A note on the accuracy of the generalized‐α scheme for the incompressible Navier‐Stokes equations
A note on the accuracy of the generalized‐α scheme for the incompressible Navier‐Stokes equations
复制标题
关于不可压缩纳维-斯托克斯方程的广义-α格式精度的说明
DOI：
10.1002/nme.6550
复制
发表时间：
2020
影响因子：
2.9
通讯作者：
Marsden, Alison L.
中科院分区：
文献类型：
--
作者：
Liu, Ju;Lan, Ingrid S.;Tikenogullari, Oguz Z.;Marsden, Alison L.
我们研究了不可压缩Navier-Stokes方程的两种广义格式的时间精度。在广泛采用的方法中，压力在时间步长n +1处配置，而Navier-Stokes方程的其余部分则按照广义格式离散。该方案已被声称besecond-order准确的时间。我们开发了一套数值代码，使用非超稳定的高阶非均匀有理B样条（NURBS）元素进行空间离散。在这样做，我们能够实现高的空间精度和调查渐近时间收敛行为。数值证据表明，在上述时间离散化方法中，至少对于压力，仅实现了一阶精度。另一方面，在中间时间步长处评估压力可以提高二阶精度，并且简化了数值实现。我们推荐第二种方法作为积分不可压缩Navier-Stokes方程时的首选广义格式。
We investigate the temporal accuracy of two generalized‐schemes for the incompressible Navier‐Stokes equations. In a widely‐adopted approach, the pressure is collocated at the time steptn+ 1while the remainder of the Navier‐Stokes equations is discretized following the generalized‐scheme. That scheme has been claimed to besecond‐order accurate in time. We developed a suite of numerical code using inf‐sup stable higher‐order non‐uniform rational B‐spline (NURBS) elements for spatial discretization. In doing so, we are able to achieve high spatial accuracy and to investigate asymptotic temporal convergence behavior. Numerical evidence suggests that onlyfirst‐order accuracyis achieved, at least for the pressure, in this aforesaid temporal discretization approach. On the other hand, evaluating the pressure at the intermediate time steprecovers second‐order accuracy, and the numerical implementation is simplified. We recommend this second approach as the generalized‐scheme of choice when integrating the incompressible Navier‐Stokes equations.