全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

相关文章

更多...
计算数学  2015 

多边形网格上扩散方程新的单调格式

, PP. 316-336

Keywords: 扩散方程,有限体积格式,单调,多边形网格

Full-Text   Cite this paper   Add to My Lib

Abstract:

本文在星形多边形网格上,构造了扩散方程新的单调有限体积格式.该格式与现有的基于非线性两点流的单调格式的主要区别是,在网格边的法向流离散模板中包含当前边上的点,在推导离散法向流的表达式时采用了定义于当前边上的辅助未知量,这样既可适应网格几何大变形,同时又兼顾了当前网格边上物理量的变化.在光滑解情形证明了离散法向流的相容性.对于具有强各向异性、非均匀张量扩散系数的扩散方程,证明了新格式是单调的,即格式可以保持解析解的正性.数值结果表明在扭曲网格上,所构造的格式是局部守恒和保正的,对光滑解有高于一阶的精度,并且,针对非平衡辐射限流扩散问题,数值结果验证了新格式在计算效率和守恒精度上优于九点格式.

References

[1]  Berman A and Plemmons R J. Nonnegative matrices in the mathematical sciences[M]. Academic Press, New York, 1979.
[2]  Burman E and Ern A. Discrete maximum principle for Galerkin approximations of the Laplace operator on arbitrary meshes[J]. C. R. Acad. Sci. Paris, Ser. I, 2004, 338:641-646.
[3]  Draganescu A, Dupont T F and Scott L R. Failure of the discrete maximum principle for an elliptic finite element problem[J]. Math. Comp., 2004, 74(249):1-23.
[4]  Hoteit H, Mose R, Philippe B, Ackerer Ph and Erhel J. The maximum principle violations of the mixed-hybrid finite-element method applied to diffusion equations[J]. Numer. Meth. Engng., 2002, 55(12):1373-1390.
[5]  Kapyrin I. A family of monotone methods for the numerical solution of three-dimensional diffusion problems on unstructured tetrahedral meshes[J]. Dokl. Math., 2007, 76(2):734-738.
[6]  Korotov S, Krizek M and Neittaanm?ki P. Weakened acute type condition for tetrahedral triangulations and the discrete maximum principle[J]. Math. Comp., 2000, 70:107-119.
[7]  Lipnikov K, Shashkov M, Svyatskiy D and Vassilevski Yu. Monotone finite volume schemes for diffusion equations on unstructured triangular and shape-regular polygonal meshes[J]. J. Comput. Phys., 2007, 227:492-512.
[8]  Lipnikov K, Svyatskiy D and Vassilevski Yu. Interpolation-free monotone finite volume method for diffusion equations on polygonal meshes[J]. J. Comput. Phys., 2009, 228:703-716.
[9]  Lipnikov K, Svyatskiy D and Vassilevski Y. A monotone finite volume method for advectiondiffusion equations on unstructured polygonal meshes[J]. J. Comput. Phys. 2010, 229:4017-4032.
[10]  Liska R and Shashkov M. Enforcing the discrete maximum principle for linear finite element solutions of second-Order elliptic problems[J]. Commun. Comput. Phys., 2008, 3:852-877.
[11]  Mishev I D. Finite Volume methods on Voronoi meshes[J]. Numer. Meth. Part. D. E., 1998, 12(2):193-212.
[12]  Mousseau V A and Knoll D A. Temporal Accuracy of the Nonequilibrium Radiation Diffusion Equations Applied to Two-Dimensional Multimaterial Simulations[J]. Nucl. Sci. Eng., 2006, 154:174-189.
[13]  Nordbotten J M and Aavatsmark I. Monotonicity conditions for control volume methods on uniform parallelogram grids in homogeneous media[J]. Computat. Geosci., 2005, 9:61-72.
[14]  Nordbotten J M, Aavatsmark I and Eigestad G T. Monotonicity of control volume methods[J]. Numer. Math., 2007, 106:255-288.
[15]  Olson G L, Auer L H and Hall M L. Diffusion, P1, and other approximate forms of radiation transport[J]. J. Quant. Spectrosc. Radiat. Transfer, 2000, 64:619-634.
[16]  Le Potier C. Finite volume monotone scheme for highly anisotropic diffusion operators on unstructured triangular meshes[J]. C. R. Acad. Sci. Paris, Ser. I, 2005, 341:787-792.
[17]  Potier C L. Finite volume scheme satisfying maxcimum and minimum preinciples for anisotropic diffusion operators, in:R. Eymard, J.-M. H. (eds.) (Eds.), Finite Volumes for Complex Applications V, 2008, 103-118.
[18]  Prateek Sharma and Gregory W. Hammett, Preserving monotonicity in anisotropic diffusion[J]. J. Comput. Phys., 2007, 227:123-142.
[19]  Sheng Z and Yuan G. A nine point scheme for the approximation of diffusion operators on distorted quadrilateral meshes[J]. SIAM J. Sci. Comput., 2008, 30:1341-1361.
[20]  Sheng Z and Yuan G. The finite volume scheme preserving extremum principle for diffusion equations on polygonal meshes[J]. J. Comput. Phys., 2010, 230:2588-2604.
[21]  Sheng Z, Yue J and Yuan G. Monotone finite volume schemes of nonequilibrium radiation diffusion equations on distorted meshes[J]. SIAM J Sci Comput., 2009, 31:2915-2934.
[22]  Yuan G and Sheng Z. Monotone finite volume schemes for diffusion equations on polygonal meshes[J]. J. Comput. Phys., 2008, 227:6288-6312.

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133