The barely implicit correction algorithm for low-Mach-Number flows
The barely implicit correction algorithm for low-Mach-Number flows
复制标题
低马赫数流的隐式修正算法
DOI：
10.1016/j.compfluid.2018.08.019
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发表时间：
2018
影响因子：
2.8
通讯作者：
Oran, Elaine S.
中科院分区：
文献类型：
--
作者：
Zhang, Xiao;Chung, Joseph D.;Kaplan, Carolyn R.;Oran, Elaine S.
针对低马赫数流的模拟问题，提出了一种新的勉强隐式校正（BIC）算法。这种新算法是基于G. Patnaik等人提出的原始算法。帕特奈克，R. H. Guirguis， J. P. Boris和E. S. Oran，通量修正输运的基本隐式修正。在：Journal of Computational Physics 71.1 (1987), pp. 120]，这是一个求解过程，包括一个显式的预测步骤来求解Navier-Stokes方程的对流部分，以及一个隐式的校正步骤来消除积分时间步上的声学限制。显式预测器使用高阶单调算法，而隐式校正器求解椭圆方程，用于压力校正以平衡声波。在本文中，我们发展和扩展了多维粘性流动的BIC。我们引入了一个新的滤波器来进一步稳定算法，并阐明了包含粘性通量的求解过程。通过三个难度依次增加的测试问题对新算法进行检验。首先，模拟了二维盖子驱动的空腔流动，以验证BIC求解稳态旋流的能力。使用大于显式极限至少100倍的时间步长，与前人的不可压缩计算相比，得到了很好的一致性。以二维双周期剪切层流动为例，验证了该算法在求解强涡度梯度瞬态流动中的应用。最后，利用三维旋流中的涡流击穿进一步验证了该算法的稳定性和性能。同时比较了二维双周期剪切层和三维涡旋击穿的显式和隐式BIC计算。他们证明了新的BIC算法能够使用从接近显式稳定性极限到数十倍和数百倍大的时间步长来预测准确和鲁棒的解决方案。与其它算法的结果进行比较，得到了很好的一致性。我们讨论了我们对这些计算和特征的观察，这些计算和特征对于稳健地模拟低速、高动态流动至关重要。
A new Barely Implicit Correction (BIC) algorithm is presented for the simulation of low-Mach-number flows. This new algorithm is based on the original, introduced by G. Patnaik et al. [G. Patnaik, R. H. Guirguis, J. P. Boris and E. S. Oran, A barely implicit correction for flux-corrected transport. In: Journal of Computational Physics 71.1 (1987), pp. 120], which was a solution procedure including an explicit predictor step to solve the convective portion of the Navier–Stokes equations and an implicit corrector step to remove the acoustic limit on the integration time-step. The explicit predictor uses a high-order monotone algorithm while the implicit corrector solves an elliptic equation for a pressure correction to equilibrate acoustic waves. In this paper, we develop and extend BIC for multidimensional viscous flows. We introduce a new filter to further stabilize the algorithm and clarify the solution procedure for the inclusion of the viscous fluxes. The new algorithm is examined in three test problems with successively increased difficulty. First, a two-dimensional lid-driven cavity flow is simulated to demonstrate the ability of BIC on solving steady-state swirling flows. Using time steps at least 100 times larger than the explicit limit, good agreements are obtained for solutions when compared with an incompressible calculation by a prior work. A two-dimensional (2D) doubly periodic shear layer flow is simulated to examine the algorithm on solving a transient flow with strong vorticity gradients. Finally, vortex breakdown in three-dimensional (3D) swirling flows are used to further test the stability and performance of the new BIC algorithm. Comparisons of explicit and implicit BIC calculations of both the 2D doubly periodic shear layer and 3D vortex breakdown are presented side by side. They demonstrate that the new BIC algorithm is able to predict accurate and robust solutions using time steps varying from near the explicit stability limit to tens and hundreds of times larger. Excellent agreement is also obtained when compared with results from other algorithms. We discuss our observations of these computations and features which were found to be critical for robustly simulating low-speed, highly dynamic flows.
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