AAM  >> Vol. 4 No. 2 (May 2015)

    A High-Resolution Finite Volume Scheme Based on Newtonian Interpolation

  • 全文下载: PDF(1013KB) HTML   XML   PP.150-161   DOI: 10.12677/AAM.2015.42020  
  • 下载量: 1,738  浏览量: 7,648   国家科技经费支持


高 巍,张 庆,李 宏,刘 洋:内蒙古大学数学科学学院,内蒙古 呼和浩特

对流扩散方程Newton插值多项式CBC准则TVD准则Convection Diffusion Equation Newton Interpolation Polynomial Convection Boundness Criterion (CBC) Total Variation Diminishing (TVD)



Finite volume method plays an important role in fluid flow and heat transfer numerical calculation. How to eliminate unphysical oscillations caused by numerical solution of convection diffusion equation selecting discontinuity wave as the initial condition is a key task for studying finite volume method. New high-resolution schemes were constructed by Newton interpolation polynomial based on convection boundness criterion (CBC). Classic test cases demonstrated that the present numerical scheme possesses high resolution and good stability for high gradient and discontinuous solution.

高巍, 张庆, 李宏, 刘洋. 基于牛顿插值的高分辨率有限体积格式[J]. 应用数学进展, 2015, 4(2): 150-161. http://dx.doi.org/10.12677/AAM.2015.42020


[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.
[2] Lax, P.D. and Wendroff, B. (1960) Systems of conservations laws. Communications on Pure and Applied Mathematics, 13, 217-237.
[3] Leonard, B.P. (1979) A stable and accurate modeling procedure based on quadratic interpolation. Computer Method in Applied Mechanics and Engineering, 19, 59-98.
[4] Agarwal, R.K. (1981) A third-order-accurate upwind scheme for Navi-er-Stokes solutions at high Reynolds numbers. American Institute of Aeronautics and Astronautics, 19th Aerospace Sciences Meeting, St. Louis, 12-15 January 1981.
[5] Roe, P.L. (1986) Character-based schemes for the Euler equa-tions. Annual Review of Fluid Mechanics, 18, 337-365.
[6] Harten, A. (1983) High resolution scheme for hyperbolic conservation law. Journal of computational Physics, 49, 357- 393.
[7] Sweby, P.K. (1984) High resolution scheme using flux limiters for hyperbolic conservation laws. SIAM Journal on Numerical Analysis, 21, 995-1011.
[8] Lenard, B.P. (1988) Simple high-accuracy resolution program for convective modeling of discontinuities. International Journal for Numerical Methods in Fluids, 8, 1291-1318.
[9] Gaskell, P.H. and Lau, A.K.C. (1988) Curvature-compensated convective transport: SMART, A new boundedness- preserving transport algorithm. International Journal for Numerical Methods in Fluids, 8, 617-641.
[10] 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.
[11] Wei, J.J., Yu, B. and Tao, W.Q. (2003) A new high-order-accurate and bounded scheme for incompres-sible flow. Numerical Heat Transfer: Part B: Fundamentals, 43, 19-41.
[12] Yu, W.Q., Tao, D.S., Zhang, Q.W. and Wang, B. (2001) Discussion on numerical stability and boundedness of convective discretized scheme. Numerical Heat Transfer: Part B: Fundamentals, 40, 343-365.
[13] 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.
[14] Gottlieb, S. and Shu, C.W. (1998) Total variation diminishing Runge-Kutta schemes. Mathematics of Computation, 67, 73-85.