An extension of the SIMPLE based discontinuous Galerkin solver to unsteady incompressible flows
An extension of the SIMPLE based discontinuous Galerkin solver to unsteady incompressible flows
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基于 SIMPLE 的间断伽辽金求解器对不稳定不可压缩流的扩展
DOI：
10.1002/fld.3994
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发表时间：
2015
影响因子：
1.8
通讯作者：
Oberlack
中科院分区：
文献类型：
--
作者：
Kummer;Oberlack
本文针对非定常不可压缩流动的不连续伽辽金方法，提出了一种基于SIMPLE的非定常不可压缩流动求解算法。时间离散化是完全隐式的，使用从1到4不等阶的后向微分公式（BDF）。我们表明，可以使用源自对称内部惩罚（SIP）方法的等效算子来修改压力校正的原始方程，从而减小模板尺寸。为了评估该方案的准确性、稳定性和性能，进行了三种不同的测试用例：Taylor涡旋流、平面泊泽维尔流的Orr‐Sommerfeld稳定性问题和流过方形圆柱体的流动。(1)模拟Taylor涡流，验证了不同BDF格式的时间精度。使用混合阶公式，空间收敛研究得出速度和压力的收敛率分别为k+ 1和k+ 2范数。对于等阶公式，我们得到近似相同的收敛速率，而绝对误差更小。(2)通过模拟Orr-Sommerfeld稳定性问题，验证了该方法的稳定性。采用混合阶公式并调整对称内罚法的惩罚参数对粘性部分进行离散化，证明了该算法的长期稳定性。使用压力稳定，在不改变惩罚参数的情况下，等阶公式是稳定的。(3)最后，通过方柱体流动的计算结果与数值参考解和实验结果吻合良好。版权所有©2015 John Wiley & Sons， Ltd
In this paper, we present a SIMPLE based algorithm in the context of the discontinuous Galerkin method for unsteady incompressible flows. Time discretization is done fully implicit using backward differentiation formulae (BDF) of varying order from 1 to 4. We show that the original equation for the pressure correction can be modified by using an equivalent operator stemming from the symmetric interior penalty (SIP) method leading to a reduced stencil size.To assess the accuracy as well as the stability and the performance of the scheme, three different test cases are carried out: the Taylor vortex flow, the Orr‐Sommerfeld stability problem for plane Poiseuille flow and the flow past a square cylinder. (1) Simulating the Taylor vortex flow, we verify the temporal accuracy for the different BDF schemes. Using the mixed‐order formulation, a spatial convergence study yields convergence rates ofk+ 1 andkin theL2‐norm for velocity and pressure, respectively. For the equal‐order formulation, we obtain approximately the same convergence rates, while the absolute error is smaller. (2) The stability of our method is examined by simulating the Orr–Sommerfeld stability problem. Using the mixed‐order formulation and adjusting the penalty parameter of the symmetric interior penalty method for the discretization of the viscous part, we can demonstrate the long‐term stability of the algorithm. Using pressure stabilization the equal‐order formulation is stable without changing the penalty parameter. (3) Finally, the results for the flow past a square cylinder show excellent agreement with numerical reference solutions as well as experiments. Copyright © 2015 John Wiley & Sons, Ltd.
纳维-斯托克斯方程的谱配置方法
影响因子：
4.1
作者：
M. Malik;T. Zang;M. Hussaini
通讯作者：
M. Hussaini
DOI：
10.1016/j.cma.2005.06.014
发表时间：
2006-05
影响因子：
7.2
作者：
B. Rivière;V. Girault
通讯作者：
B. Rivière;V. Girault
影响因子：
4.1
作者：
Klein, Benedikt;Kummer, Florian;Oberlack, Martin
通讯作者：
Oberlack, Martin