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The relevance of conservation for stability and accuracy of numerical methods for fluid-structure interaction

机译：守恒与流固耦合数值方法的稳定性和准确性的相关性

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Numerical simulation of fluid-structure interactions has typically been done using partitioned solution methods. However, partitioned methods are inherently non-conservative and generally numerically unstable. The deficiencies of partitioned methods have motivated the investigation of monolithic solution methods. Conservation is possible for monolithic methods, the conditions have recently been presented [E.H. van Brummelen, S.J. Hulshoff, R. de Borst, Energy conservation under incompatibility for fluid-structure interaction problems, Comput. Methods Appl. Mech. Engrg. 192 (2003) 2727-2748]. In the present paper we investigate the relevance of maintaining conservation for a model fluid-structure interaction problem, viz., the piston problem. To distinguish the effect of the error induced by the interface coupling from the fluid and structure discretization errors, we use fluid subcycling and an exact time-integration method for the structure. A comparison between conservative and non-conservative monolithic methods as well as partitioned methods is made. We show that maintaining conservation has considerable impact on the stability and accuracy of the numerical method. These results also indicate that only for a conservative monolithic scheme the improvement in accuracy over partitioned methods warrants the computational cost associated with a monolithic solution. Moreover, we illustrate the implications that particular combinations of fluid and structure discretizations can have on the conservation properties of the fluid-structure interaction problem.
机译：流体-结构相互作用的数值模拟通常是使用分区求解方法完成的。但是，分区方法本质上是非保守的，并且通常在数值上不稳定。分区方法的不足促使了整体解决方法的研究。整体方法的保存是可能的，最近已经提出了条件[E.H.范·布鲁梅伦（S.J. Hulshoff，R. de Borst，“流体与结构相互作用问题不兼容下的节能”，计算机。方法应用。机甲gr 192（2003）2727-2748]。在本文中，我们研究了模型流体与结构相互作用问题（即活塞问题）的保持守恒的相关性。为了区分界面耦合引起的误差与流体和结构离散误差的影响，我们对结构使用流体子循环和精确的时间积分方法。比较了保守的和非保守的整体方法以及分区方法。我们表明，保持守恒对数值方法的稳定性和准确性有相当大的影响。这些结果还表明，仅对于保守的整体方案，与分区方法相比，准确性的提高才保证了与整体方案相关的计算成本。此外，我们说明了流体和结构离散化的特定组合可能对流体-结构相互作用问题的守恒性质产生的影响。

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