基于牛顿插值的高分辨率有限体积格式
A High-Resolution Finite Volume Scheme Based on Newtonian Interpolation
摘要: 有限体积方法在计算流体和热传导的数值计算中占据重要的地位。在数值格式构造的过程中，如何消除对流扩散方程选取间断波为初始条件时数值解所产生的非物理震荡，是有限体积方法主要的研究内容。本文基于对流有界准则(CBC)原理，通过Newton插值多项式的方法构造新的高分辨率有限体积格式。经典算例表明，本文构造的数值格式对于大梯度或间断解有较好的分辨率和数值稳定性。
Abstract: 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.
文章引用：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. https://dx.doi.org/10.12677/AAM.2015.42020

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.
[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.

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