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Traditional computational fluid dynamics calculates the physical information of the flow field by solving partial differential equations, which takes a long time to calculate and consumes a lot of computational resources. We build a fluid…
This paper focuses on an inverse problem associated with the plate equation which is derived from models in fluid mechanics and elasticity. We establish the unique identifying results in simultaneously determining both the unknown density…
In this work, we will present a physically consistent theory to derive the governing equations of the Large Eddy Simulation (LES) framework based on first principles rather than the motivation to conduct computationally affordable…
In the present work a simple kinetic model based on the Enskog equation is solved to get the rheological properties of a hard-disk fluid under shear far from equilibrium, as functions of the density and shear rate. Comparison with Monte…
We are concerned with underlying connections between fluids, elasticity, isometric embedding of Riemannian manifolds, and the existence of wrinkled solutions of the associated nonlinear partial differential equations. In this paper, we…
We consider the inverse problem of the detection of a single body, immersed in a bounded container filled with a fluid which obeys the stationary Navier-Stokes equations, from a single measurement of force and velocity on a portion of the…
The neural network method of solving differential equations is used to approximate the electric potential and corresponding electric field in the slit-well microfluidic device. The device's geometry is non-convex, making this a challenging…
This paper is devoted to the existence of a weak solution to a system describing a self-propelled motion of a rigid body in a viscous fluid in the whole $\mathbb{R}^3$. The fluid is modelled by the incompressible nonhomogeneous…
This study examines the stability of a flexible material interface between two fluids of the same viscosity in interaction with a free surface. When the layers are motionless, we provide evidence for the onset of a novel instability by…
Approximating solutions to partial differential equations (PDEs) is fundamental for the modeling of dynamical systems in science and engineering. Physics-informed neural networks (PINNs) are a recent machine learning-based approach, for…
The equations in conservative form for nonlinear waves modeling on a liquid film flowing down a vertical plane have been investigated. It has been found that in the computational domain extended along the transverse axis the equations with…
An initial-and boundary-value problem for the Kelvin-Voigt system, modeling a mixture of n incompressible and viscoelastic fluids, with non-constant density, is investigated in this work. The existence of global-in-time weak solutions is…
In this paper we present a new strategy to model the subgrid-scale scalar flux in a three-dimensional turbulent incompressible flow using physics-informed neural networks (NNs). When trained from direct numerical simulation (DNS) data,…
In this paper we show a structural stability result for water waves. The main motivation for this result is that we would like to exhibit a water wave whose interface starts as a graph and ends in a splash. Numerical simulations lead to an…
It has been considered that the effective bending rigidity of fluid membranes should be reduced by thermal undulations. However, recent thorough investigation by Pinnow and Helfrich revealed significance of measure factors for the partition…
In this paper we consider the numerical approximation of the two-phase membrane (obstacle) problem by finite difference method. First, we introduce the notion of viscosity solution for the problem and construct certain discrete nonlinear…
The present research is devoted to the problem of stability of the fluid flow moving in a channel with flexible walls and interacting with the walls, which are subject to traveling waves. Experimental data shows that the energy of the…
Perfect fluid spheres, both Newtonian and relativistic, have attracted considerable attention as the first step in developing realistic stellar models (or models for fluid planets). Whereas there have been some early hints on how one might…
In this work, we study the mechanical behavior of solids with microstructure using the framework of Cosserat elasticity with a single unit director. This formulation captures the coupling between deformation and orientational fields that…
This paper presents a complete inverse optimality study for a linearized tank-liquid system where the liquid is described by the viscous Saint-Venant model with surface tension and possible wall friction. We define an appropriate weak…