# Longer time simulation of the unsteady Navier-Stokes equations based on a modified convective formulation

@article{Li2021LongerTS, title={Longer time simulation of the unsteady Navier-Stokes equations based on a modified convective formulation}, author={Xu Li and Hongxing Rui}, journal={ArXiv}, year={2021}, volume={abs/2112.02330} }

For the discretization of the convective term in the Navier-Stokes equations (NSEs), the commonly used convective formulation (CONV) does not preserve the energy if the divergence constraint is only weakly enforced. In this paper, we apply the skew-symmetrization technique in [B. Cockburn, G. Kanschat and D. Schötzau, Math. Comp., 74 (2005), pp. 1067-1095] to conforming finite element methods, which restores energy conservation for CONV. The crucial idea is to replace the discrete advective…

## Figures from this paper

## References

SHOWING 1-10 OF 51 REFERENCES

### Longer time accuracy for incompressible Navier-Stokes simulations with the EMAC formulation

- MathematicsArXiv
- 2020

### Efficient discretizations for the EMAC formulation of the incompressible Navier–Stokes equations

- MathematicsApplied Numerical Mathematics
- 2019

### A locally conservative LDG method for the incompressible Navier-Stokes equations

- MathematicsMath. Comput.
- 2005

A new local discontinuous Galerkin method for the incompressible stationary Navier-Stokes equations is proposed and analyzed, which confirms the independence of the number of fixed point iterations with respect to the discretization parameters and works well for a wide range of Reynolds numbers.

### Analysis of the grad-div stabilization for the time-dependent Navier–Stokes equations with inf-sup stable finite elements

- Computer ScienceAdv. Comput. Math.
- 2018

Taking into account the loss of regularity suffered by the solution of the Navier–Stokes equations at the initial time in the absence of nonlocal compatibility conditions of the data, error bounds of order O(h2)$\mathcal O( h^{2})$ in space are proved.

### On the Divergence Constraint in Mixed Finite Element Methods for Incompressible Flows

- Computer ScienceSIAM Rev.
- 2017

Several approaches for improving the discrete mass balance or even for computing divergence-free solutions will be discussed: grad-div stabilization, higher order mixed methods derived on the basis of an exact de Rham complex, $H(div)$-conforming finite ...

### On the role of the Helmholtz decomposition in mixed methods for incompressible flows and a new variational crime

- Computer Science
- 2014

### Divergence-Free H(div)-FEM for Time-Dependent Incompressible Flows with Applications to High Reynolds Number Vortex Dynamics

- PhysicsJ. Sci. Comput.
- 2018

Focussing on dynamic high Reynolds number examples with vortical structures, the proposed H(div)-FEM method proves to be capable of reliably handling the planar lattice flow problem, Kelvin–Helmholtz instabilities and freely decaying two-dimensional turbulence.

### Pressure-robust analysis of divergence-free and conforming FEM for evolutionary incompressible Navier–Stokes flows

- PhysicsJ. Num. Math.
- 2017

For divergence-free approximations, in a semi-discrete formulation, it is proved that error estimates for the velocity that hold independently of both pressure and Reynolds number are proved.