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首页> 外文期刊>Zeitschrift fur Angewandte Mathematik und Mechanik >Predictor/corrector co-simulation approaches for solver coupling with algebraic constraints
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Predictor/corrector co-simulation approaches for solver coupling with algebraic constraints

机译:具有代数约束的求解器耦合的预测器/校正器联合仿真方法

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In the paper at hand, co-simulation approaches are analyzed for coupling two solvers. The solvers are assumed to be coupled by algebraic constraint equations. We discuss 2 different coupling methods. Both methods are semi-implicit, i.e. they are based on a predictor/corrector approach. Method 1 makes use of the well-known Baumgarte-stabilization technique. Method 2 is based on a weighted multiplier approach. For both methods, we investigate formulations on index-3, index-2 and index-1 level and analyze the convergence, the numerical stability and the numerical error. The presented approaches require Jacobian matrices. Since only partial derivatives with respect to the coupling variables are needed, calculation of the Jacobian matrices may very easily be calculated numerically and in parallel with the predictor step. For that reason, the presented methods can in a straightforward manner be applied to couple commercial simulation tools without full solver access. The only requirement on the subsystem solvers is that the macro-time step can be repeated once in order to accomplish the corrector step. Within the paper, we introduce methods for coupling mechanical systems. The presented approaches can, however, also be applied to couple arbitrary non-mechanical dynamical systems.
机译:在本文中,分析了耦合两个求解器的协同仿真方法。假定求解器通过代数约束方程式耦合。我们讨论了2种不同的耦合方法。两种方法都是半隐式的,即它们基于预测器/校正器方法。方法1利用了众所周知的鲍姆加特稳定技术。方法2基于加权乘数法。对于这两种方法,我们研究指数3,指数2和指数1的公式,并分析其收敛性,数值稳定性和数值误差。提出的方法需要雅可比矩阵。由于仅需要关于耦合变量的偏导数,因此可以非常容易地在数值上并与预测器步骤并行地计算雅可比矩阵的计算。出于这个原因,提出的方法可以直接方式应用于耦合商业仿真工具,而无需完全求解器访问。子系统求解器的唯一要求是,宏时间步骤可以重复一次以完成校正器步骤。在本文中,我们介绍了耦合机械系统的方法。但是,所提出的方法也可以应用于耦合任意非机械动力系统。

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