共查询到20条相似文献,搜索用时 187 毫秒
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给出数值求解一维双曲守恒律方程的新方法——龙格-库塔控制体积间断有限元方法(RKCVDFEM),其中空间离散基于控制体积有限元方法,时间离散基于二阶TVB Runge-Kutta技术,有限元空间选取为分段线性函数空间.理论分析表明,格式具有总变差有界(TVB)的性质,而且空间和时间离散形式上具有二阶精度.数值算例表明,数值解收敛到熵解并且对光滑解的收敛阶是最优的,优于龙格-库塔间断Galerkin方法(RKDGM)的计算结果. 相似文献
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对多车种LWR交通流模型,给出一种半离散中心迎风格式,该格式以五阶WENO-Z重构和半离散中心迎风数值通量为基础.WENO-Z重构方法的引入提高了格式的精度,并保证格式具有基本无振荡的性质.时间的离散采用保持强稳定性的Runge-Kutta方法.通过数值算例验证了格式的有效性. 相似文献
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研究自适应Runge-Kutta间断Galerkin (RKDG)方法求解双曲守恒律方程组,并提出两种生成相容三角形网格的自适应算法.第一种算法适用于规则网格,实现简单、计算速度快.第二种算法基于非结构网格,设计一类基于间断界面的自适应网格加密策略,方法灵活高效.两种方法都具有令人满意的计算效果,而且降低了RKDG的计算量. 相似文献
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The discontinuous Petrov-Galerkin method for one-dimensional compressible Euler equations in the Lagrangian coordinate 下载免费PDF全文
In this paper, a Petrov-Galerkin scheme named the Runge-Kutta control volume (RKCV) discontinuous finite element method is constructed to solve the one-dimensional compressible Euler equations in the Lagrangian coordinate. Its advantages include preservation of the local conservation and a high resolution. Compared with the Runge-Kutta discontinuous Galerkin (RKDG) method, the RKCV method is easier to implement. Moreover, the advantages of the RKCV and the Lagrangian methods are combined in the new method. Several numerical examples are given to illustrate the accuracy and the reliability of the algorithm. 相似文献
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龙格库塔间断有限元方法在计算爆轰问题中的应用 总被引:1,自引:1,他引:0
构造求解带源项守恒律方程组的龙格库塔间断有限元(RKDG)方法,并分别结合源项的Strang分裂法和无分裂法数值求解模型守恒律方程和反应欧拉方程.为了和有限体积型WENO方法进行比较,设计计算源项的WENO重构格式.对一维带源项守恒律的计算表明,对于非刚性问题,RKDG方法比有限体积型WENO方法的误差更小;对于刚性问题,RKDG方法对于间断面位置的捕捉更为精确.对于一二维爆轰波问题的计算结果表明,RKDG方法对爆轰波结构的分辨和爆轰波位置的捕捉能力更强. 相似文献
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An RKDG finite element method for the one-dimensional inviscid compressible gas dynamics equations in a Lagrangian coordinate 下载免费PDF全文
In this paper,Runge-Kutta Discontinuous Galerkin(RKDG) finite element method is presented to solve the onedimensional inviscid compressible gas dynamic equations in a Lagrangian coordinate.The equations are discretized by the DG method in space and the temporal discretization is accomplished by the total variation diminishing Runge-Kutta method.A limiter based on the characteristic field decomposition is applied to maintain stability and non-oscillatory property of the RKDG method.For multi-medium fluid simulation,the two cells adjacent to the interface are treated differently from other cells.At first,a linear Riemann solver is applied to calculate the numerical ?ux at the interface.Numerical examples show that there is some oscillation in the vicinity of the interface.Then a nonlinear Riemann solver based on the characteristic formulation of the equation and the discontinuity relations is adopted to calculate the numerical ?ux at the interface,which suppresses the oscillation successfully.Several single-medium and multi-medium fluid examples are given to demonstrate the reliability and efficiency of the algorithm. 相似文献
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A RKDG finite element method for the one-dimensional inviscid compressible gas dynamics equations in Lagrangian coordinate 下载免费PDF全文
In this paper, Runge-Kutta Discontinuous Galerkin (RKDG) finite element method is presented to solve the one-dimensional inviscid compressible gas dynamic equations in Lagrangian coordinate. The equations are discretized by the DG method in space and the temporal discretization is accomplished by the total variation diminishing Runge-Kutta method. A limiter based on the characteristic field decomposition is applied to maintain stability and non-oscillatory property of the RKDG method. For multi-medium fluid simulation, the two cells adjacent to the interface are treated differently from other cells. At first, a linear Riemann solver is applied to calculate the numerical flux at the interface. Numerical examples show that there is some oscillation in the vicinity of the interface. Then a nonlinear Riemann solver based on the characteristic formulation of the equation and the discontinuity relations is adopted to calculate the numerical flux at the interface, which suppress the oscillation successfully. Several single-medium and multi-medium fluid examples are given to demonstrate the reliability and efficiency of the algorithm. 相似文献
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将龙格库塔间断有限元方法(RDDG)与自适应方法相结合,求解三维欧拉方程.区域剖分采用非结构四面体网格,依据数值解的变化采用自适应技术对网格进行局部加密或粗化,减少总体网格数目,提高计算效率.给出四种自适应策略并分析不同自适应策略的优缺点.数值算例表明方法的有效性. 相似文献
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A Comparison of the Performance of Limiters for Runge-Kutta Discontinuous Galerkin Methods 下载免费PDF全文
Hongqiang Zhu Yue Cheng & Jianxian Qiu 《advances in applied mathematics and mechanics.》2013,5(3):365-390
Discontinuities usually appear in
solutions of nonlinear conservation laws even though the initial
condition is smooth, which leads to great difficulty in computing
these solutions numerically. The Runge-Kutta discontinuous Galerkin
(RKDG) methods are efficient methods for solving nonlinear
conservation laws, which are high-order accurate and highly
parallelizable, and can be easily used to handle complicated
geometries and boundary conditions. An important component of RKDG
methods for solving nonlinear conservation laws with strong
discontinuities in the solution is a nonlinear limiter, which is
applied to detect discontinuities and control spurious oscillations
near such discontinuities. Many such limiters have been used in the
literature on RKDG methods. A limiter contains two parts, first to
identify the "troubled cells", namely, those cells which might
need the limiting procedure, then to replace the solution
polynomials in those troubled cells by reconstructed polynomials
which maintain the original cell averages (conservation). [SIAM
J. Sci. Comput., 26 (2005), pp. 995-1013] focused on discussing the
first part of limiters. In this paper, focused on the second part,
we will systematically investigate and compare a few different
reconstruction strategies with an objective of obtaining the most
efficient and reliable reconstruction strategy. This work can help
with the choosing of right limiters so one can resolve sharper
discontinuities, get better numerical solutions and save the
computational cost. 相似文献
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二维多介质可压缩流的RKDG有限元方法 总被引:1,自引:0,他引:1
应用RKDG(Runge-Kutta Discontinuous Galerkin)有限元方法、Level Set方法和Ghost Fluid方法数值模拟二维多介质可压缩流,其中Euler方程组、Level Set方程和重新初始化方程的空间离散采用DG(Discontinuous Galerkin)有限元方法,时间离散采用Runge-Kutta方法.对二维的气-气和气-液两相流进行了数值计算,得到了分辨率较高的计算结果. 相似文献