Related papers: Thermodynamically Consistent Algorithms for Models…
Reduced basis methods are popular for approximately solving large and complex systems of differential equations. However, conventional reduced basis methods do not generally preserve conservation laws and symmetries of the full order model.…
Partial differential equations (PDEs) describing thermodynamically isolated systems typically possess conserved quantities (like mass, momentum, and energy) and dissipated quantities (like entropy). Preserving these conservation and…
A thermodynamically consistent particle-based model for fluid dynamics with continuous velocities and a non-ideal equation of state is presented. Excluded volume interactions are modeled by means of biased stochastic multiparticle…
Developing high-order numerical schemes for two-phase flow in porous media that preserve key physical properties remains a significant challenge in numerical analysis. In this article, we propose a general framework to construct fully…
In the context of mathematical modeling, it is sometimes convenient to integrate models of different nature. These types of combinations, however, might entail difficulties even when individual models are well-understood, particularly in…
In this paper, we investigate ultraspherical spectral method for the Ohta-Kawasaki (OK) and Nakazawa-Ohta (NO) models in the disk domain, representing diblock and triblock copolymer systems, respectively. We employ ultraspherical spectral…
Accurate prediction of phase equilibria remains a central challenge in chemical engineering. Physics-consistent machine learning methods that incorporate thermodynamic structure into neural networks have recently shown strong performance…
We present and analyze two stabilized finite element methods for solving numerically the Poisson--Nernst--Planck equations. The stabilization we consider is carried out by using a shock detector and a discrete graph Laplacian operator for…
The dynamics of thermally fluctuating conserved order parameters are described by stochastic conservation laws. Thermal equilibrium in such systems requires the dissipative and stochastic components of the flux to be related by detailed…
In this paper we study a new model for patterns in two dimensions, inspired by diblock copolymer melts with a dominant phase. The model is simple enough to be amenable not only to numerics but also to analysis, yet sophisticated enough to…
Local master equations are a widespread tool to model open quantum systems, especially in the context of many-body systems. These equations, however, are believed to lead to thermodynamic anomalies and violation of the laws of…
We build a transient multidimensional multiphysical model based on continuum theories, involving the coupled mechanical, thermal and electrochemical phenomena occurring simultaneously in the discharge or charge of lithium-ion batteries. The…
In this study, we have derived a thermodynamically consistent phase-field model for two-phase flows with thermocapillary effects. This model accommodates variations in physical properties such as density, viscosity, heat capacity, and…
Atmospheric systems incorporating thermal dynamics must be stable with respect to both energy and entropy. While energy conservation can be enforced via the preservation of the skew-symmetric structure of the Hamiltonian form of the…
We show that any second order linear ordinary diffrential equation with constant coefficients (including the damped and undumped harmonic oscillator equation) admits an exact discretization, i.e., there exists a difference equation whose…
A dynamic linear thermo-poroelasticity model, containing inertial and relaxation terms with second-order time derivatives, is investigated in this paper. The mathematical and numerical analysis of this model is performed in the frequency…
A novel energy minimization formulation of electrostatics that allows computation of the electrostatic energy and forces to any desired accuracy in a system with arbitrary dielectric properties is presented. An integral equation for the…
We construct a discrete model of fluid particles according to the GENERIC formalism. The model has the form of Smoothed Particle Hydrodynamics including correct thermal fluctuations. A slight variation of the model reproduces the…
Convection-diffusion-reaction equations are a class of second-order partial differential equations widely used to model phenomena involving the change of concentration/population of one or more substances/species distributed in space.…
A finite element discretization using a method of lines approached is proposed for approximately solving the Poisson-Nernst-Planck (PNP) equations. This discretization scheme enforces positivity of the computed solutions, corresponding to…