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This paper presents a robust, adaptive numerical scheme for simulating high density ratio and high shear multiphase flows on locally refined Cartesian grids that adapt to the evolving interfaces and track regions of high vorticity. The…
In this note, we address the validity of certain exact results from turbulence theory in the deterministic setting. The main tools, inspired by the work of Duchon-Robert (Inertial energy dissipation for weak solutions of incompressible…
An efficient numerical scheme based on the scalar auxiliary variable (SAV) and marker and cell scheme (MAC) is constructed for the Navier-Stokes equations. A particular feature of the scheme is that the nonlinear term is treated explicitly…
Fluid flows are omnipresent in nature and engineering disciplines. The reliable computation of fluids has been a long-lasting challenge due to nonlinear interactions over multiple spatio-temporal scales. The compressible Navier-Stokes…
A new model for the "rapid" part of the velocity/pressure-gradient correlation in the Reynolds averaged Navier-Stokes equations is suggested. It is shown that in an inhomogeneous incompressible turbulent flow, the model that is linear in…
In this paper, we examine a finite element approximation of the steady $p(\cdot)$-Navier-Stokes equations ($p(\cdot)$ is variable dependent) and prove orders of convergence by assuming natural fractional regularity assumptions on the…
The Navier-Stokes (NS) equations as a turbulence model have been widely applied in lots of fields. The NS equations contain such a fundamental assumption that all small physical/artificial disturbances could be neglected. Is this assumption…
Scaling up new scientific technologies from laboratory to industry often involves demonstrating performance on a larger scale. Computer simulations can accelerate design and predictions in the deployment process, though traditional…
Direct numerical simulation of turbulence at realistic Reynolds numbers is still beyond current computational capability, necessitating models that reduce the number of resolved spatial scales. Motivated by phenomenology and recent…
In Navier--Stokes (NS) turbulence, large-scale turbulent flows inevitably determine small-scale flows. Previous studies using data assimilation with the three-dimensional NS equations indicate that employing observational data resolved down…
Using Constantin-Iyer representation also known more generally as Euler-Lagrangian approach, we prove the local existence of the Navier-Stokes equations in weighted Sobolev spaces with external forcing on $\mathbf{R}^{d}$, for any dimension…
A few basic, intuitive, properties of the Navier-Stokes system of equations for incompressible fluid flows are discussed in this paper. We present a rephrased interpretation of the Navier-Stokes equation in a space having an arbitrary…
In this paper we investigate the stress concentration problem that occurs when two convex rigid particles are closely immersed in a fluid flow. The governing equations for the fluid flow are the stationary incompressible Navier-Stokes…
The NS equation is considered (in 2 & 3 dimensions) with a fixed forcing on large scale; the stationary states form a family of probability distributions on the fluid velocity fields depending on a parameter R (Reynolds number). It is…
We present a new high-order accurate computational fluid dynamics model based on the incompressible Navier-Stokes equations with a free surface for the accurate simulation of nonlinear and dispersive water waves in the time domain. The…
Data-driven reduced-order models of the dynamics of complex flows are important for tasks related to design, understanding, prediction, and control. Many flows obey symmetries, and the present work illustrates how these can be exploited to…
In the present paper we study slow-fast systems of coupled equations from fluid dynamics, where the fast component is perturbed by additive noise. We prove that, under a suitable limit of infinite separation of scales, the slow component of…
Inf-sup stable FEM applied to time-dependent incompressible Navier-Stokes flows are considered. The focus lies on robust estimates for the kinetic and dissipation energies in a twofold sense. Firstly, pressure-robustness ensures the…
The goal of this paper is to study convergence and error estimates of the Monte Carlo method for the Navier-Stokes equations with random data. To discretize in space and time, the Monte Carlo method is combined with a suitable deterministic…
The presented research paper illustrates the development of a new methodology to solve 2-dimensional (2D) Navier-Stoke equations, which Pukhnachev proposed through introducing unknown functions in the stream and pressure functions of fluid…