On a holistic investigation of implicit/explicit/semi-implicit GS4-I framework and time step control for unsteady fluid dynamics

IF 4 3区 工程技术 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Yazhou Wang, Kumar K. Tamma, Dean J. Maxam, Tao Xue
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引用次数: 0

Abstract

Purpose

This paper aims to design and analyze implicit/explicit/semi-implicit schemes and a universal error estimator within the Generalized Single-step Single-Solve computational framework for First-order transient systems (GS4-I), which also fosters the adaptive time-stepping procedure to improve stability, accuracy and efficiency applied for fluid dynamics.

Design/methodology/approach

The newly proposed child-explicit and semi-implicit schemes emanate from the parent implicit GS4-I framework, providing numerous options with flexible and controllable numerical properties to the analyst. A universal error estimator is developed based on the consistent algorithmic variables and it works for all the developed methods. Applications are demonstrated by merging the developed algorithms into the iterated pressure-projection method for incompressible Navier–Stokes equations.

Findings

The child-explicit GS4-I has improved solution accuracy and stability properties, and the most stable option is the child explicit GS4-I(0,0)/second-order backward differentiation formula/Gear’s methods, which is new and novel. Numerical tests validate that the universal error estimator emanating from implicit designs works well for the newly proposed explicit/semi-implicit algorithms. The iterative pressure-correction projection algorithm is efficiently fostered by the error estimator-based adaptive time-stepping.

Originality/value

The implicit/explicit/semi-implicit methods within a unified computational framework are easy to implement and have flexible options in practical applications. In contrast to traditional error estimators, which work only on an algorithm-by-algorithm basis, the proposed error estimator is universal. They work for the entire class of implicit/explicit/semi-implicit linear multi-step methods that are second-order time accurate. Based on the accurately estimated local error, balance amongst stability, accuracy and efficiency can be well achieved in the dynamic simulation.

非定常流体动力学隐式/显式/半隐式GS4-I框架及时间步进控制的综合研究
目的设计和分析一阶瞬态系统广义单步单解计算框架(GS4-I)中的隐式/显式/半隐式格式和通用误差估计器,促进自适应时步程序的发展,以提高流体动力学应用的稳定性、精度和效率。设计/方法/方法新提出的子显式和半隐式方案源自父隐式GS4-I框架,为分析人员提供了许多具有灵活和可控数值特性的选项。提出了一种基于一致性算法变量的通用误差估计器,它适用于所有已开发的方法。通过将所开发的算法合并到不可压缩Navier-Stokes方程的迭代压力投影法中,证明了其应用。结果子显式GS4-I具有较好的解精度和稳定性,其中最稳定的选择是子显式GS4-I(0,0)/二阶后向微分公式/Gear方法,这是一种新颖的方法。数值实验验证了基于隐式设计的通用误差估计器对新提出的显式/半隐式算法的有效性。基于误差估计的自适应时间步进有效地促进了迭代压力校正投影算法。原创性/价值在统一的计算框架内,隐式/显式/半隐式方法易于实现,在实际应用中具有灵活的选择。传统的误差估计器只能在逐个算法的基础上工作,与之相反,所提出的误差估计器具有通用性。它们适用于所有二阶时间精确的隐式/显式/半隐式线性多步方法。基于准确估计的局部误差,可以在动态仿真中很好地实现稳定性、精度和效率之间的平衡。
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来源期刊
CiteScore
9.50
自引率
11.90%
发文量
100
审稿时长
6-12 weeks
期刊介绍: The main objective of this international journal is to provide applied mathematicians, engineers and scientists engaged in computer-aided design and research in computational heat transfer and fluid dynamics, whether in academic institutions of industry, with timely and accessible information on the development, refinement and application of computer-based numerical techniques for solving problems in heat and fluid flow. - See more at: http://emeraldgrouppublishing.com/products/journals/journals.htm?id=hff#sthash.Kf80GRt8.dpuf
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