共查询到19条相似文献,搜索用时 218 毫秒
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为了降低经典的三阶加权本质无振荡(WENO)格式的数值耗散,提出了一种新的三阶WENO格式的修正模板近似方法.改进了经典WENO-JS格式中各候选模板上数值通量的一阶多项式逼近,通过加入二次项使模板逼近达到三阶精度.计算了相应的候选通量,并且通过引入可调函数φ(x),使得新的格式具有ENO性质.最后给出了一系列数值算例,证明了该方法的有效性. 相似文献
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首先通过理论推导给出了三阶WENO格式(WENO-JS3格式)满足收敛精度的充分条件.采用Taylor(泰勒)级数展开的方法,分析发现传统的三阶WENO-Z格式(WENO-Z3格式)在光滑流场极值点处精度降低.为了提高WENO-Z3格式在极值点处的计算精度,根据收敛精度的充分条件构造一种改进的三阶WENO-Z格式(WENO-NZ3格式),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WENO-NZ3格式在光滑流场极值点区域逼近三阶精度.选用Sod激波管、激波与熵波相互作用、Rayleigh-Taylor不稳定性、二维Riemann(黎曼)问题经典算例,进一步证实了本文提出的WENO-NZ3格式相较其他格式(WENO-JS3、WENOZ3、WENO-N3),不仅提高了计算精度,而且提高了对复杂流场结构的分辨率. 相似文献
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基于WENO(Weighted Essentially Non-Oscillatory)的思想,提出了一种在非结构网格上求解二维Hamilton-Jacobi(简称H-J)方程的数值方法.该方法利用Abgrall提出的数值通量,在每个三角形单元上构造三次加权插值多项式,得到了一个求解H-J方程的高阶精度格式.数值实验结果表明,该方法计算速度较快,具有较高的精度,而且对导数间断有较高的分辨率. 相似文献
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低耗散、高分辨率激波捕捉格式对含激波流场的数值模拟具有重要意义.在传统三阶WENO格式(WENO-JS3)和三阶WENO Z格式(WENO-Z3)基础上,基于映射函数,给出WENO-M3、WENO MZ3格式.选用Sod激波管、激波与熵波相互作用、双爆轰波碰撞及双Mach(马赫)反射等经典算例,考察上述格式的计算性能.数值结果表明,WENO-MZ3格式相较其他格式具有耗散低、对流场结构分辨率高的特性.为了进一步扩展WENO-MZ3格式的应用范围,采用该格式数值研究封闭方形舱室内柱形高压、高密度气体爆炸波传播过程,波系演化规律以及壁面典型测点压力载荷.数值计算结果表明WENO-MZ3格式能够较好地模拟包含高压比、高密度比的爆炸波且给出数值耗散较小的壁面压力载荷. 相似文献
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非线性Schr(o)dinger方程初边值问题的守恒数值格式 总被引:1,自引:1,他引:0
该文对非线性Schr(o)dinger方程提出了一种新的守恒差分格式,并证明了该格式的收敛性与稳定性,通过数值计算获得如下结论,提出的差分格式在取适当的参数后,精度上好于文[7]中的格式. 相似文献
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给出了一种真正多维的HLL Riemann解法器.采用TV(Toro-Vázquez)分裂将通量分裂成对流通量和压力通量,其中对流通量的计算采用类似于AUSM格式的迎风方法,压力通量的计算采用波速基于压力系统特征值的HLL格式,并将HLL格式耗散项中的密度差用压力差代替,来克服传统的HLL格式不能分辨接触间断的缺点.为了实现数值格式真正多维的特性,分别计算网格界面中点和角点上的数值通量,并且采用Simpson公式加权中点和角点上的数值通量来得到网格界面上的数值通量.采用基于SDWLS(solution dependent weighted least squares)梯度的线性重构来获得空间的二阶精度,时间离散采用二阶Runge-Kutta格式.数值实验表明,相比于传统的一维HLL格式,该文的真正多维HLL格式具有能够分辨接触间断,消除慢行激波波后振荡以及更大的时间步长等优点.并且,与其他能够分辨接触间断的格式(例如HLLC格式)不同的是,真正多维的HLL格式在计算二维问题时不会出现数值激波不稳定现象. 相似文献
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Fine structures for the solutions of the two-dimensional Riemann problems by high-order WENO schemes
The two-dimensional Riemann problem with polytropic gas is considered. By a restriction on the constant states of each quadrant of the computational domain such that there is only one planar centered wave connecting two adjacent quadrants, there are nineteen genuinely different initial configurations of the problem. The configurations are numerically simulated on a fine grid and compared by the 5th-order WENO-Z5, 6th-order WENO-??6, and 7th-order WENO-Z7 schemes. The solutions are very well approximated with high resolution of waves interactions phenomena and different types of Mach shock reflections. Kelvin-Helmholtz instability-like secondary-scaled vortices along contact continuities are well resolved and visualized. Numerical solutions show that WENO-??6 outperforms the comparing WENO-Z5 and WENO-Z7 in terms of shock capturing and small-scaled vortices resolution. A catalog of the numerical solutions of all nineteen configurations obtained from the WENO-??6 scheme is listed. Thanks to their excellent resolution and sharp shock capturing, the numerical solutions presented in this work can be served as reference solutions for both future numerical and theoretical analyses of the 2D Riemann problem. 相似文献
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Nelida Črnjarić-Žic Senka Maćešić Bojan Crnković 《Annali dell'Universita di Ferrara》2007,53(2):199-215
Most of the standard papers about the WENO schemes consider their implementation to uniform meshes only. In that case the
WENO reconstruction is performed efficiently by using the algebraic expressions for evaluating the reconstruction values and
the smoothness indicators from cell averages. The coefficients appearing in these expressions are constant, dependent just
on the scheme order, not on the mesh size or the reconstruction function values, and can be found, for example, in Jiang and
Shu (J Comp Phys 126:202–228, 1996). In problems where the geometrical properties must be taken into account or the solution
has localized fine scale structure that must be resolved, it is computationally efficient to do local grid refinement. Therefore,
it is also desirable to have numerical schemes, which can be applied to nonuniform meshes. Finite volume WENO schemes extend
naturally to nonuniform meshes although the reconstruction becomes quite complicated, depending on the complexity of the grid
structure. In this paper we propose an efficient implementation of finite volume WENO schemes to nonuniform meshes. In order
to save the computational cost in the nonuniform case, we suggest the way for precomputing the coefficients and linear weights
for different orders of WENO schemes. Furthermore, for the smoothness indicators that are defined in an integral form we present
the corresponding algebraic expressions in which the coefficients obtained as a linear combination of divided differences
arise. In order to validate the new implementation, resulting schemes are applied in different test examples.
相似文献
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In this paper, space adaptivity is introduced to control the error in the numerical solution of hyperbolic systems of conservation laws. The reference numerical scheme is a new version of the discontinuous Galerkin method, which uses an implicit diffusive term in the direction of the streamlines, for stability purposes. The decision whether to refine or to unrefine the grid in a certain location is taken according to the magnitude of wavelet coefficients, which are indicators of local smoothness of the numerical solution. Numerical solutions of the nonlinear Euler equations illustrate the efficiency of the method. 相似文献
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The system of shallow water equations admits infinitely many conservation laws. This paper investigates weak local residuals as smoothness indicators of numerical solutions to the shallow water equations. To get a weak formulation, a test function and integration are introduced into the shallow water equations. We use a finite volume method to solve the shallow water equations numerically. Based on our numerical simulations, the weak local residual of a simple conservation law with a simple test function is identified to be the best as a smoothness indicator. 相似文献
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In this continuing paper of (Zhu and Qiu, J Comput Phys 318 (2016), 110–121), a new fifth order finite difference weighted essentially non‐oscillatory (WENO) scheme is designed to approximate the viscosity numerical solution of the Hamilton‐Jacobi equations. This new WENO scheme uses the same numbers of spatial nodes as the classical fifth order WENO scheme which is proposed by Jiang and Peng (SIAM J Sci Comput 21 (2000), 2126–2143), and could get less absolute truncation errors and obtain the same order of accuracy in smooth region simultaneously avoiding spurious oscillations nearby discontinuities. Such new WENO scheme is a convex combination of a fourth degree accurate polynomial and two linear polynomials in a WENO type fashion in the spatial reconstruction procedures. The linear weights of three polynomials are artificially set to be any random positive constants with a minor restriction and the new nonlinear weights are proposed for the sake of keeping the accuracy of the scheme in smooth region, avoiding spurious oscillations and keeping sharp discontinuous transitions in nonsmooth region simultaneously. The main advantages of such new WENO scheme comparing with the classical WENO scheme proposed by Jiang and Peng (SIAM J Sci Comput 21 (2000), 2126–2143) are its efficiency, robustness and easy implementation to higher dimensions. Extensive numerical tests are performed to illustrate the capability of the new fifth WENO scheme. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1095–1113, 2017 相似文献
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WENO5 uses a convex combination of the polynomials reconstructed on the three stencils of ENO3 in order to achieve higher accuracy on smooth profiles. However, in some cases WENO5 generates oscillations or smears near discontinuities due to the time scheme used. Here, we present a method to reduce those oscillations without damping and this yields a sharper approximation. Our technique uses smoothness indicators to identify severe shocks and switches from WENO5 to ENO3. Numerical tests show that the behaviour of WENO5 is improved near discontinuities while preserving high accuracy on smooth profiles. 相似文献
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This paper is concerned with a family of nonstationary, interpolatory subdivision schemes that have the capability of reproducing
functions in a finite-dimensional subspace of exponential polynomials. We give conditions for the existence and uniqueness
of such schemes, and analyze their convergence and smoothness. It is shown that the refinement rules of an even-order exponentials
reproducing scheme converge to the Dubuc—Deslauriers interpolatory scheme of the same order, and that both schemes have the
same smoothness. Unlike the stationary case, the application of a nonstationary scheme requires the computation of a different
rule for each refinement level. We show that the rules of an exponentials reproducing scheme can be efficiently derived by
means of an auxiliary orthogonal scheme , using only linear operations. The orthogonal schemes are also very useful tools in fitting an appropriate space of exponential
polynomials to a given data sequence. 相似文献
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Chebyshev polynomials of the first kind are employed in a space-time least-squares spectral element formulation applied to
linear and nonlinear hyperbolic scalar equations. No stabilization techniques are required to render a stable, high order
accurate scheme. In parts of the domain where the underlying exact solution is smooth, the scheme exhibits exponential convergence
with polynomial enrichment, whereas in parts of the domain where the underlying exact solution contains discontinuities the
solution displays a Gibbs-like behavior. An edge detection method is employed to determine the position of the discontinuity.
Piecewise reconstruction of the numerical solution retrieves a monotone solution. Numerical results will be given in which
the capabilities of the space-time formulation to capture discontinuities will be demonstrated. 相似文献