Abstract

To simulate incompressible Navier–Stokes equation, a temporal splitting scheme in time and high-order symmetric interior penalty Galerkin (SIPG) method in space discretization are employed, while the local Lax-Friedrichs flux is applied in the discretization of the nonlinear term. Under a constraint of the Courant–Friedrichs–Lewy (CFL) condition, two benchmark problems in 2D are simulated by the fully discrete SIPG method. One is a lid-driven cavity flow and the other is a circular cylinder flow. For the former, we compute velocity field, pressure contour and vorticity contour. In the latter, while the von Kármán vortex street appears with Reynolds number 50≤Re≤400, we simulate different dynamical behavior of circular cylinder flows, and numerically estimate the Strouhal numbers comparable to the existing experimental results. The calculations on vortex dominated flows are carried out to investigate the potential application of the SIPG method.

Highlights

  • IntroductionThe Navier–Stokes equations are a concise physics model of low Knudsen number (i.e. non-rarefied) fluid dynamics

  • The Navier–Stokes equations are a concise physics model of low Knudsen number fluid dynamics

  • Σe shall be chosen sufficiently large to guarantee coercivity, more accurately, the threshold values of σe in [22] are given for β 1⁄4 1 in the above formula, which is referred to an symmetric interior penalty Galerkin (SIPG) scheme

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Summary

Introduction

The Navier–Stokes equations are a concise physics model of low Knudsen number (i.e. non-rarefied) fluid dynamics. The velocity field develops into an oscillating separation line on the upper and lower surfaces This manifests as a series of shed vortices forming and convecting downstream with the mean flow. Both pressure and velocity field can be solved successively from linear elliptic and Helmholtz-type problems, respectively.

Temporal splitting scheme
The spatial discretizations
Numerical results
Conclusions
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