AAM  >> Vol. 5 No. 4 (November 2016)

    对流占优问题的一种修正CUI格式
    A Modified CUI Scheme for Convection-Dominated Equations

  • 全文下载: PDF(2096KB) HTML   XML   PP.716-727   DOI: 10.12677/AAM.2016.54083  
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作者:  

吕娜,高巍:内蒙古大学数学科学学院,内蒙古 呼和浩特;
谢桃枫:内蒙古医科大学计算机信息学院,内蒙古 呼和浩特

关键词:
CUI格式Hermite插值CBC/TVDmCUI格式CUI Scheme Hermite Interpolation Polynomial CBC/TVD mCUI Scheme

摘要:

对流扩散方程是一类重要的模型方程,构造对流项的高分辨率离散格式是数值计算的关键,本文基于CBC (Convection Boundedness Criterion)准则和TVD (Total Variational Diminishing Constraint)准则,利用Hermite插值,构造一种改进的CUI格式。经典的算例表明,此数值方法不仅能很好的抑制线性对流离散格式的数值振荡,也表现出良好的数值计算精度。

In this paper, a modified CUI scheme is presented for discretizing the convection term. Coupled with Herimite interpolation, CBC (Convection Boundedness Criterion) and TVD (Total Variational Diminishing Constraint) are applied to suppress numerical oscillations. Typical test cases demonstrate that the present scheme possesses the boundedness of convection and high accuracy.

文章引用:
吕娜, 谢桃枫, 高巍. 对流占优问题的一种修正CUI格式[J]. 应用数学进展, 2016, 5(4): 716-727. http://dx.doi.org/10.12677/AAM.2016.54083

参考文献

[1] Spalding, D.B. (1972) A Novel Finite Difference Formulation for Differential Expressions Involving Both First and Second Derivatives. International Journal for Numerical Methods in Engineering, 4, 551-559.
https://doi.org/10.1002/nme.1620040409
[2] Leonard, B.P. (1979) A Stable and Accurate Modeling Procedure Based on Quadratic Interpolation. Computer Method in Applied Mechanics and Engineering, 19, 59-98.
https://doi.org/10.1016/0045-7825(79)90034-3
[3] Agarwal, R.K. (1981) A Third-Order-Accurate Upwind Scheme for Navier-Stokes Solutions at high Reynolds Numbers. 19th Aerospace Sciences Meeting, American Institute of Aeronautics and Astronautics, St. Louis, 12-15 January 1981.
https://doi.org/10.2514/6.1981-112
[4] Harten, A.(1983) High Resolution Scheme for Hyperbolic Conservation Law. Journal of computational Physics, 49, 357-393.
https://doi.org/10.1016/0021-9991(83)90136-5
[5] Sweby, P.K. (1984) High Resolution Scheme Using Flux Limiters for Hyperbolic Conservation Laws. SLAM Journal on Numerical Analysis, 21, 995-1011.
https://doi.org/10.1137/0721062
[6] Lenard, B.P. (1988) Simple High-Accuracy Resolution Program for Convective Modeling of Discontinuities. International Journal for Numerical Methods in Fluids, 8, 1291-1318.
https://doi.org/10.1002/fld.1650081013
[7] Gaskell, P.H. and Lau, A.K.C. (1988) Curvature-Compensated Convective Transport: SMART, A New Boundedness- preserving trans-port algorithm. International Journal for Numerical Methods in Fluids, 8, 617-641.
https://doi.org/10.1002/fld.1650080602
[8] Zhu, J. (1991) A Low-Diffusive and Oscillation-Free Convective Scheme. International Journal for Numerical Methods in Biomedical Engineering, 7, 225-232.
[9] Wei, J.J., Yu, B., Tao, W.Q., Kawaguchi, Y. and Wang, H.S. (2003) A New High-Order-Accurate and Bounded Scheme for Incompressible Flow. Numerical Heat Transfer, Part B: Fundamentals, 43, 19-41.
https://doi.org/10.1080/713836153
[10] Alves, M.A., Oliveire, P.J. and Pinho, F.T. (2003) A Convergent and Universally Bounded Interpolation Scheme for the Treatment of Advection. International Journal for Numerical Methods in Fluids, 41, 47-75.
[11] Lax, P.D. and Wendroff, B. (1960) Systems of Conservations Laws. Communications on Pure and Applied Mathematics, 13, 217-237.
https://doi.org/10.1002/cpa.3160130205
[12] Hou, P.L., Tao, W.Q. and Yu, M.Z. (2003) Refinement of the Convective Boundedness Criterion of Gaskell and Lau. Engineering Computations, 20, 1023-1043.
https://doi.org/10.1108/02644400310503008
[13] Gottlieb, S. and Shu, C.-W. (1998) Total Variational Diminishing Runge-Kutta Schemes. Mathematics of Computation, 67, 73-85.
https://doi.org/10.1090/S0025-5718-98-00913-2
[14] Van Leer, B. (1974) Towards the Ultimate Conservative Difference Scheme: II. Monotonicity and Conservation Combined in a Second-Order Scheme. Journal of Computation Physics, 14, 361-370.
https://doi.org/10.1016/0021-9991(74)90019-9
[15] Doswell, C.A. (1998) A Kinematic Analysis of Frontogenesis Associated with a Nondivergent Vortex. Journal of the Atmospheric Sciences, 41, 1242-1248.