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We explore the unsupervised clustering technique introduced in [25] to identify viscous/turbulent from inviscid regions in incompressible flows. The separation of regions allows solving the Navier-Stokes equations including Large Eddy…
We propose an efficient, accurate and robust implicit solver for the incompressible Navier-Stokes equations, based on a DG spatial discretization and on the TR-BDF2 method for time discretization. The effectiveness of the method is…
We prove the global existence and uniqueness of strong solutions for a compressible multifluid described by the barotropic Navier-Stokes equations in dim = 1. The result holds when the diffusion coefficient depends on the pressure. It…
We study a low-rank iterative solver for the unsteady Navier-Stokes equations for incompressible flows with a stochastic viscosity. The equations are discretized using the stochastic Galerkin method, and we consider an all-at-once…
In this paper, we introduce a method of imposing asymmetric conditions on the velocity vector with respect to independent variables and a method of moving frame for solving the three dimensional Navier-Stokes equations. Seven families of…
We investigate a one dimensional flow described with the non-compressible coupled Euler and non-compressible Navier-Stokes equations in Cartesian coordinate systems. We couple the two fluids through the continuity equation where different…
We present a second-order monolithic method for solving incompressible Navier--Stokes equations on irregular domains with quadtree grids. A semi-collocated grid layout is adopted, where velocity variables are located at cell vertices, and…
A new high order accurate semi-implicit space-time Discontinuous Galerkin method on staggered grids, for the simulation of viscous incompressible flows on two-dimensional domains is presented. The designed scheme is of the Arbitrary…
In this paper we consider the numerical approximation of the incompressible surface Navier--Stokes equations on an evolving surface. For the discrete representation of the moving surface we use parametric finite elements of degree $\ell…
For the N>=2 dimensional incompressible Naver-Stokes Equation, We have got its solution as a power series of time t, in which the coefficients are all known functions determined only by the initial velocity v0. We also prove that the…
We present nsCouette, a highly scalable software tool to solve the Navier-Stokes equations for incompressible fluid flow between differentially heated and independently rotating, concentric cylinders. It is based on a pseudospectral spatial…
We present an novel algorithm for tracking massless solid particles in a divergence-free velocity field that is only available at discrete points in space and time such as those arising from a direct numerical simulation of Navier-Stokes.…
The local existence of solutions to nonhomogeneous Navier-Stokes equations in cylindrical domains with arbitrary large flux is demonstrated. The existence is proved by the method of successive approximations. To show the existence with the…
The aim of this contribution is to make a connection between two recent results concerning the dynamics of vortices in incompressible planar flows. The first one is an asymptotic expansion, in the vanishing viscosity limit, of the solution…
This article is an updated version of the article that was published in the Electronic Journal of Differential Equations on 10. July 2010. Two footnotes have been added. One corrects a minor error not influencing the proof, the second is…
In this paper, we establish the existence of probabilistically strong, measure-valued solutions for the stochastic incompressible Navier--Stokes equations and prove their convergence, in the vanishing viscosity limit, to probabilistically…
Accurately modeling the dynamics of high-density ratio ($\mathcal{O}(10^5)$) two-phase flows is important for many material science and manufacturing applications. This work considers numerical simulations of molten metal oscillations in…
We revisit and present new linear spaces of explicit solutions to incompressible Euler and Navier-Stokes equations on $\mathbb{R}^n$, as well as the rotating Boussinesq equations on $\mathbb{R}^3$. We cast these solutions are superpositions…
In this paper we study a finite-depth layer of viscous incompressible fluid in dimension $n \ge 2$, modeled by the Navier-Stokes equations. The fluid is assumed to be bounded below by a flat rigid surface and above by a free, moving…
This paper is concerned with self-similar solutions of the steady Navier-Stokes system in a two-dimensional sector with the no-slip boundary condition. We give necessary and sufficient conditions in terms of the angle of the sector and the…