共查询到20条相似文献,搜索用时 250 毫秒
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提出一种自适应结构网格(SAMR)上求解扩散方程的隐式时间积分算法.该算法从粗网格到细网格逐层进行时间积分,通过多层迭代同步校正保证粗细界面的流连续和计算区域的扩散平衡.分析算法复杂度,并给出评估算法低复杂度的准则.典型算例表明,相对于一致加密情形,本文算法能够在保持相同计算精度的前提下,大幅度降低网格规模和计算量,且具有低复杂度.将算法应用于辐射流体力学数值模拟中非线性扩散方程组求解,相对于一致加密网格,SAMR计算将计算量下降一个量级以上,计算效率提高33.2倍. 相似文献
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针对三维球形靶丸内爆高效模拟需求和传统笛卡尔正交网格上辐射加源困难的问题, 发展一种多块结构非正交网格生成方法, 并基于此种计算网格提出高效的三维扩散格式并行算法, 将其应用于辐射流体方程组的求解和三维内爆不对称性的数值模拟, 数值结果显示了算法的有效性。并行性能测试显示该算法可扩展到5400个核上, 并行效率达到69%。 相似文献
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本文将非均匀网格直接离散的高阶紧致格式从二维推广到三维,结合附加修正多重网格方法提高了传统迭代方法的收敛效率,并且验证了该格式在不同边界条件的数值表现。结果表明:该方法可以有效的求解NS方程中的压力泊松方程. 相似文献
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针对传统谱元法在每个单元内只能存在单一均匀介质,应用在复杂非均匀介质的波传播模拟中可能造成极大计算规模的问题,发展了多网格谱元法。该方法在谱元法单元内引入独立的辅助网格,用于精细描述单元内的介质和外力分布变化,在较稀疏的主网格上进行波场的求解。基于声波和弹性波方程推导了多网格谱元法公式,并对几种典型模型进行了波场的数值模拟。与传统谱元法的对比结果表明,此算法在复杂非均匀介质的弹性波传播模拟中可以利用较少的网格点数达到不低于传统算法的精度。此外,实现了并行化的多网格谱元法,获得了较好的并行效率。 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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We introduce and study numerically a scalable parallel finite element solver for the simulation of blood flow in compliant arteries. The incompressible Navier–Stokes equations are used to model the fluid and coupled to an incompressible linear elastic model for the blood vessel walls. Our method features an unstructured dynamic mesh capable of modeling complicated geometries, an arbitrary Lagrangian–Eulerian framework that allows for large displacements of the moving fluid domain, monolithic coupling between the fluid and structure equations, and fully implicit time discretization. Simulations based on blood vessel geometries derived from patient-specific clinical data are performed on large supercomputers using scalable Newton–Krylov algorithms preconditioned with an overlapping restricted additive Schwarz method that preconditions the entire fluid–structure system together. The algorithm is shown to be robust and scalable for a variety of physical parameters, scaling to hundreds of processors and millions of unknowns. 相似文献
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High resolution and scalable parallel algorithms for the shallow water equations on the sphere are very important for modeling the global climate. In this paper, we introduce and study some highly scalable multilevel domain decomposition methods for the fully implicit solution of the nonlinear shallow water equations discretized with a second-order well-balanced finite volume method on the cubed-sphere. With the fully implicit approach, the time step size is no longer limited by the stability condition, and with the multilevel preconditioners, good scalabilities are obtained on computers with a large number of processors. The investigation focuses on the use of semismooth inexact Newton method for the case with nonsmooth topography and the use of two- and three-level overlapping Schwarz methods with different order of discretizations for the preconditioning of the Jacobian systems. We test the proposed algorithm for several benchmark cases and show numerically that this approach converges well with smooth and nonsmooth bottom topography, and scales perfectly in terms of the strong scalability and reasonably well in terms of the weak scalability on machines with thousands and tens of thousands of processors. 相似文献
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Analysis of Two-Grid Methods for Nonlinear Parabolic Equations by Expanded Mixed Finite Element Methods 下载免费PDF全文
Yanping Chen Peng Luan & Zuliang Lu 《advances in applied mathematics and mechanics.》2009,1(6):830-844
In this paper, we present an efficient method of two-grid scheme for
the approximation of two-dimensional nonlinear parabolic equations
using an expanded mixed finite element method. We use two Newton
iterations on the fine grid in our methods. Firstly, we solve an
original nonlinear problem on the coarse nonlinear grid, then we use
Newton iterations on the fine grid twice. The two-grid idea is from
Xu$'$s work [SIAM J. Numer. Anal., 33 (1996), pp. 1759-1777] on
standard finite method. We also obtain the error estimates for the
algorithms of the two-grid method. It is shown that the algorithm
achieves asymptotically optimal approximation rate with the two-grid
methods as long as the mesh sizes satisfy
$h=\mathcal{O}(H^{(4k+1)/(k+1)})$. 相似文献
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Marc R.J. Charest Clinton P.T. Groth Ömer L. Gülder 《Journal of computational physics》2012,231(8):3023-3040
The discrete ordinates method (DOM) and finite-volume method (FVM) are used extensively to solve the radiative transfer equation (RTE) in furnaces and combusting mixtures due to their balance between numerical efficiency and accuracy. These methods produce a system of coupled partial differential equations which are typically solved using space-marching techniques since they converge rapidly for constant coefficient spatial discretization schemes and non-scattering media. However, space-marching methods lose their effectiveness when applied to scattering media because the intensities in different directions become tightly coupled. When these methods are used in combination with high-resolution limited total-variation-diminishing (TVD) schemes, the additional non-linearities introduced by the flux limiting process can result in excessive iterations for most cases or even convergence failure for scattering media. Space-marching techniques may also not be quite as well-suited for the solution of problems involving complex three-dimensional geometries and/or for use in highly-scalable parallel algorithms. A novel pseudo-time marching algorithm is therefore proposed herein to solve the DOM or FVM equations on multi-block body-fitted meshes using a highly scalable parallel-implicit solution approach in conjunction with high-resolution TVD spatial discretization. Adaptive mesh refinement (AMR) is also employed to properly capture disparate solution scales with a reduced number of grid points. The scheme is assessed in terms of discontinuity-capturing capabilities, spatial and angular solution accuracy, scalability, and serial performance through comparisons to other commonly employed solution techniques. The proposed algorithm is shown to possess excellent parallel scaling characteristics and can be readily applied to problems involving complex geometries. In particular, greater than 85% parallel efficiency is demonstrated for a strong scaling problem on up to 256 processors. Furthermore, a speedup of a factor of at least two was observed over a standard space-marching algorithm using a limited scheme for optically thick scattering media. Although the time-marching approach is approximately four times slower for absorbing media, it vastly outperforms standard solvers when parallel speedup is taken into account. The latter is particularly true for geometrically complex computational domains. 相似文献
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A fast implicit Newton–Krylov finite volume algorithm has been developed for high-order unstructured steady-state computation of inviscid compressible flows. The matrix-free generalized minimal residual (GMRES) algorithm is used for solving the linear system arising from implicit discretization of the governing equations, avoiding expensive and complex explicit computation of the high-order Jacobian matrix. The solution process has been divided into two phases: start-up and Newton iterations. In the start-up phase an approximate solution with the general characteristics of the steady-state flow is computed by using a defect correction procedure. At the end of the start-up phase, the linearization of the flow field is accurate enough for steady-state solution, and a quasi-Newton method is used, with an infinite time step and very rapid convergence. A proper limiter implementation for efficient convergence of the high-order discretization is discussed and a new formula for limiting the high-order terms of the reconstruction polynomial is introduced. The accuracy, fast convergence and robustness of the proposed high-order unstructured Newton–Krylov solver for different speed regimes is demonstrated for the second, third and fourth-order discretization. The possibility of reducing computational cost required for a given level of accuracy by using high-order discretization is examined. 相似文献
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Rafail V. Abramov 《Journal of computational physics》2009,228(1):96-108
In a recent paper we developed a new algorithm for the moment-constrained maximum entropy problem in a multidimensional setting, using a multidimensional orthogonal polynomial basis in the dual space of Lagrange multipliers to achieve numerical stability and rapid convergence of the Newton iterations. Here we introduce two new improvements for the existing algorithm, adding significant computational speedup in situations with many moment constraints, where the original algorithm is known to converge slowly. The first improvement is the use of the BFGS iterations to progress between successive polynomial reorthogonalizations rather than single Newton steps, typically reducing the total number of computationally expensive polynomial reorthogonalizations for the same maximum entropy problem. The second improvement is a constraint rescaling, aimed to reduce relative difference in the order of magnitude between different moment constraints, improving numerical stability of iterations due to reduced sensitivity of different constraints to changes in Lagrange multipliers. We observe that these two improvements can yield an average wall clock time speedup of 5–6 times compared to the original algorithm. 相似文献
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荧光分子断层成像正向问题的并行计算 总被引:2,自引:0,他引:2
针对荧光分子断层成像中相应于激发光和发射光的两个正向方程必须串行求解的实际情况,提出了一种可同时对两个扩散方程进行求解的并行算法。其思想是通过引入乘子矩阵对耦合方程进行解耦来实现并行计算,并利用有限元方法进行了二维数值模拟,将算法求解所得结果与基于串行方法,以Ralf B.Schulz等提出的并行算法所得到的数值模拟结果进行了综合比较。实验表明,该算法一方面适合于任何大小的斯托克斯频移条件,具有更广泛的适应性;另一方面提高了荧光分子断层成像正向问题的求解速度和精度,从而有利于整个荧光分子断层成像的快速精确求解。 相似文献
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Experimental and numerical determination of heat release in counterflow premixed laminar flames 总被引:1,自引:0,他引:1
A. Fayoux K. Zhringer O. Gicquel J.C. Rolon 《Proceedings of the Combustion Institute》2005,30(1):251-257
This paper presents an experimental and numerical study of heat release in atmospheric laminar counterflow premixed flames. The measurements are based on simultaneous planar laser-induced fluorescence (PLIF) of OH and HCHO. These measurements are compared to numerical results obtained using detailed chemistry and multicomponent transport properties. A low Mach number formulation along the stagnation streamline is employed to describe the reactive flow. The conservation equations are completed with CHEMKIN and EGLIB packages. They are solved using finite differences, Newton iterations, and an adaptive gridding technique. The comparison is done along the burner axis for both, maximum heat release location and heat release profile width. It is shown that the product of OH and HCHO concentrations yields a result closely related to the heat release. These comparisons lead to the conclusion that the experimental method used seems to be a good tool for the determination of heat release in flames. 相似文献
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M. Barrault B. Lathuilière P. Ramet J. Roman 《Journal of computational physics》2011,230(5):2004-2020
A reactivity computation consists of computing the highest eigenvalue of a generalized eigenvalue problem, for which an inverse power algorithm is commonly used. Very fine modelizations are difficult to treat for our sequential solver, based on the simplified transport equations, in terms of memory consumption and computational time.A first implementation of a Lagrangian based domain decomposition method brings to a poor parallel efficiency because of an increase in the power iterations [1]. In order to obtain a high parallel efficiency, we improve the parallelization scheme by changing the location of the loop over the subdomains in the overall algorithm and by benefiting from the characteristics of the Raviart–Thomas finite element. The new parallel algorithm still allows us to locally adapt the numerical scheme (mesh, finite element order). However, it can be significantly optimized for the matching grid case. The good behavior of the new parallelization scheme is demonstrated for the matching grid case on several hundreds of nodes for computations based on a pin-by-pin discretization. 相似文献
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基于两重网格离散方法,提出三种求解大雷诺数定常Navier-Stokes方程的两水平亚格子模型稳定化有限元算法.其基本思想是首先在一粗网格上求解带有亚格子模型稳定项的Navier-Stokes方程,然后在细网格上分别用三种不同的校正格式求解一个亚格子模型稳定化的线性问题,以校正粗网格解.通过适当的稳定化参数和粗细网格尺寸的选取,这些算法能取得最优渐近收敛阶的有限元解.最后,用数值模拟验证三种算法的有效性. 相似文献