Simulation of linear and nonlinear advection–diffusion–reaction problems by a novel localized scheme

Lin, Ji; Xu, Yi; Zhang, Yuhui

doi:10.1016/j.aml.2019.106005

Cited by 55 publications

(16 citation statements)

References 15 publications

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“…An important property of Eq. (7) is that its solution linearly scales in Da ( Lin, Xu & Zhang, 2020 ). For example, if Da is increased 2-fold at a fixed Pe condition, the concentrations of signaling molecule are doubled.…”

Section: Methodsmentioning

confidence: 99%

Numerical investigation of microbial quorum sensing under various flow conditions

Jung¹,

Meile²

2020

PeerJ

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Microorganisms efficiently coordinate phenotype expressions through a decision-making process known as quorum sensing (QS). We investigated QS amongst distinct, spatially distributed microbial aggregates under various flow conditions using a process-driven numerical model. Model simulations assess the conditions suitable for QS induction and quantify the importance of advective transport of signaling molecules. In addition, advection dilutes signaling molecules so that faster flow conditions require higher microbial densities, faster signal production rates, or higher sensitivities to signaling molecules to induce QS. However, autoinduction of signal production can substantially increase the transport distance of signaling molecules in both upstream and downstream directions. We present empirical approximations to the solutions of the advection–diffusion–reaction equation that describe the concentration profiles of signaling molecules for a wide range of flow and reaction rates. These empirical relationships, which predict the distribution of dissolved solutes along pore channels, allow to quantitatively estimate the effective communication distances amongst multiple microbial aggregates without further numerical simulations.

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Section: Methodsmentioning

confidence: 99%

Numerical investigation of microbial quorum sensing under various flow conditions

Jung¹,

Meile²

2020

PeerJ

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“…An important property of Eq. 7 is that its solution linearly scales in Da (Lin et al 2020). For example, if Da is increased 2-fold at a fixed Pe condition, the concentrations of signaling molecule are doubled.…”

Section: Methodsmentioning

confidence: 99%

Peer Review #1 of "Numerical investigation of microbial quorum sensing under various flow conditions (v0.2)"

Secchi¹

2020

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Microorganisms efficiently coordinate phenotype expressions through a decision-making process known as quorum sensing (QS). We investigated QS amongst distinct, spatially distributed microbial aggregates under various flow conditions using a process-driven numerical model. Model simulations assess the conditions suitable for QS induction and quantify the importance of advective transport of signaling molecules. In addition, advection dilutes signaling molecules so that faster flow conditions require higher microbial densities, faster signal production rates, or higher sensitivities to signaling molecules to induce QS. However, autoinduction of signal production can substantially increase the transport distance of signaling molecules in both upstream and downstream directions. We present empirical approximations to the solutions of the advection-diffusionreaction equation that describe the concentration profiles of signaling molecules for a wide range of flow and reaction rates. These empirical relationships, which predict the distribution of dissolved solutes along pore channels, allow to quantitatively estimate the effective communication distances amongst multiple microbial aggregates without further numerical simulations.

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“…Based on a set of scattered nodes, mesh-less methods overcome certain limitations of grid methods. The Kansa method [9], the boundary knot method (BKM) [10], the backward substitution method [11,12], and the method of fundamental solutions (MFS) [13][14][15] are such methods. Nevertheless, the MFS shows superiority of stability over the LRBF.…”

Section: Introductionmentioning

confidence: 99%

Numerical Solution of Steady-State Free Boundary Problems Using the Singular Boundary Method

sci¹

2021

AAMM

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In this paper, the recently-developed singular boundary method is applied to address free boundary problems. This mesh-less numerical method is based on the use of the origin intensity factors with fundamental solutions. Three numerical examples and their results are compared with the results obtained using traditional methods. The comparisons indicate that the proposed scheme yields good results in determining the position of the free boundary.

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Simulation of linear and nonlinear advection–diffusion–reaction problems by a novel localized scheme

Cited by 55 publications

References 15 publications

Numerical investigation of microbial quorum sensing under various flow conditions

Numerical investigation of microbial quorum sensing under various flow conditions

Peer Review #1 of "Numerical investigation of microbial quorum sensing under various flow conditions (v0.2)"

Numerical Solution of Steady-State Free Boundary Problems Using the Singular Boundary Method

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