Advection-dominated-transport-past-isolated-disordered-sinks-stepping-beyond-homogenization-main.zip
Creators: name: Price, George
name: Chernyavsky, Igor
name: Jensen, Oliver E.
Publisher: name: figshare
Year: 2022
Subjects: subject: 10299 Applied Mathematics not elsewhere classified
subject: FOS: Mathematics

description: Description of each file: <strong>Exp_C2_Uniform_1D.m</strong> – Calculates the expectation of 1D corrections. Is used in Exp_C2_Uniform_nD_plotting.m &amp; Variance_Uniform_1D. <strong>Exp_C2_Uniform_2D.m</strong> – Calculates the expectation of 2D corrections. Is used in Exp_C2_Uniform_nD_plotting.m, Exp_C2_Uniform_nD_effective_plotting.m &amp; Variance_Uniform_2D.m. <strong>Exp_C2_Uniform_3D.m</strong> – Calculates the expectation of 3D corrections. Is used in Exp_C2_Uniform_nD_plotting.m &amp; Exp_C2_Uniform_nD_effective_plotting.m. <strong>Exp_C2_Uniform_nD_effective_plotting.m</strong> – Plots the 2D numerical expectation, 2D &amp; 3D expected corrections and 2D &amp; 3D effective uptake parameters for Figure 5(b). <strong>Exp_C2_Uniform_nD_plotting.m</strong> - Plots the 1D &amp; 2D numerical expectation and 1D, 2D &amp; 3D expected corrections for Figure 5(a). <strong>GreensFunction1D.m</strong> – Calculates the 1D Green’s function for Figure 3(a) &amp; (b). <strong>Realisations_Uniform_1D_moments.m</strong> – Calculates the numerical 1D moments. Is used in Exp_C2_Uniform_nD_plotting.m &amp; Variance_Uniform_1D.m. <strong>Realisations_Uniform_2D.m</strong> - Calculates the 2D numerical realisation and plots the 2D numerical realisation, expectation and variance given in Figure 2(a), (b) &amp; (c) respectively. <strong>Realisations_Uniform_2D_moments.m</strong> - Calculates the numerical 2D moments. Is used in Realisations_Uniform_2D.m, Exp_C2_Uniform_nD_plotting.m, Exp_C2_Uniform_nD_effective_plotting.m &amp; Variance_Uniform_2D.m. <strong>Uniform.m</strong> – Calculates 1D numerical realisations and statistics for Figure 1. <strong>Variance_Uniform_1D.m</strong> – Calculates the variance of 1D corrections and plots the 1D numerical variance and 1D correction’s variance for Figure 4(a). <strong>Variance_Uniform_2D.m</strong> – Calculates the variance of 2D corrections and plots the 2D numerical variance and 2D correction’s variance for Figure 4(b). <br> These files offer supporting content for the following paper:<br> Title: Advection-dominated transport past isolated disordered sinks: stepping beyond homogenization Authors: George F. Price, Igor L. Chernyavsky &amp; Oliver E. Jensen Abstract: We investigate the transport of a solute past isolated sinks in a bounded domain when advection is dominant over diffusion, evaluating the effectiveness of homogenization approximations when sinks are distributed uniformly randomly in space. Corrections to such approximations can be non-local, non-smooth and non-Gaussian, depending on the physical parameters (a Péclet number Pe, assumed large, and a Damköhler number Da) and the compactness of the sinks. In one spatial dimension, solute distributions develop a staircase structure for large Pe, with corrections being better described with credible intervals than with traditional moments. In two and three dimensions, solute distributions are near-singular at each sink (and regularized by sink size), but their moments can be smooth as a result of ensemble averaging over variable sink locations. We approximate corrections to a homogenization approximation using a moment-expansion method, replacing the Green's function by its free-space form, and test predictions against simulation. We show how, in two or three dimensions, the leading-order impact of disorder can be captured in a homogenization approximation for the ensemble mean concentration through a modification to Da that grows with diminishing sink size. Arxiv link: https://arxiv.org/abs/2201.04574 <br>