In this study we use a fast Fourier spectral technique to simulate the Navier-Stokes equations with no-slip boundary conditions. This is enforced by an immersed boundary technique called volumepenalization. The approach has been justified by analytical proofs of the convergence with respect to the penalization parameter. However, the solution of the penalized Navier-Stokes equations is not smoo...

This report performs a complete analysis of convergence and rates of convergence of finite element approximations of the Navier-Stokes-α (NS-α) regularization of the NSE, under a zero-divergence constraint on the velocity, to the true solution of the NSE. Convergence of the discrete NS-α approximate velocity to the true Navier-Stokes velocity is proved and rates of convergence derived, under no...

A new method will be introduced for the derivation of thermodynamically consistent boundary conditions for the full Cahn-Hilliard-Navier-Stokes-Fourier system for two immiscible fluids, where the phase field variable (order parameter) is given in terms of concentrations or partial densities. Five different types of models will be presented and discussed. The article can be considered as a conti...

We consider the flow of a class of incompressible fluids which are constitutively defined by the symmetric part of the velocity gradient being a function, which can be nonmonotone, of the deviator of the stress tensor. These models are generalizations of the stress power-law models introduced and studied by J. Málek, V. Pr̊uša, K.R. Rajagopal : Generalizations of the Navier-Stokes fluid from a n...

Abstract. In the setting of the CE/SE method, a new and unified wall boundary treatment for the Navier-Stokes and Euler Equations is proposed. In essence, the shear stress exerted on the fluid by a wall is modeled as a source term as a part of local space-time flux conservation in the vicinity of a wall boundary. When the fluid is inviscid, the source term vanishes and the boundary condition re...

Several relations from the Kolmogorov theory of fully-developed threedimensional turbulence are rigorously established for finite-time averages over LerayHopf weak solutions of the Navier-Stokes equations. The Navier-Stokes equations are considered with periodic or no-slip boundary conditions and an external forcing term. The main parameter is the Grashof number associated with the forcing term...

We propose a mixed finite element method for the motion of a strongly viscous, ideal, and isentropic gas. At the boundary we impose a Navier–slip condition such that the velocity equation can be posed in mixed form with the vorticity as an auxiliary variable. In this formulation we design a finite element method, where the velocity and vorticity is approximated with the divand curlconforming Né...

Measuring the relaxation time involved in the levelling of a free surface of a Newtonian fluid laid on a substrate can give access to material parameters. It is shown here how most favourable pattern geometries of the free surface and film thicknesses can be defined for the measures of viscosity and Navier slip length at the fluid-solid interface, respectively. Moreover, we put special emphasis...

A difficulty in the classical hydrodynamic analysis of moving contact-line problems, associated with the no-slip wall boundary condition resulting in an unbalanced divergence of the viscous stresses, is reexamined with a smoothed, finite-width interface model. The analysis in the sharp-interface limit shows that the singularity of the viscous stress can be balanced by another singularity of the...

Abstract. Pumping performance of a disk-type drag pump is studied numerically and experimentally. Molecular transition and slip flows that arise in a spiral channel on the rotating disk are simulated by using particle and continuum methods. The particle approach employs the direct simulation Monte Carlo (DSMC) method, and the continuum approach solves the Navier-Stokes (N-S) equations. A new DS...