Related papers: Tracking complex singularities of fluids on log-la…
Can every physical system simulate any Turing machine? This is a classical problem which is intimately connected with the undecidability of certain physical phenomena. Concerning fluid flows, Moore asked in [15] if hydrodynamics is capable…
The simulation of large open water surface is challenging using a uniform volumetric discretization of the Navier-Stokes equations. Simulating water splashes near moving objects, which height field methods for water waves cannot capture,…
We report the first simulations of the Faraday instability using the full three-dimensional Navier-Stokes equations in domains much larger than the characteristic wavelength of the pattern. We use a massively parallel code based on a hybrid…
A basic issue for Navier-Stokes (NS) fluids is their characterization in terms of the so-called NS phase-space classical dynamical system, which provides a mathematical model for the description of the dynamics of infinitesimal (or…
We propose a method to stabilise a solution to equations describing the interface of thin liquid films falling under gravity with a finite number of actuators and restricted observations. As for many complex systems, full observation of the…
We present the Fully cOUpled loCAl model of sUperfLuid Turbulence (FOUCAULT) that describes the dynamics of finite temperature superfluids. The superfluid component is described by the vortex filament method while the normal fluid is…
We consider the thin-film equation $\partial_t h + \nabla \cdot \left(h^2 \nabla \Delta h\right) = 0$ in physical space dimensions (i.e., one dimension in time $t$ and two lateral dimensions with $h$ denoting the height of the film in the…
We consider the flow of two viscous and incompressible fluids within a bounded domain modeled by means of a two-phase Navier-Stokes system. The two fluids are assumed to be immiscible, meaning that they are separated by an interface. With…
Immersed methods discretize boundary conditions for complex geometries on background Cartesian grids. This makes such methods especially suitable for two-way coupled flow-body problems, where the body mechanics are partially driven by…
The paper extends a stabilized fictitious domain finite element method initially developed for the Stokes problem to the incompressible Navier-Stokes equations coupled with a moving solid. This method presents the advantage to predict an…
The subject of this work is the instability mechanism of simple shear flows, like Hagen-Poiseuille pipe flow, which is a long-standing problem in fluid mechanics [1,2]. A possible analogy with phenomenological theory of ideal plasticity in…
We address the question whether a singularity in a three-dimensional incompressible inviscid fluid flow can occur in finite time. Analytical considerations and numerical simulations suggest high-symmetry flows being a promising candidate…
A perfectly elastic beam is situated on top of a two dimensional fluid canister. The beam is deforming in accordance to an interaction with a Navier-Stokes fluid. Hence a hyperbolic equation is coupled to the Navier-Stokes equation. The…
We study a triple singular limit for the scaled barotropic Navier-Stokes system modeling the motion of a rotating, compressible, and viscous fluid, where the Mach and Rossby numbers are proportional to a small parameter, while the Reynolds…
Kinetic approaches, i.e., methods based on the lattice Boltzmann equations, have long been recognized as an appealing alternative for solving incompressible Navier-Stokes equations in computational fluid dynamics. However, such approaches…
Direct numerical simulations of a temporally-developing, low-speed, variable-density, turbulent, plane mixing layer are performed. The Navier-Stokes equations in the low-Mach number approximation are solved using a novel algorithm based on…
We study the Navier-Stokes equations governing the motion of isentropic compressible fluid in three dimensions driven by a multiplicative stochastic forcing. In particular, we consider a stochastic perturbation of the system as a function…
We consider here the stationary Micropolar fluid equations which are a particular generalization of the usual Navier-Stokes system where the microrotations of the fluid particles must be taken into account. We thus obtain two coupled…
A new approach to the old-standing problem of the anomaly of the scaling exponents of nonlinear models of turbulence has been proposed and tested through numerical simulations. This is achieved by constructing, for any given nonlinear…
We construct non-unique Leray solutions of the forced Navier-Stokes equations in bounded domains via gluing methods. This demonstrates a certain locality and robustness of the non-uniqueness discovered by the authors in [1].