A pressure-robust discretization of Oseen's equation using stabilization in the vorticity equation

07/08/2020
by   Naveed Ahmed, et al.
0

Discretization of Navier-Stokes' equations using pressure-robust finite element methods is considered for the high Reynolds number regime. To counter oscillations due to dominating convection we add a stabilization based on a bulk term in the form of a residual-based least squares stabilization of the vorticity equation supplemented by a penalty term on (certain components of) the gradient jump over the elements faces. Since the stabilization is based on the vorticity equation, it is independent of the pressure gradients, which makes it pressure-robust. Thus, we prove pressure-independent error estimates in the linearized case, known as Oseen's problem. In fact, we prove an O(h^k+1/2) error estimate in the L^2-norm that is known to be the best that can be expected for this type of problem. Numerical examples are provided that, in addition to confirming the theoretical results, show that the present method compares favorably to the classical residual-based SUPG stabilization.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

05/12/2022

Continuous Interior Penalty stabilization for divergence-free finite element methods

In this paper we propose, analyze, and test numerically a pressure-robus...
02/27/2020

A nonconforming pressure-robust finite element method for the Stokes equations on anisotropic meshes

Most classical finite element schemes for the (Navier-)Stokes equations ...
11/10/2019

Second order pressure estimates for the Crank-Nicolson discretization of the incompressible Navier-Stokes Equations

We provide optimal order pressure error estimates for the Crank-Nicolson...
09/01/2020

Pressure-robust error estimate of optimal order for the Stokes equations on domains with edges

The velocity solution of the incompressible Stokes equations is not affe...
02/26/2020

Quasi-optimal and pressure robust discretizations of the Stokes equations by moment- and divergence-preserving operators

We approximate the solution of the Stokes equations by a new quasi-optim...
11/05/2020

The Darcy problem with porosity depending exponentially on the pressure

We consider the flow of a viscous incompressible fluid through a porous ...
07/08/2021

Topological synthesis of fluidic pressure-actuated robust compliant mechanisms

This paper presents a density-based topology optimization approach for s...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.