Energetic Stable Discretization for Non-Isothermal Electrokinetics Model
Simo Wu, Chun Liu, Ludmil Zitakanov
TL;DR
This paper introduces an edge averaged finite element discretization for the Heat-PNP equations, ensuring positivity and thermodynamic consistency, with numerical validation demonstrating its effectiveness.
Contribution
The paper presents a novel discretization method that enforces positivity and thermodynamic consistency for Heat-PNP equations, improving stability and physical fidelity.
Findings
Positivity of charge density and temperature functions is maintained.
The method provides a thermodynamically consistent energy estimate.
Numerical examples validate the proposed discretization's effectiveness.
Abstract
We propose an edge averaged finite element(EAFE) discretization to solve the Heat-PNP (Poisson-Nernst-Planck) equations approximately. Our method enforces positivity of the computed charged density functions and temperature function. Also the thermodynamic consistent discrete energy estimate which resembles the thermodynamic second law of the Heat-PNP system is prescribed. Numerical examples are provided.
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Taxonomy
TopicsModel Reduction and Neural Networks · Nanopore and Nanochannel Transport Studies · Geophysical and Geoelectrical Methods