Some recent advances in energetic variational approaches

Y Wang, C Liu - Entropy, 2022 - mdpi.com
In this paper, we summarize some recent advances related to the energetic variational
approach (EnVarA), a general variational framework of building thermodynamically …

Energetic variational approach for prediction of thermal electrokinetics in charging and discharging processes of electrical double layer capacitors

X Ji, C Liu, P Liu, S Zhou - Journal of Power Sources, 2022 - Elsevier
This work proposes a new variational, thermodynamically consistent model to predict
thermal electrokinetics in electric double layer capacitors (EDLCs) by using an energetic …

Field theory of reaction-diffusion: Law of mass action with an energetic variational approach

Y Wang, C Liu, P Liu, B Eisenberg - Physical Review E, 2020 - APS
We extend the energetic variational approach so it can be applied to a chemical reaction
system with general mass action kinetics. Our approach starts with an energy-dissipation …

Structure-preserving numerical approximations to a non-isothermal hydrodynamic model of binary fluid flows

S Sun, J Li, J Zhao, Q Wang - Journal of Scientific Computing, 2020 - Springer
We present two second order, structure-preserving numerical schemes for a newly derived
thermodynamically consistent, non-isothermal hydrodynamical phase field model for …

The Brinkman-Fourier system with ideal gas equilibrium

C Liu, JE Sulzbach - arXiv preprint arXiv:2007.07304, 2020 - arxiv.org
In this work, we will introduce a general framework to derive the thermodynamics of a fluid
mechanical system, which guarantees the consistence between the energetic variational …

Global existence of the non-isothermal Poisson–Nernst–Planck–Fourier system

CY Hsieh, TC Lin, C Liu, P Liu - Journal of Differential Equations, 2020 - Elsevier
In this paper, we use the Energetic Variational Approach to derive a non-isothermal
electrokinetic model. The charge transport is described through the Poisson–Nernst–Planck …

Positivity of temperature for some non-isothermal fluid models

NA Lai, C Liu, A Tarfulea - Journal of Differential Equations, 2022 - Elsevier
We establish three partial differential equation models describing the thermodynamic
behavior of a fluid by combining the energetic variational approach, appropriate constitutive …

On an incompressible inertial nematic electrolyte model of liquid crystal flow

D Ma, Y Ma - Applicable Analysis, 2024 - Taylor & Francis
We study the Cauchy problem of the new model of the three dimensional inertial nematic
electrolyte, which models the N-species charged particles diffuse and advect in the nematic …

A convergent finite element scheme for a fourth-order liquid crystal model

S Metzger - IMA Journal of Numerical Analysis, 2022 - academic.oup.com
In this manuscript we propose and analyse a fully discrete, unconditionally stable finite
element scheme for a recently developed director model for liquid crystalline flows (Metzger …

Well-posedness for the reaction-diffusion equation with temperature in a critical Besov space

C Liu, JE Sulzbach - Journal of Differential Equations, 2022 - Elsevier
We derive a model for the non-isothermal reaction-diffusion equation. Combining ideas from
non-equilibrium thermodynamics with the energetic variational approach we obtain a …