共查询到20条相似文献，搜索用时 15 毫秒
1.
Shengye Wang Guangxue Wang Dan Xu Dongfang Wang 《International Journal of Computational Fluid Dynamics》2016,30(7-10):469-488
Efficiency improvements of high-order weighted compact nonlinear scheme (WCNS) are verified using a series of benchmark cases, proposed at the International Workshop on High-Order CFD Methods. A seventh-order tri-diagonal compact one of WCNSs (WCNS-E8T7), constructed in recent years, is investigated as a basic scheme, and compared to a typical fifth-order explicit WCNS (WCNS-E6E5) and a traditional second-order TVD scheme MUSCL. Among these tests, a symmetrical conservative metric method (SCMM) is adopted to ensure the accuracy and robustness of WCNSs when solving cases in the curvilinear coordinates. The computational efficiency of schemes is evaluated based on a non-dimensional cost in achieving the same level of accuracy. Related results show that WCNS-E8T7 has a better performance than WCNS-E6E5 with the same interpolation stencils. Moreover, the opinion that high-order methods can obtain higher computational efficiency than second-order methods is demonstrated on the cases ranging from academic problems to real-life computations. 相似文献
2.
A traveling wave solution to the Aw-Rascle traffic flow model that includes the relaxation and diffusion terms is investigated. The model can be approximated by the well-known Kortweg-de Vries (KdV) equation. A numerical simulation is conducted by the first-order accurate Lax-Friedrichs scheme, which is known for its ability to capture the entropy solution to hyperbolic conservation laws. Periodic boundary conditions are applied to simulate a lengthy propagation, where the profile of the derived KdV solution is taken as the initial condition to observe the change of the profile. The simulation shows good agreement between the approximated KdV solution and the numerical solution. 相似文献
3.
为了提高三阶WENO-Z格式在极值点处的计算精度,通过理论推导给出三阶WENO格式满足收敛精度的充分条件。采用泰勒级数展开的方式,推导给出所构造格式非线性权重的计算公式,并综合权衡计算精度和计算稳定性确定所构造格式的参数。通过两个典型的精度测试,验证了改进格式在光滑流场极值点区域逼近三阶精度。进一步选用激波与熵波相互作用和Richtmyer-Meshkov不稳定性等经典算例,证实了本文提出的改进格式WENO-PZ3相较其他格式（WENO-JS3和WENO-Z3）不仅具有较高的精度,而且降低了格式的耗散,提高了对流场结构的分辨率。 相似文献
4.
In this paper,the maximum-principle-preserving(MPP)and positivitypreserving(PP)flux limiting technique will be generalized to a class of high-order weighted compact nonlinear schemes(WCNSs)for scalar conservation laws and the compressible Euler systems in both one and two dimensions.The main idea of the present method is to rewrite the scheme in a conservative form,and then define the local limiting parameters via case-by-case discussion.Smooth test problems are presented to demonstrate that the proposed MPP/PP WCNSs incorporating a third-order Runge-Kutta method can attain the desired order of accuracy.Other test problems with strong shocks and high pressure and density ratios are also conducted to testify the performance of the schemes. 相似文献
5.
The present work is devoted to the numerical approximation of a system which arises when modelling a two‐phase flow in a pipeline. Two particular difficulties are of special interest, the non‐conservativity and the weakly hyperbolicity of this system. Some elementary waves are characterized and a relaxation system, unconditionally hyperbolic, is proposed. The stability criteria of the resulting relaxation method are achieved by a Chapmann–Enskog‐like expansion. A numerical scheme based on the relaxation system is proposed and computations are performed on a shock tube. Validation is performed by comparison with the exact solution and also to the solution from a modified HLL scheme. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
6.
Yize Wang;Kunlei Zhao;Li Yuan; 《国际流体数值方法杂志》2024,96(10):1631-1652
A modified fifth-order WENO-Z scheme is proposed by analogy with the non-normalized weights of the reformulated fifth-order adaptive order (AO) WENO scheme. We show that if the original fifth-order WENO-AO scheme is rewritten as the form of the conventional WENO combination, the resulting non-normalized weights can be divided into three parts: a constant one term, a local stencil smoothness measure term and a global stencil smoothness measure term. In order to make use of the latter two terms for constructing a modified WENO-Z scheme with enhanced performance, we change the form of the third term and introduce an adaptive scaling factor to adjust the contributions from the second and third terms. Numerical examples show that the modified fifth-order WENO-Z scheme has the advantage of high resolution in smooth regions and sharp capturing of discontinuities, and it can obtain evidently better results for shocked flows with small-scale structures compared with the recently developed WENO-Z+ and WENO-Z+M schemes. 相似文献
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Fei Zhao Zhiqiang Sheng Guangwei Yuan 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2020,100(5):e201900320
We present a novel monotone scheme which is a combination of linear scheme and nonlinear monotone scheme for solving diffusion problems on general polygonal meshes. It will be called as a combination scheme and consists of two steps. Firstly, a second-order accurate linear scheme is used to obtain an approximate solution. Secondly, a nonlinear monotone scheme is used to solve the diffusion equation, where the unknowns in the nonlinear coefficient of the nonlinear monotone scheme are taken as the approximate solution of the linear scheme above, i.e., a linearized monotone scheme is obtained. So the combination scheme does not require nonlinear iterations for solving linear diffusion problems, moreover, it benefits from the accuracy and efficiency of the linear scheme, as well as the monotonicity of nonlinear monotone scheme. We also analyze some properties satisfied by the combination scheme, such as conservation, stability, monotonicity and convergence. Numerical results are presented to show the performance of the monotone combination scheme on distorted meshes, especially some numerical comparisons among our combination scheme with some existing linear and nonlinear monotone schemes are given. 相似文献
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In this article, we present two improved third‐order weighted essentially nonoscillatory (WENO) schemes for recovering their design‐order near first‐order critical points. The schemes are constructed in the framework of third‐order WENO‐Z scheme. Two new global smoothness indicators, τL3 and τL4, are devised by a nonlinear combination of local smoothness indicators (ISk) and reference values (ISG) based on Lagrangian interpolation polynomial. The performances of the proposed schemes are evaluated on several numerical tests governed by one‐dimensional linear advection equation or one‐ and two‐dimensional Euler equations. Numerical results indicate that the presented schemes provide less dissipation and higher resolution than the original WENO3‐JS and subsequent WENO3‐N scheme. 相似文献
12.
方建会 《应用数学和力学(英文版)》2000,21(7):836-840
ＩｎｔｒｏｄｕｃｔｉｏｎＣｏｎｓｅｒｖａｔｉｏｎｌａｗｏｆｍｅｃｈａｎｉｃａｌｓｙｓｔｅｍｎｏｔｏｎｌｙｈａｓｉｍｐｏｒｔａｎｃｅｉｎｍａｔｈｅｍａｔｉｃｓｂｕｔａｌｓｏｒｅｖｅａｌｓｐｒｏｆｏｕｎｄｐｈｙｓｉｃａｌｌａｗ .Ｔｈｅｒｅａｒｅｍａｎｙｍｅｔｈｏｄｓｉｎｆｉｎｄｉｎｇｃｏｎｓｅｒｖａｔｉｏｎｌａｗｏｆａｍｅｃｈａｎｉｃａｌｓｙｓｔｅｍ .Ｉｎａｎａｌｙｔｉｃａｌｍｅｃｈａｎｉｃｓｔｈｅｔｒａｄｉｔｉｏｎａｌｍｅｔｈｏｄｉｓｔｏｄｉｒｅｃｔｌｙｄｅｒｉｖｅｔｈｅｃｉｒｃｕｌａｒｉｎｔｅｇ… 相似文献
13.
Stephen Schecter Bradley J. Plohr Dan Marchesin 《Journal of Dynamics and Differential Equations》2001,13(3):523-588
We investigate solutions of Riemann problems for systems of two conservation laws in one spatial dimension. Our approach is to organize Riemann solutions into strata of successively higher codimension. The codimension-zero stratum consists of Riemann solutions that are structurally stable: the number and types of waves in a solution are preserved under small perturbations of the flux function and initial data. Codimension-one Riemann solutions, which constitute most of the boundary of the codimension-zero stratum, violate structural stability in a minimal way. At the codimension-one stratum, either the qualitative structure of Riemann solutions changes or solutions fail to be parameterized smoothly by the flux function and the initial data. In this paper, we give an overview of the phenomena associated with codimension-one Riemann solutions. We list the different kinds of codimension-one solutions, and we classify them according to their geometric properties, their roles in solving Riemann problems, and their relationships to wave curves. 相似文献
14.
Liu Duan 《Acta Mechanica Sinica》1989,5(2):167-175
In this paper conservation laws of nonholonomic nonconservative dynamical systems are studied by using the differential variational
principles of Jourdain and the generalized Noether's identities of nonconservative systems subject to first order nonlinear
nonholonomic constraints are provided.
The project is supported by the National Natural Science Foundation of China. 相似文献
15.
Stephen Schecter 《Journal of Dynamics and Differential Equations》2002,14(2):295-348
This paper is the fifth in a series that undertakes a systematic investigation of Riemann solutions of systems of two conservation laws in one spatial dimension. In this paper, three degeneracies that can occur only in Riemann solutions that contain doubly sonic transitional shock waves, together with the degeneracies that pair with them, are studied in detail. Conditions for a codimension-one degeneracy are identified in each case, as are conditions for folding of the Riemann solution surface. Simple examples are given, including a numerically computed Riemann solution that contains a doubly sonic transitional shock wave. 相似文献
16.
以Noether定理为基础,系统地研究热机电耦合的热释电体非保守动力学系统的守恒定律,引进熵流矢量和温度耗散函数描述热释电体系统的耗散现象,提出了热释电体非保衬动力学系统的Lagrange函数以及广义Hamilton最小作用量原理,论证了不变性变换群的存在条件,提出了并证明了广义Noether定理,由此得到了一组守恒定律及J。M积分。 相似文献
17.
M. Breuß 《ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik》2004,84(8):568-575
We apply the theory of the functional analysis of discretization algorithms in order to describe a new strategy for a constructive proof of the existence of entropy solutions for 1‐D scalar equations in the sense of Kruzhkov. 相似文献
18.
本文应用Jourdain微分变分原理研究了非完整非保守力学系统的守恒定律,给出了受一阶非线性非完整约束的非保守系统的广义Noether等式. 相似文献
19.
ＩｎｔｒｏｄｕｃｔｉｏｎＩｎｒｅｃｅｎｔｙｅａｒｓａｒｅｍａｒｋａｂｌｅｄｅｖｅｌｏｐｍｅｎｔｈａｓｔａｋｅｎｐｌａｃｅｉｎｔｈｅｓｔｕｄｙｏｆｎｏｎｌｉｎｅａｒｅｖｏｌｕｔｉｏｎａｒｙｐａｒｔｉａｌｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ.Ａｎｅｘａｍｐｌｅｉｓｔｈｅ“Ｇｏｏｄ”Ｂｏｕｓｓｉｎｅｓｑ (Ｇ .Ｂ .)ｅｑｕａｔｉｏｎｕｔｔ =-ｕｘｘｘｘ+ｕｘｘ+ (ｕ2 ) ｘｘ ( 1 )ｗｈｉｃｈｄｅｓｃｒｉｂｅｓｓｈａｌｌｏｗｗａｔｅｒｗａｖｅｓｐｒｏｐａｇａｔｉｎｇｉｎｂｏｔｈｄｉｒｅｃｔｉｏｎｓ.Ｔｈｅａ… 相似文献
20.
Jonathan Goodman Judith R. Miller 《Journal of Dynamics and Differential Equations》1999,11(2):255-277
We prove nonlinear stability in L1 of planar shock front solutions to a viscous conservation law in two spatial dimensions and obtain an expression for the asymptotic form of small perturbations. The leading-order behavior is shown rigorously to be governed by an effective diffusion coefficient depending on forces transverse to the shock front. The proof is based on a spectral analysis of the linearized problem. 相似文献