Related papers: Implicit-explicit schemes for incompressible flow …
We present an unconditionally energy-stable scheme for approximating the incompressible Navier-Stokes equations on domains with outflow/open boundaries. The scheme combines the generalized Positive Auxiliary Variable (gPAV) approach and a…
In this paper, we investigate a system coupled by nonhomogeneous incompressible Navier-Stokes equations and Allen-Cahn equations describing a diffuse interface for two-phase flow of viscous fluids with different densities in a bounded…
The lattice Boltzmann method (LBM) has gained increasing popularity in incompressible viscous flow simulations, but it uses many more variables than necessary. This defect was overcome by a recent approach that solves the more actual…
We present a numerical scheme for approximating the incompressible Navier-Stokes equations based on an auxiliary variable associated with the total system energy. By introducing a dynamic equation for the auxiliary variable and…
This article focusses on the analysis of a conforming finite element method for the time-dependent incompressible Navier-Stokes equations. For divergence-free approximations, in a semi-discrete formulation, we prove error estimates for the…
We advance the computation of physical modal expansions for unsteady incompressible flows. Point of departure is a linearization of the Navier-Stokes equations around its fixed point in a frequency domain formulation. While the most…
We investigate the time-asymptotic stability of solutions to the one-dimensional Navier-Stokes-Fourier system in the half-space, focusing on the outflow and impermeable wall problems. When the prescribed boundary and far-field conditions…
We study topology optimization governed by the incompressible Navier-Stokes flows using a phase field model. Novel stabilized semi-implicit schemes for the gradient flows of Allen-Cahn and Cahn-Hilliard types are proposed for solving the…
This paper aims to compare and evaluate various obstacle approximation techniques employed in the context of the steady incompressible Navier-Stokes equations. Specifically, we investigate the effectiveness of a standard volume penalization…
The existence and dynamical role of particular unstable Navier-Stokes solutions (exact coherent structures) is revealed in laboratory studies of weak turbulence in a thin, electromagnetically-driven fluid layer. We find that the dynamics…
We propose a fourth order Navier-Stokes solver based on the immersed interface method (IIM), for flow problems with stationary and one-way coupled moving boundaries and interfaces. Our algorithm employs a Runge-Kutta-based projection method…
Variable viscosity arises in many flow scenarios, often imposing numerical challenges. Yet, discretisation methods designed specifically for non-constant viscosity are few, and their analysis is even scarcer. In finite element methods for…
We develop a multirate timestepper for semi-implicit solutions of the unsteady incompressible Navier-Stokes equations (INSE) based on a recently-developed multidomain spectral element method (SEM). For {\em incompressible} flows, multirate…
We present a novel combination of numerical techniques to improve the efficiency, accuracy, and robustness of multi-component compressible flow simulations. At the core of our approach is an Entropy-Stable formulation that preserves kinetic…
In this work we study the asymptotic behavior of viscous incompressible 2D flow in the exterior of a small material obstacle. We fix the initial vorticity $\omega_0$ and the circulation $\gamma$ of the initial flow around the obstacle. We…
We consider a construction proposed in \cite{acharyaQAM} that builds on the notion of weak solutions for incompressible fluids to provide a scheme that generates variationally a certain type of dual solutions. If these dual solutions are…
A stable partitioned algorithm for fluid-structure interaction (FSI) problems that couple viscous incompressible flow with structural shells or beams is described. This added-mass partitioned (AMP) scheme uses Robin (mixed) interface…
Long-time and large-data existence of weak solutions for initial- and boundary-value problems concerning three-dimensional flows of \emph{incompressible} fluids is nowadays available not only for Navier--Stokes fluids but also for various…
In this paper, we study the behaviour at low Mach number of numerical schemes based on staggered discretizations for the barotropic Navier-Stokes equations. Three time discretizations are considered: the implicit-in-time scheme and two…
In this paper, a new family of implicit compact finite difference schemes for computation of unsteady convection-diffusion equation with variable convection coefficient is proposed. The schemes are fourth order accurate in space and second…