共查询到17条相似文献,搜索用时 343 毫秒
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针对结构自适应加密网格(SAMR)上扩散方程的求解,分析几种有限体格式的逼近性,同时设计和分析一种两层网格算法.首先,讨论一种常见的守恒型有限体格式,并给出网格加密区域和细化/粗化插值算子的条件;接着,通过在粗细界面附近引入辅助三角形单元,消除粗细界面处的非协调单元,设计了一种保对称有限体元(SFVE)格式,分析表明,该格式具有更好的逼近性,且对网格加密区域和插值算子的限制更弱;最后,为SFVE格式构造一种两层网格(TL)算法,理论分析和数值实验表明该算法的一致收敛性. 相似文献
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D. Lagrava O. Malaspinas J. Latt B. Chopard 《Journal of computational physics》2012,231(14):4808-4822
Grid refinement has been addressed by different authors in the lattice Boltzmann method community. The information communication and reconstruction on grid transitions is of crucial importance from the accuracy and numerical stability point of view. While a decimation is performed when going from the fine to the coarse grid, a reconstruction must performed to pass form the coarse to the fine grid. In this context, we introduce a decimation technique for the copy from the fine to the coarse grid based on a filtering operation. We show this operation to be extremely important, because a simple copy of the information is not sufficient to guarantee the stability of the numerical scheme at high Reynolds numbers. Then we demonstrate that to reconstruct the information, a local cubic interpolation scheme is mandatory in order to get a precision compatible with the order of accuracy of the lattice Boltzmann method.These two fundamental extra-steps are validated on two classical 2D benchmarks, the 2D circular cylinder and the 2D dipole–wall collision. The latter is especially challenging from the numerical point of view since we allow strong gradients to cross the refinement interfaces at a relatively high Reynolds number of 5000. A very good agreement is found between the single grid and the refined grid cases.The proposed grid refinement strategy has been implemented in the parallel open-source library Palabos. 相似文献
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We present an algorithm for finding high order numerical approximations of minimal surfaces with a fixed boundary. The algorithm employs parametrization by high order polynomials and a linearization of the weak formulation of the Laplace–Beltrami operator to arrive at an iterative procedure to evolve from a given initial surface to the final minimal surface. For the steady state solution we measure the approximation error in a few cases where the exact solution is known. In the framework of parametric interpolation, the choice of interpolation points (mesh nodes) is directly affecting the approximation error, and we discuss how to best update the mesh on the evolutionary surface such that the parametrization remains smooth. In our test cases we may achieve exponential convergence in the approximation of the minimal surface as the polynomial degree increases, but the rate of convergence greatly differs with different choices of mesh update algorithms. The present work is also of relevance to high order numerical approximation of fluid flow problems involving free surfaces. 相似文献
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A Revisit on the Derivation of the Particular Solution for the Differential Operator ∆2 ± λ2 下载免费PDF全文
Guangming Yao C. S. Chen & Chia Cheng Tsai 《advances in applied mathematics and mechanics.》2009,1(6):750-768
In this paper, we applied the polyharmonic splines as the basis functions
to derive particular solutions for the differential operator ∆2 ± λ2. Similar to the
derivation of fundamental solutions, it is non-trivial to derive particular solutions
for higher order differential operators. In this paper, we provide a simple algebraic
factorization approach to derive particular solutions for these types of differential
operators in 2D and 3D. The main focus of this paper is its simplicity in the sense
that minimal mathematical background is required for numerically solving higher
order partial differential equations such as thin plate vibration. Three numerical
examples in both 2D and 3D are given to validate particular solutions we derived. 相似文献
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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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Chaopeng Shen Jing-Mei Qiu Andrew Christlieb 《Journal of computational physics》2011,230(10):3780-3802
In this paper, we propose a finite difference AMR-WENO method for hyperbolic conservation laws. The proposed method combines the adaptive mesh refinement (AMR) framework and with the high order finite difference weighted essentially non-oscillatory (WENO) method in space and the total variation diminishing (TVD) Runge–Kutta (RK) method in time (WENO-RK) and by a high order coupling. Our goal is to realize mesh adaptivity in the AMR framework, while maintaining very high (higher than second) order accuracy of the WENO-RK method in the finite difference setting. The high order coupling of AMR and WENO-RK is accomplished by high order prolongation in both space (WENO interpolation) and time (Hermite interpolation) from coarse to fine grid solutions, and at ghost points. The resulting AMR-WENO method is accurate, robust and efficient, due to the mesh adaptivity and very high order spatial and temporal accuracy. We have experimented with both the third and the fifth order AMR-WENO schemes. We demonstrate the accuracy of the proposed scheme using smooth test problems, and their quality and efficiency using several 1D and 2D nonlinear hyperbolic problems with very challenging initial conditions. The AMR solutions are observed to perform as well as, and in some cases even better than, the corresponding uniform fine grid solutions. We conclude that there is significant improvement of the fifth order AMR-WENO over the third order one, not only in accuracy for smooth problems, but also in its ability in resolving complicated solution structures, due to the very low numerical diffusion of high order schemes. In our work, we found that it is difficult to design a robust AMR-WENO scheme that is both conservative and high order (higher than second order), due to the mass inconsistency of coarse and fine grid solutions at the initial stage in a finite difference scheme. Resolving these issues as well as conducting comprehensive evaluation of computational efficiency constitute our future work. 相似文献