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A well-established numerical approach to solve the Navier--Stokes equations for incompressible fluids is Chorin's projection method, whereby the fluid velocity is explicitly updated, and then an elliptic problem for the pressure is solved,…

This work proposes a new stabilized $P_1\times P_0$ finite element method for solving the incompressible Navier--Stokes equations. The numerical scheme is based on a reduced Bernardi--Raugel element with statically condensed face bubbles…

In the present thesis, we are interested in the description of the dynamics of flows on large scales. In this context, the fluids are governed by rotational, weak compressibility and stratification effects, whose importance is measured by…

In this paper, we present a numerical scheme for the diffuse-interface model in [Abels, Garcke, Gr\"un, M3AS 22(3), 2012] for two-phase flow of immiscible, incompressible fluids. As that model is in particular consistent with…

Normalizing flows are invertible neural networks with tractable change-of-volume terms, which allow optimization of their parameters to be efficiently performed via maximum likelihood. However, data of interest are typically assumed to live…

In this article we study the asymptotic behavior of incompressible, ideal, time-dependent two dimensional flow in the exterior of a single smooth obstacle when the size of the obstacle becomes very small. Our main purpose is to identify the…

Extreme events play a crucial role in fluid turbulence. Inspired by methods from field theory, these extreme events, their evolution and probability can be computed with help of the instanton formalism as minimizers of a suitable action…

A mathematical model that governs turbulent flows through permeable media is considered in this work. The model under consideration is based on a double-averaging concept which in turn is described by the time-averaging technique…

Turbulence in quantum fluids has, surprisingly, a lot in common with its classical counterpart. Recently, cold atomic gases has emerged as a well controlled experimental platform to study turbulent dynamics. In this work, we introduce a…

Optical flow refers to the visual motion observed between two consecutive images. Since the degree of freedom is typically much larger than the constraints imposed by the image observations, the straightforward formulation of optical flow…

The central problem in the physics of immiscible two-phase flow in porous media is to find a proper description of the flow at scales large enough so that the medium may be regarded as a continuum: the scale-up problem. So far, the only…

This paper develops a consistent particle method for capturing the highly non-linear behavior of violent free-surface flows, based on an Enhanced Weakly Compressible Moving Particle Semi-implicit (EWC-MPS) method. It pays special attention…

Viscoelastic fluids are a common subclass of rheologically complex materials that are encountered in diverse fields from biology to polymer processing. Often the flows of viscoelastic fluids are unstable in situations where ordinary…

Normalizing flows are objects used for modeling complicated probability density functions, and have attracted considerable interest in recent years. Many flexible families of normalizing flows have been developed. However, the focus to date…

We show that a rather simple, steady modification of the streamwise velocity profile in a pipe can lead to a complete collapse of turbulence and the flow fully relaminarizes. Two different devices, a stationary obstacle (inset) and a device…

We investigate a compressible two-fluid Navier-Stokes type system with a single velocity field and algebraic closure for the pressure law. The constitutive relation involves densities of both fluids through an implicit function. We are…

Numerical simulation of multi-component flow systems characterized by the simultaneous presence of pressure-velocity coupling and pressure-density coupling dominated regions remains a significant challenge in computational fluid dynamics.…

In this paper, we present the results of a numerical study of air-water turbulent bubbly flow in a periodic vertical square duct. The study is conducted using a novel numerical technique which leverages Volume of Fluid method for interface…

A new time discretization scheme for the numerical simulation of two-phase flow governed by a thermodynamically consistent diffuse interface model is presented. The scheme is consistent in the sense that it allows for a discrete in time…

This paper presents an innovative framework for analyzing the regularity of solutions to the stochastic Navier-Stokes equations by integrating Sobolev-Besov hybrid spaces with fractional operators and quantum-inspired dynamics. We propose…