algorithm achieves comparable accuracy to the results from discrete stochastic simulation of spatially resolved species transport in a Lagrangian frame of reference. The good consistency shows that our proposed method is efficient in simulating chemical transport in a convective flow. The proposed method is computationally efficient and quantitatively reliable, providing an alternative technique to investigate various advection–diffusion processes.
Publisher: AIP Publishing
Date: 04-2021
DOI: 10.1063/5.0048467
Abstract: Transport phenomena in homogeneous and inhomogeneous media are commonly encountered in many practical and industrial applications, which are modeled by advection-diffusion equations (ADEs) with constant or variable diffusivities, respectively. This paper provides a new perspective on how to solve advection-diffusion equations that model different transport phenomena in low Reynolds number flows. A mathematical description of the Lie group method is conducted first and then its potential in solving advection-diffusion equations for passive scalars transport with no-slip and no-flux boundary conditions is explored. The key step is to recast advection-diffusion equations as homogeneous diffusion processes on unimodular matrix Lie groups. Consequently, an approximate solution can be obtained from mean and covariance propagation techniques developed for diffusion equations on these Lie groups. The motivation to transform the advection-diffusion equation from Euclidean space to Lie groups is to exploit the available solutions of diffusion equation on these Lie groups so that the original equation can be solved in a simple way. In this paper, methodological details have been illustrated in solving ADEs modeling three kinds of transport phenomena. Two of them govern homogeneous transport and the solutions from mean and covariance propagation on the Lie group agree well with available results in published papers. We also use this method to solve more complicated ADEs governing inhomogeneous transport in one-dimensional compressible flows with spatially varying diffusivity, which is beyond the capabilities of existing approaches. The three real problems solved by the Lie group method illustrate the potential of this method. Instead of numerical calculations, the proposed closed-form method provides a simple alternative to study mass transfer encountered in various complex physical and industrial processes.
Publisher: Elsevier BV
Date: 11-2016
Publisher: Informa UK Limited
Date: 27-08-2014
Publisher: Elsevier BV
Date: 11-2017
Publisher: Elsevier BV
Date: 07-2017
Publisher: Elsevier BV
Date: 02-2014
No related grants have been discovered for Yubiao Sun.