A novel Lax–Wendroff type procedure of two-derivative time-stepping schemes for Euler and Navier–Stokes equations

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-11-06 DOI:10.1016/j.cnsns.2024.108436

Xueyu Qin, Xin Zhang, Jian Yu, Chao Yan

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引用次数: 0

Abstract

In this paper, we developed a novel Lax–Wendroff (LW) type procedure of two-derivative time-stepping schemes for the Euler and Navier–Stokes equations. The explicit two-derivative time-stepping schemes, including the two-derivative Runge–Kutta schemes and variable step size two-derivative multistep schemes, are proposed and the optimized time-stepping schemes are determined by the strong stability preserving theory. The novel LW procedure greatly simplifies the intricate symbolic calculations of the original LW procedure, particularly for the Navier–Stokes equations. The novel LW procedure also ensures both the order accuracy and numerical stability compared to the original LW procedure. Moreover, we presented a simplified positivity-preserving limiter for LW procedure, enabling the temporal schemes to handle demanding computations. When employing high-order spatial methods, numerical tests highlighted that two-derivative time-stepping schemes utilizing the novel LW procedure effectively improve the stability and computational efficiency compared to the Runge–Kutta schemes.

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针对欧拉方程和纳维-斯托克斯方程的新型 Lax-Wendroff 型两衍生时间步进方案程序

本文针对欧拉方程和纳维-斯托克斯方程开发了一种新颖的 Lax-Wendroff (LW) 型双衍时间步进方案程序。本文提出了显式二衍时间步进方案，包括二衍 Runge-Kutta 方案和可变步长二衍多步方案，并通过强稳定性理论确定了优化的时间步进方案。新型 LW 程序大大简化了原始 LW 程序中复杂的符号计算，尤其是 Navier-Stokes 方程。与原始 LW 程序相比，新型 LW 程序还确保了阶次精度和数值稳定性。此外，我们还提出了一种简化的 LW 程序正向保留限制器，使时间方案能够处理苛刻的计算。在采用高阶空间方法时，数值测试表明，与 Runge-Kutta 方案相比，利用新型 LW 程序的二衍生时间步进方案有效地提高了稳定性和计算效率。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.