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粒子输运方程的线性间断有限元方法 总被引:1,自引:0,他引:1
将空间线性间断有限元方法应用于动态粒子输运方程的求解.数值算例表明,空间线性间断有限元方法在网格边界的数值精度方面明显高于指数格式和菱形格式,并且通量在时间上的微分曲线相对光滑,避免了指数格式、菱形格式数值解的非物理振荡现象. 相似文献
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辐射输运菱形差分SN方程的扩散综合加速方法 总被引:1,自引:1,他引:0
讨论辐射输运菱形差分SN方程的源迭代加速方法,在一维情形下给出与输运算子离散相容的线性多频灰体加速计算格式.数值算例表明该加速算法是健壮有效的. 相似文献
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本文导出了一维球几何定态中子输运方程菱形格式的扩散综合加速方程,并给出了差分公式。所给出的加速方法可以加速菱形格式的输运方程的迭代求解。并给出了部分模型的数值计算结果。 相似文献
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针对实际应用中辐射和中子输运数值模拟,讨论球一维和柱二维几何粒子输运方程确定论计算方法的研究现状,包括离散纵标、球谐函数、迭代加速、并行计算等方法.重点讨论输运计算方法所取得的若干研究进展,包括离散纵标求积组、自适应时间离散格式、本征值迭代求解方法、简化球谐函数方法、修正的子网格隅角平衡方法、灰体综合加速方法、迭代初值选取方法、输运与扩散耦合方法、基于预估校正的并行格式等.简要介绍了相关输运计算程序的研制情况,并分析输运计算方法存在的难点,提出待开展研究的内容. 相似文献
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王丽丽 《工程物理研究院科技年报》2004,(1):352-352
用TVD格式结合VOF界面处理方法编制了二维多介质高分辨欧拉程序,以解决冲击波和多介质界面处理。程序包括单介质网格高精度流体力学计算、多介质网格内界面重构、各种介质输运和压力驰豫平衡过程。其中单介质网格的计算采用Harten二阶TVD格式结合MacCormark方法计算含有源项的非齐次守恒定律方程组,通过4节点限制函数保证格式单调。多介质网格采用Youngs方法构造界面,采用x,y方向分裂格式计算体积份额输运,再根据体积份额输运计算质量、动量和能量的输运,最后利用等熵条件计算各种介质的压力驰豫平衡过程。 相似文献
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针对隐式蒙特卡罗方法模拟高温热辐射输运问题时存在的“辐射强度计算误差时间空间分布严重不均匀”现象,通过理论分析和数值模拟手段,找到决定误差大小的主要因素为“网格内的辐射径迹长度记录数”.据此提出“隐式蒙特卡罗全局降方差方法”并推导相应的计算公式.该方法主要包含如下3个关键技术:1)针对辐射输运蒙特卡罗模拟的自适应动态分配源粒子方法; 2)与自适应动态分配源粒子相匹配的动态权窗设计技术及粒子权无偏估计算法; 3)辐射强度的解析估计降方差方法.针对这3个关键技术,设计蒙特卡罗数值模拟方案,编写相应的数值模拟程序模块.典型辐射输运问题模拟结果显示:隐式蒙特卡罗全局降方差方法能够使网格辐射强度计算误差在整个时空范围内分布相对比较均匀,最大误差可控,计算效率提升10倍左右.新方法在激光惯性约束聚变的黑腔辐射输运模拟应用中取得了显著效果. 相似文献
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通过构造新的平衡分布函数和结合分区自适应网格加密方法,对不带扩散项的平衡辐射流体力学方程,构造二阶的分子动理学BGK-AMR格式.一方面在关心的计算区域中局部加密计算网格,提高计算精度的同时大大节省了计算网格数量和计算时间;另一方面,不同于已有的参数强耦合平衡分布函数,新构造的平衡分布函数中各参数不相互依赖,简化了辐射流体力学分子动理学格式的计算.一维和二维的数值算例显示了格式的性能. 相似文献
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单个守恒型方程熵耗散格式中熵耗散函数的构造 总被引:4,自引:0,他引:4
对于一维单个守恒律方程,文[8]设计了一种非线性守恒型差分格式.此格式为二阶Godunov型的,用的是分片线性重构(reconstruction),重构函数的斜率是根据熵耗散得到的.格式满足熵条件.与传统的守恒格式不同的是此格式在计算过程中不仅用到了数值解还用到了数值熵.在此格式中一个所谓的熵耗散函数起到了很重要的作用,它在每一个网格的计算中耗散熵,以保证格式满足熵条件.文[8]中设计的熵耗散函数比较复杂,并且不是很完善.故数值地分析了在格式的构造中为何应给熵以一定的耗散,及应耗散多少.并且给出了一个新的以数值解的二阶差分作为基本模块的熵耗散函数.最后给出了相应的数值算例. 相似文献
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Assessing the Performance of a Three Dimensional Hybrid Central-WENO Finite Difference Scheme with Computation of a Sonic Injector in Supersonic Cross Flow 下载免费PDF全文
Wai-Sun Don Antonio de Gregorio Jean-Piero Suarez & Gustaaf B. Jacobs 《advances in applied mathematics and mechanics.》2012,4(6):719-736
A hybridization of a high order WENO-Z finite difference scheme and a high order
central finite difference method for computation of the two-dimensional Euler
equations first presented in [B. Costa and W. S. Don, J. Comput. Appl. Math., 204(2) (2007)]
is extended to three-dimensions and for parallel computation. The Hybrid scheme
switches dynamically from a WENO-Z scheme to a central scheme at any grid location
and time instance if the flow is sufficiently smooth and vice versa if the flow is
exhibiting sharp shock-type phenomena. The smoothness of the flow is determined by
a high order multi-resolution analysis. The method is tested on a benchmark sonic
flow injection in supersonic cross flow. Increase of the order of the method reduces
the numerical dissipation of the underlying schemes, which is shown to improve the
resolution of small dynamic vortical scales. Shocks are captured sharply in an
essentially non-oscillatory manner via the high order shock-capturing WENO-Z scheme.
Computations of the injector flow with a WENO-Z scheme only and with the Hybrid
scheme are in very close agreement. Thirty percent of grid points require a
computationally expensive WENO-Z scheme for high-resolution capturing of shocks,
whereas the remainder of grid points may be solved with the computationally more
affordable central scheme. The computational cost of the Hybrid scheme can be up
to a factor of one and a half lower as compared to computations with a WENO-Z scheme
only for the sonic injector benchmark. 相似文献
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在反应堆物理-热工耦合过程中,网格划分尺度会影响计算精度和计算时间。利用蒙特卡罗程序和FLUENT程序,对压水堆单棒模型进行不同尺度的网格划分,评估网格划分尺度对耦合结果的影响,得到单个网格中密度差值、温度差值对有效增殖因子和功率分布引入的误差。研究表明当燃料温度差值小于50 K,慢化剂密度差值3 kg/m3时,有效增殖因子相对误差小于10-4,功率相对误差小于1%。使用该规律,对典型的压水堆单棒模型和33通道模型进行网格划分并进行耦合计算。结果表明,单棒模型网格总数减少至1/100,计算时间减少至1/4,33通道模型网格总数减少至1/50,计算时间减少至1/10,但其结果仍然精确有效。 相似文献
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复杂地表条件下快速推进法地震波走时计算 总被引:3,自引:0,他引:3
为获得计算复杂地表条件下地震波走时的方法,对常规快速推进法(Fast marching method,简写为FMM)做了两点改进:①引入不等距差分格式,用于地表和界面处的局部走时计算;②增加新的网格节点类型,用于实现不规则边界条件下的窄带技术.通过对算法的计算精度、效率及实例的分析可得,算法计算精度高,其中反射波走时计算的精度高于初至波;不会因为处理不规则边界而引入过多额外的计算量;能灵活稳定地处理各种强起伏复杂地形、近地表及地下复杂介质等问题.计算结果满足复杂地表条件下地震波的传播规律. 相似文献
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We develop a sixth order finite difference discretization strategy to solve the two dimensional Poisson equation, which is based on the fourth order compact discretization, multigrid method, Richardson extrapolation technique, and an operator based interpolation scheme. We use multigrid V-Cycle procedure to build our multiscale multigrid algorithm, which is similar to the full multigrid method (FMG). The multigrid computation yields fourth order accurate solution on both the fine grid and the coarse grid. A sixth order accurate coarse grid solution is computed by using the Richardson extrapolation technique. Then we apply our operator based interpolation scheme to compute sixth order accurate solution on the fine grid. Numerical experiments are conducted to show the solution accuracy and the computational efficiency of our new method, compared to Sun–Zhang’s sixth order Richardson extrapolation compact (REC) discretization strategy using Alternating Direction Implicit (ADI) method and the standard fourth order compact difference (FOC) scheme using a multigrid method. 相似文献
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Songze Chen Changqiu Jin Cunbiao Li Qingdong Cai 《Journal of computational physics》2011,230(5):2045-2059
The present paper concerns the improvement of the gas-kinetic scheme (GKS) for low speed flow computation. In the modified GKS scheme, the flow distributions with discontinuous derivatives are used as an initial condition at the cell interface for the flux evaluation. This discontinuity is determined by considering both the flow characteristic and grid’s resolution. Compared with GKS method with a continuous slope for the flow variables at a cell interface, the new scheme is more robust and accurate. In the under resolved flow computation, the new scheme presents much less numerical oscillation. The extension of the current scheme to unstructured mesh is straightforward. To validate the method, both computations of 2D lid-driven cavity flow and 3D flow past a sphere are performed. The numerical results validate the current method. 相似文献
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Keizo Fujimoto 《Journal of computational physics》2011,230(23):8508-8526
A new electromagnetic particle-in-cell (EMPIC) model with adaptive mesh refinement (AMR) has been developed to achieve high-performance parallel computation in distributed memory system. For minimizing the amount and frequency of inter-processor communications, the present study uses the staggering grid scheme with the charge conservation method, which consists only of the local operations. However, the scheme provides no numerical damping for electromagnetic waves regardless of the wavenumber, which results in significant noise in the refinement region that eventually covers over physical signals. In order to suppress the electromagnetic noise, the present study introduces a smoothing method which gives numerical damping preferentially for short wavelength modes. The test simulations show that only a weak smoothing results in drastic reduction in the noise, so that the implementation of the AMR is possible in the staggering grid scheme. The computational load balance among the processors is maintained by a new method termed the adaptive block technique for the domain decomposition parallelization. The adaptive block technique controls the subdomain (block) structure dynamically associated with the system evolution, such that all the blocks have almost the same number of particles. The performance of the present code is evaluated for the simulations of the current sheet evolution. The test simulations demonstrate that the usage of the adaptive block technique as well as the staggering grid scheme enhances significantly the parallel efficiency of the AMR-EMPIC model. 相似文献