共查询到16条相似文献,搜索用时 46 毫秒
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一类高精度TVD差分格式及其应用 总被引:2,自引:0,他引:2
构造了一维非线性双曲型守恒律的一个新的高精度、高分辨率的守恒型TvD差分格式。其构造思想是:首先,将计算区间划分为若干个互不相交的小区间,再根据精度要求等分小区间,通过各细小区间上的单元平均状态变量,重构各细小区间交界面上的状态变量,并加以校正;其次,利用近似Riemann解计算细小区间交界面上的数值通量,并结合高阶Runge—Kutta TVD方法进行时间离散,得到了高精度的全离散方法。证明了该格式的TVD特性。该格式适合于使用分量形式计算而无须进行局部特征分解。通过计算几个典型的问题,验证了格式具有高精度、高分辨率且计算简单的优点。 相似文献
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非线性双曲型守恒律的高精度MmB差分格式 总被引:1,自引:0,他引:1
构造了一维非线性双曲型守恒律方程的一个高精度、高分辨率的广义G odunov型差分格式。其构造思想是:首先将计算区间划分为若干个互不相交的小区间,再根据精度要求等分小区间,通过各细小区间上的单元平均状态变量,重构各等分小区间交界面上的状态变量,并加以校正;其次,利用近似R iem ann解算子求解细小区间交界面上的数值通量,并结合高阶R unge-K u tta TVD方法进行时间离散,得到了高精度的全离散方法。证明了该格式的Mm B特性。然后,将格式推广到一、二维双曲型守恒方程组情形。最后给出了一、二维Eu ler方程组的几个典型的数值算例,验证了格式的高效性。 相似文献
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给出了求解一维双曲型守恒律的一种半离散三阶中心迎风格式,并利用逐维进行计算的方法将格式推广到二维守恒律。构造格式时利用了波传播的单侧局部速度,三阶重构方法的引入保证了格式的精度。时间方向的离散采用三阶TVD Runge—Kutta方法。本文格式保持了中心差分格式简单的优点,即不需用Riemann解算器,避免了进行特征分解过程。用该格式对一维和二维守恒律进行了大量的数值试验,结果表明本文格式是高精度、高分辨率的。 相似文献
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针对经典的五阶加权本质无振荡(WENO)格式在间断附近耗散过大以及临界点不能保精度的问题,本文提出了一种新的修正模板近似方法。改进了经典五阶WENO-JS格式中各候选子模板上数值通量的二阶多项式逼近,通过加入三次修正项使模板逼近达到四阶精度,并且通过引入可调函数φ使得新的格式具有ENO性质,理论分析新的格式具有保精度特性,通过一系列数值算例说明了新格式的高效性。 相似文献
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直接把Nessyahu和Tadmor^[1,2]的思想推广到三维非线性双曲型守恒律情形,以交错形式Lax—Friedrichs格式为基本模块,使用二阶分片线性逼近代替一阶分片常数逼近,减少了Lax—Friedrichs格式的过多数值粘性,通过对混合导数离散形式的适当处理,构造了一类不须解Riemann问题、具有时空二阶精度高分辨率的MmB差分格式。这些差分格式很容易推广到向量系统中去。最后,一些数值模拟计算结果也证明了这些差分格式的有效性。 相似文献
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Yousef Hashem Zahran 《国际流体数值方法杂志》2008,57(6):745-760
We describe a hybrid method for the solution of hyperbolic conservation laws. A third‐order total variation diminishing (TVD) finite difference scheme is conjugated with a random choice method (RCM) in a grid‐based adaptive way. An efficient multi‐resolution technique is used to detect the high gradient regions of the numerical solution in order to capture the shock with RCM while the smooth regions are computed with the more efficient TVD scheme. The hybrid scheme captures correctly the discontinuities of the solution and saves CPU time. Numerical experiments with one‐ and two‐dimensional problems are presented. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
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In this work we present an upwind‐based high resolution scheme using flux limiters. Based on the direction of flow we choose the smoothness parameter in such a way that it leads to a truly upwind scheme without losing total variation diminishing (TVD) property for hyperbolic linear systems where characteristic values can be of either sign. Here we present and justify the choice of smoothness parameters. The numerical flux function of a high resolution scheme is constructed using wave speed splitting so that it results into a scheme that truly respects the physical hyperbolicity property. Bounds are given for limiter functions to satisfy TVD property. The proposed scheme is extended for non‐linear problems by using the framework of relaxation system that converts a non‐linear conservation law into a system of linear convection equations with a non‐linear source term. The characteristic speed of relaxation system is chosen locally on three point stencil of grid. This obtained relaxation system is solved using composite scheme technique, i.e. using a combination of proposed scheme with the conservative non‐standard finite difference scheme. Presented numerical results show higher resolution near discontinuity without introducing spurious oscillations. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
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In this article, we present an improved third-order finite difference weighted essentially nonoscillatory (WENO) scheme to promote the order of convergence at critical points for the hyperbolic conservation laws. The improved WENO scheme is an extension of WENO-ZQ scheme. However, the global smoothness indicator has a little different from WENO-ZQ scheme. In this follow-up article, a convex combination of a second-degree polynomial with two linear polynomials in a traditional WENO fashion is used to compute the numerical flux at cell boundary. Although the same three-point information is adopted by the improved third-order WENO scheme, the truncation errors are smaller than some other third-order WENO schemes in L∞ and L2 norms. Especially, the convergence order is not declined at critical points, where the first and second derivatives vanish but not the third derivative. At last, the behavior of improved scheme is proved on a variety of one- and two-dimensional standard numerical examples. Numerical results demonstrate that the proposed scheme gives better performance in comparison with other third-order WENO schemes. 相似文献
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We introduce a new fourth order, semi-discrete, central-upwind scheme for solving systems of hyperbolic conservation laws. The scheme is a combination of a fourth order non-oscillatory reconstruction, a semi-discrete central-upwind numerical flux and the third order TVD Runge-Kutta method. Numerical results suggest that the new scheme achieves a uniformly high order accuracy for smooth solutions and produces non-oscillatory profiles for discontinuities. This is especially so for long time evolution problems. The scheme combines the simplicity of the central schemes and accuracy of the upwind schemes. The advantages of the new scheme will be fully realized when solving various examples. 相似文献
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Application of a fourth-order relaxation scheme to hyperbolic systems of conservation laws 总被引:5,自引:0,他引:5
A fourth-order relaxation scheme is derived and applied to hyperbolic systems of conservation laws in one and two space dimensions.
The scheme is based on a fourth-order central weighted essentially nonoscillatory (CWENO) reconstruction for one-dimensional
cases, which is generalized to two-dimensional cases by the dimension-by-dimension approach. The large stability domain Runge-Kutta-type
solver ROCK4 is used for time integration. The resulting method requires neither the use of Riemann solvers nor the computation
of Jacobians and therefore it enjoys the main advantage of the relaxation schemes. The high accuracy and high-resolution properties
of the present method are demonstrated in one- and two-dimensional numerical experiments.
The project supported by the National Natural Science Foundation of China (60134010)
The English text was polished by Yunming Chen. 相似文献
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A local pseudo arc-length method(LPALM)for solving hyperbolic conservation laws is presented in this paper.The key idea of this method comes from the original arc-length method,through which the critical points are bypassed by transforming the computational space.The method is based on local changes of physical variables to choose the discontinuous stencil and introduce the pseudo arc-length parameter,and then transform the governing equations from physical space to arc-length space.In order to solve these equations in arc-length coordinate,it is necessary to combine the velocity of mesh points in the moving mesh method,and then convert the physical variable in arclength space back to physical space.Numerical examples have proved the effectiveness and generality of the new approach for linear equation,nonlinear equation and system of equations with discontinuous initial values.Non-oscillation solution can be obtained by adjusting the parameter and the mesh refinement number for problems containing both shock and rarefaction waves. 相似文献