相关论文: Global Well-posedness for the Primitive Equations …

Recently, meshless methods have become popular in numerically solving partial differential equations and have been employed to solve equations governing fluid flows, heat transfer, and species transport. In the present study, a numerical…

When a liquid melt is cooled, a glass or phase transition can be obtained depending on the cooling rate. Yet, this behavior has not been clearly captured in energy landscape models. Here a model is provided in which two key ingredients are…

The Muskat problem models the filtration of two incompressible immiscible fluids of different characteristics in porous media. In this paper, we consider both the 2D and 3D setting of two fluids of different constant densities and different…

We present significant differences in the simulated atmospheric flow for warm, tidally-locked small Neptunes and super Earths (based on a nominal GJ 1214b) when solving the simplified, and commonly used, primitive dynamical equations or the…

We consider the dynamic Biot model describing the interaction between fluid flow and solid deformation including wave propagation phenomena in both the liquid and solid phases of a saturated porous medium. The model couples a hyperbolic…

One of the key choices for numerical models of geophysical fluids is how parametrisations of physical processes interact with the numerical methods that handle the resolved flow, known in the atmospheric community as the dynamical core. As…

It is shown that the Cauchy problem of the equations in magnetohydrodynamics in the whole space is globally well-posed for any initial smooth and localized data. In general, the mathematical structure of solution shows that the coupled…

The study of the basic model for incompressible two-phase flows with phase transitions in the case of equal densities, initiated in the paper Pr\"uss, Shibata, Shimizu, and Simonett [16], is continued here with a stability analysis of…

This study proposes deterministic and stochastic energy-aware hybrid models that should enable simulations of idealized and primitive-equations Geophysical Fluid Dynamics (GFD) models at low resolutions without compromising on quality…

In the present paper, a continuum model is introduced for fluid flow in a deformable porous medium, where the fluid may undergo phase transitions. Typically, such problems arise in modeling liquid-solid phase transformations in groundwater…

The hypothesis on complete integrability of equations describing the potential motion of incompressible ideal fluid with free surface in 2-D space in presence and absence of gravity was formulated by Dyachenko and Zakharov in 1994 [1].…

We present a novel approach to kinetic theory modeling enabling the simulation of a generic, real gas presented by its corresponding equation of state. The model is based on mass, momentum and energy conservation, and unlike the lattice…

This paper is concerned with the analysis of the quasi-static thermo-poroelastic model. This model is nonlinear and includes thermal effects compared to the classical quasi-static poroelastic model (also known as Biot's model). It consists…

In this paper, we consider a complex fluid modeling nematic liquid crystal flows, which is described by a system coupling Navier-Stokes equations with a parabolic Q-tensor system. We first prove the global existence of weak solutions in…

In this paper, we consider the initial boundary value problem in a cylindrical domain to the three dimensional primitive equations with full eddy viscosity in the momentum equations but with only horizontal eddy diffusivity in the…

This work is devoted to the consistent modeling of a three-phase mixture of a gas, a liquid and its vapor. Since the gas and the vapor are mis-cible, the mixture is subjected to a non-symmetric constraint on the volume. Adopting the Gibbs…

A consistent and conservative Phase-Field method, including both the model and scheme, is developed for multiphase flows with an arbitrary number of immiscible and incompressible fluid phases. The consistency of mass conservation and the…

In this paper, we study a hydrodynamic phase-field system modeling the deformation of functionalized membranes in incompressible viscous fluids. The governing PDE system consists of the Navier-Stokes equations coupled with a convective…

We establish the global well-posedness of classical solutions to the vacuum free boundary problem of the 1-D viscous Saint-Venant system with large data. Since the depth $\rho$ of the fluid vanishes on the moving boundary, the momentum…

We investigated theoretically water evaporation from concentrated supramolecular mixtures, such as solutions of polymers or amphiphilic molecules, using numerical resolutions of a one dimensional model based on mass transport equations.…