论文标题
双曲线方法在四面盖驱动的腔中探索多样性流动溶液
Hyperbolic method to explore multiplicity flow solutions in a four-sided lid-driven cavity
论文作者
论文摘要
在这项研究中，采用双曲线方法来探索四面盖子驱动的方形腔中不可压缩流的流场状态。特别是，我们专注于在关键的雷诺数$ r_e \ simeq 130 $上获得的流分叉。在双曲线方法中，扩散项通过引入扩散通量项而转化为双曲线术语，这是附加方程的解决方案。因此，用于完整的通量（分裂为对流和扩散零件），用于解决稳态不可压缩的Navier-Stokes方程。流量的不可压缩性是通过人工伪压缩方法处理的。结果表明，我们的数值代码能够通过分析伪时间迭代过程中的残留项松弛来检测分叉。此外，根据两个空间方向的坡度限制器的组合选择，我们的方法能够在我们的研究中选择第一个或第二个稳定的解决方案。
In this study, the hyperbolic method is adopted to explore the flow field states of incompressible flow in a four-sided lid-driven square cavity. In particular, we focus on the flow bifurcation obtained at the critical Reynolds number $R_e \simeq 130$. In the hyperbolic method, the diffusive term is transformed into an hyperbolic one by introducing a diffusion flux term, which is the solution of an additional equation. A classical Riemann-like solver with a finite-volume discretization is thus employed for the full flux (splitted into advective and diffusive parts), in order to solve the steady-state incompressible Navier-Stokes equation. The incompressibility of the flow is treated via the artificial pseudo-compressibility method. It is shown that our numerical code is able to detect the bifurcation, by the analysis of the residual term relaxation during the pseudo-time iteration procedure. Moreover, depending on the combination choice of slope limiters for the two spatial directions, our method is able to select the first or the second stable solution among the double flow field state obtained when the Reynolds number is higher than the critical value that is estimated to be $129.4$ in our study.
