首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到19条相似文献,搜索用时 125 毫秒
1.
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   

2.
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   

3.
通过在单元交界面处进行高阶WENO重构,得到了一种求解双曲型守恒律方程的WENO型熵相容格式。用该格式对一维Burgers方程和Euler方程进行数值模拟,结果表明,该格式具有高精度、基本无振荡性等特点。  相似文献   

4.
通过Mac Cormack格式和Warming-Beam的结合,构造了一种非常简单的两步二阶TVD差分格式,该差分格式更适合于使用分量形式差分计算而无须对欧拉方程组进行特征解耦。通过对流体力学方程组的大量数值试验,并与二阶ENO格式进行了比较,充分显示了该格式高精度、高分辨并且极其简单的优良特性。  相似文献   

5.
时一空守恒元解元(CE/SE)方法综述   总被引:1,自引:0,他引:1  
时一空守恒元解元方法是近年来兴起的一种全新的高分辨率守恒型方程计算方法.它具有物理概念清晰、计算精度高和格式构造简单等优点,是一种具有广阔发展前景的计算方法.本文详细地介绍了cE/ss方法的基本原理、发展历史、应用情况和最新进展、并指出了当前研究的不足和发展方向.  相似文献   

6.
流体力学数值模拟格式总体上可分为Eulerian(欧氏)、Lagrangian(拉氏)和ALE(Arbitrary LagrangianEulerian),TVD广泛应用于Eulerian格式。本文利用具有TVD保持性质的Runge-Kutta型时间离散方法,构造了流体力学Lagrangian(拉氏)自相容格式,应用von Neumann小扰动技术分析了该格式的稳定性,并进行了相应的数值模拟,较好地抑制了激波波后非物理振荡。  相似文献   

7.
给出了一种求解双曲型守恒律的三阶半离散中心差分格式。该格式以一种推广的三阶重构为基础,同时考虑了波传播的局部速度。格式的构造方法是利用重构,先计算非一致交错网格上的均值,再将该网格均值投影回原来的非交错网格,得到新的全离散中心差分格式,该格式有半离散形式。本文半离散格式保持了中心差分格式简单的优点,即不需用R iemann解算器,避免了进行特征解耦。它具有守恒形式,数值通量满足相容性条件。数值试验结果表明该格式是高精度、高分辨率的。  相似文献   

8.
《力学学报》2012,44(5)
针对Saurel和Abgrall提出的两速度两压力的七方程可压缩多相流模型,改进了其数值解法并应用于模拟可压缩多介质流动问题.在Saurel等的算子分裂法基础上,根据Abgrall的多相流系统应满足速度和压力的均匀性不随时间改变的思想,推导了与HLLC格式一致的非守恒项离散格式以及体积分数发展方程的迎风格式.进一步,通过改变分裂步顺序,构造了稳健的结合算子分裂的三阶TVD龙格一库塔方法.最后通过几个一维和二维高密度比高压力比气液两相流算例,显示了该方法在计算精度和稳健性上的改进效果.  相似文献   

9.
二维洪水演进数值模拟   总被引:2,自引:1,他引:1  
利用非结构化的有限体积方法,建立了二维浅水方程高精度、高分辨率模型。以Roe类型的近似Rie-mann解计算界面通量,通过MUSCL和两步TVD Runge-Kutta法获得了空间和时间都具有二级精度的TVD格式。采用特征分解的方法处理底坡源项和采用半隐式方法处理摩擦源项均能保证了格式的稳定性与和谐性。通过水滴算例对模型进行验证,并应用此模型对98年胖头泡分滞洪区分洪过程进行模拟,获得滞洪区不同时段的淹没范围和淹没水深,为防洪救灾提供了依据。  相似文献   

10.
七方程可压缩多相流模型的HLLC格式及应用   总被引:1,自引:0,他引:1  
梁姗  刘伟  袁礼 《力学学报》2012,44(5):884-895
针对Saurel和Abgrall提出的两速度两压力的七方程可压缩多相流模型,改进了其数值解法并应用于模拟可压缩多介质流动问题.在Saurel等的算子分裂法基础上,根据Abgrall的多相流系统应满足速度和压力的均匀性不随时间改变的思想,推导了与HLLC格式一致的非守恒项离散格式以及体积分数发展方程的迎风格式.进一步,通过改变分裂步顺序,构造了稳健的结合算子分裂的三阶TVD龙格-库塔方法.最后通过几个一维和二维高密度比高压力比气液两相流算例,显示了该方法在计算精度和稳健性上的改进效果.  相似文献   

11.
In this paper, we investigate the accuracy of a high-order discontinuous Galerkin discretization for the coarse resolution simulation of turbulent flow. We show that a low-order approximation exhibits unacceptable numerical discretization errors, whereas a naive application of high-order discretizations in those situations is often unstable due to aliasing. Thus, for high-order simulations of underresolved turbulence, proper stabilization is necessary for a successful computation. Two different mechanisms are chosen, and their impact on the accuracy of underresolved high-order computations of turbulent flows is investigated. Results of these approximations for the Taylor–Green Vortex problem are compared to direct numerical simulation results from literature. Our findings show that the superior discretization properties of high-order approximations are retained even for these coarsely resolved computations.  相似文献   

12.
胡迎港  蒋艳群  黄晓倩 《力学学报》2022,54(11):3203-3214
Hamilton-Jacobi (HJ) 方程是一类重要的非线性偏微分方程, 在物理学、流体力学、图像处理、微分几何、金融数学、最优化控制理论等方面有着广泛的应用. 由于HJ方程的弱解存在但不唯一, 且解的导数可能出现间断, 导致其数值求解具有一定的难度. 本文提出了非稳态HJ方程的7阶精度加权紧致非线性格式 (WCNS). 该格式结合了Hamilton函数的Lax-Friedrichs型通量分裂方法和一阶空间导数左、右极限值的高阶精度混合节点和半节点型中心差分格式. 基于7点全局模板和4个4点子模板推导了半节点函数值的高阶线性逼近和4个低阶线性逼近, 以及全局模板和子模板的光滑度量指标. 为避免间断附近数值解产生非物理振荡以及提高格式稳定性, 采用WENO型非线性插值方法计算半节点函数值. 时间离散采用3阶TVD型Runge-Kutta方法. 通过理论分析验证了WCNS格式对于光滑解具有最佳的7阶精度. 为方便比较, 经典的7阶WENO格式也被推广用于求解HJ方程. 数值结果表明, 本文提出的WCNS格式能够很好地模拟HJ方程的精确解, 且在光滑区域能够达到7阶精度; 与经典的同阶WENO格式相比, WCNS格式在精度、收敛性和分辨率方面更优, 计算效率略高.   相似文献   

13.
A CLASS OF COMPACT UPWIND TVD DIFFERENCE SCHEMES   总被引:1,自引:1,他引:0  
A new method was proposed for constructing total variation diminishing (TVD) upwind schemes in conservation forms. Two limiters were used to prevent non-physical oscillations across discontinuity. Both limiters can ensure the nonlinear compact schemes TVD property. Two compact TVD (CTVD) schemes were tested, one is third-order accuracy, and the other is fifth-order. The performance of the numerical algorithms was assessed by one-dimensional complex waves and Riemann problems, as well as a two-dimensional shock-vortex interaction and a shock-boundary flow interaction. Numerical results show their high-order accuracy and high resolution, and low oscillations across discontinuities.  相似文献   

14.
High‐resolution total variation diminishing (TVD) schemes are widely used for the numerical approximation of hyperbolic conservation laws. Their extension to equations with source terms involving spatial derivatives is not obvious. In this work, efficient ways of constructing conservative schemes from the conservative, non‐conservative or characteristic form of the equations are described in detail. An upwind, as opposed to a pointwise, treatment of the source terms is adopted here, and a new technique is proposed in which source terms are included in the flux limiter functions to get a complete second‐order compact scheme. A new correction to fix the entropy problem is also presented and a robust treatment of the boundary conditions according to the discretization used is stated. Copyright © 2001 John Wiley & Sons, Ltd.  相似文献   

15.
The development of a numerical scheme for non‐hydrostatic free surface flows is described with the objective of improving the resolution characteristics of existing solution methods. The model uses a high‐order compact finite difference method for spatial discretization on a collocated grid and the standard, explicit, single step, four‐stage, fourth‐order Runge–Kutta method for temporal discretization. The Cartesian coordinate system was used. The model requires the solution of two Poisson equations at each time‐step and tridiagonal matrices for each derivative at each of the four stages in a time‐step. Third‐ and fourth‐order accurate boundaries for the flow variables have been developed including the top non‐hydrostatic pressure boundary. The results demonstrate that numerical dissipation which has been a problem with many similar models that are second‐order accurate is practically eliminated. A high accuracy is obtained for the flow variables including the non‐hydrostatic pressure. The accuracy of the model has been tested in numerical experiments. In all cases where analytical solutions are available, both phase errors and amplitude errors are very small. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   

16.
A high-precision and space-time fully decoupled numerical method is developed for a class of nonlinear initial boundary value problems. It is established based on a proposed Coiflet-based approximation scheme with an adjustable high order for the functions over a bounded interval, which allows the expansion coefficients to be explicitly expressed by the function values at a series of single points. When the solution method is used, the nonlinear initial boundary value problems are first spatially discretized into a series of nonlinear initial value problems by combining the proposed wavelet approximation and the conventional Galerkin method, and a novel high-order step-by-step time integrating approach is then developed for the resulting nonlinear initial value problems with the same function approximation scheme based on the wavelet theory. The solution method is shown to have the N th-order accuracy, as long as the Coiflet with [0, 3 N-1]compact support is adopted, where N can be any positive even number. Typical examples in mechanics are considered to justify the accuracy and efficiency of the method.  相似文献   

17.
利用多小波自适应格式求解流体力学方程   总被引:2,自引:0,他引:2  
高阶计算格式的高精度、高分辨率对提高复杂流场的计算水平有重要的意义, 为了提高AUSMPW格式对流场计算中激波等间断的分辨率,减小数值振荡,在原有AUSMPW 格式的基础之上,利用多小波对函数进行多尺度分解,并采取阈值的方法生成自适应网格, 提出了一种新的基于多小波自适应算法的AUSMPW格式,理论上可以达到任意阶精度. 将所得 的压强、密度与原格式、TVD格式及WENO格式的计算结果进行了比较分析. 结果表明改进后 的AUSMPW格式较原格式具有更高的分辨率、更强的捕捉间断的能力及更低的数值耗散.  相似文献   

18.
HIGH-ORDER DISCONTINUOUS GALERKIN SOLUTION OF N-S EQUATIONS ON HYBRID MESH   总被引:1,自引:0,他引:1  
针对层流NS方程发展了混合网格上的高阶间断有限元方法,给出了物面边界高阶近似的具体步骤以及近物面弯曲单元的处理方法。对数值离散产生的非线性方程组采用牛顿迭代进行求解,每个牛顿循环采用预处理广义最小余量法求解产生的大型稀疏线性系统。使用该方法得到了典型算例的数值结果,并跟前人的计算结果进行了比较。计算结果表明,混合网格上应用高阶间断有限元方法求解黏性流动具有很好的应用前景。  相似文献   

19.
高阶紧致格式分区并行算法   总被引:1,自引:0,他引:1  
针对超声速多尺度复杂流动问题,发展了一种高精度并行算法。计算格式采用五阶迎风紧致格式,用特征型通量限制方法抑制非物理振荡。在对接边界处采用五阶WENO格式,以保证整个计算域内计算精度一致。通过网格分区和数据交换,在MPI平台实现了并行计算。通过超声速算例对算法进行了验证,并对并行效率和加速比进行了分析。最后,将算法应用于超声速转捩、湍流问题的数值模拟。计算结果表明,提出的算法具有较高的精度和分辨率,对接边界光滑连续,并且并行效率较高,在高超声速湍流流动数值模拟中取得了较好的应用效果。  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号