A third-order entropy condition scheme for hyperbolic conservation laws

IF 1.7 4区 工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS International Journal for Numerical Methods in Fluids Pub Date : 2024-02-15 DOI:10.1002/fld.5268
Haitao Dong, Tong Zhou, Fujun Liu
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Abstract

Following the solution formula method given in Dong et al. (High order discontinuities decomposition entropy condition schemes for Euler equations. CFD J. 2002;10(4): 448–457), this article studies a type of one-step fully-discrete scheme, and constructs a third-order scheme which is written into a compact form via a new limiter. The highlights of this study and advantages of new third-order scheme are as follows: ① We proposed a very simple new methodology of constructing one-step, consistent high-order and non-oscillation schemes that do not rely on Runge–Kutta method; ② We systematically studied new scheme's theoretical problems about entropy conditions, error analysis, and non-oscillation conditions; ③ The new scheme achieves exact solution in linear cases and performing better in nonlinear cases when CFL → 1; ④ The new scheme is third order but high resolution with excellent shock-capturing capacity which is comparable to fifth order WENO scheme; ⑤ CPU time of new scheme is only a quarter of WENO5 + RK3 under same computing condition; ⑥ For engineering applications, the new scheme is extended to multi-dimensional Euler equations under curvilinear coordinates. Numerical experiments contain 1D scalar equation, 1D,2D,3D Euler equations. Accuracy tests are carried out using 1D linear scalar equation, 1D Burgers equation and 2D Euler equations and two sonic point tests are carried out to show the effect of entropy condition linearization. All tests are compared with results of WENO5 and finally indicate EC3 is cheaper in computational expense.

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双曲守恒定律的三阶熵条件方案
按照 Dong 等人(欧拉方程的高阶不连续分解熵条件方案。CFD J. 2002;10(4):448-457)中给出的求解公式方法,本文研究了一种一步全离散方案,并构造了一种三阶方案,通过一种新的限幅器将其写成紧凑的形式。本研究的重点和新三阶方案的优势如下:提出了一种不依赖 Runge-Kutta 方法的非常简单的新方法来构造一步一致的高阶和非振荡方案;② 系统地研究了新方案的熵条件、误差分析和非振荡条件等理论问题;③ 新方案在线性情况下实现了精确求解,在 CFL → 1 的非线性情况下性能更好;在相同计算条件下,新方案的 CPU 时间仅为 WENO5 + RK3 的四分之一;⑥针对工程应用,新方案扩展到曲线坐标下的多维欧拉方程。数值实验包括一维标量方程、一维、二维和三维欧拉方程。使用一维线性标量方程、一维布尔格斯方程和二维欧拉方程进行了精度测试,并进行了两次声波点测试,以显示熵条件线性化的影响。所有测试都与 WENO5 的结果进行了比较,最终表明 EC3 的计算成本更低。
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来源期刊
International Journal for Numerical Methods in Fluids
International Journal for Numerical Methods in Fluids 物理-计算机:跨学科应用
CiteScore
3.70
自引率
5.60%
发文量
111
审稿时长
8 months
期刊介绍: The International Journal for Numerical Methods in Fluids publishes refereed papers describing significant developments in computational methods that are applicable to scientific and engineering problems in fluid mechanics, fluid dynamics, micro and bio fluidics, and fluid-structure interaction. Numerical methods for solving ancillary equations, such as transport and advection and diffusion, are also relevant. The Editors encourage contributions in the areas of multi-physics, multi-disciplinary and multi-scale problems involving fluid subsystems, verification and validation, uncertainty quantification, and model reduction. Numerical examples that illustrate the described methods or their accuracy are in general expected. Discussions of papers already in print are also considered. However, papers dealing strictly with applications of existing methods or dealing with areas of research that are not deemed to be cutting edge by the Editors will not be considered for review. The journal publishes full-length papers, which should normally be less than 25 journal pages in length. Two-part papers are discouraged unless considered necessary by the Editors.
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