Abstract
Higher-order difference schemes always cause oscillation in convection calculation though they require much effort in the calculation. Overshoot and undershoot of the oscillation is troublesome particularly in the calculations of temperature, energy, and turbulence parameters. Filtering techniques improve both accuracy and stability, and some of them can completely suppress the overshoot or undershoot, when they are combined with the higher-order difference schemes. In the present study, a new min-max truncation (MMT) method is proposed. It is evaluated in two test problems of pure convection, and compared with other filtered and not-filtered difference schemes.
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Anderson, W. K.; Thomas, J. L.; Leer, B., van (1986): Comparison of finited volume flux vector s splitings for the Euler equations. AIAA J. 24, 1453–1460
Boris, J. P.; Book, D. L. (1973): Flux-corrected transport. I. SHASTA, a fluid transport algorithm that works. J. Comput. Phys. 11, 38–69
Chapman, M. (1981): FRAM—Nonlinear damping algorithms for the continuity equation. J. Comput. Phys. 44, 84–103
Daly, B. J.; Torrey, M. D. (1984): SOLA-PTS: A transient, three-dimensional algorithm for fluid-thermal mixing and wall heat transfer in complex geometries. LA-10132-MS
Dukowicz, J. K.; Ramshaw, J. D. (1979): Tensor viscosity method for convection in numerical fluid dynamics. J. Comput. Phys. 32, 71–79
Harten, A. (1984): On a class of high resolution total-variation-stable finite-difference schemes. SIAM J. Num. Anal. 21, 1–23
Hirt, C. W.; Amsden, A. A.; Cook, J. L. (1974): An arbitrary Lagrangian-Eulerian computing method for all flow speeds. J. Comput. Phys. 14, 227–253
Koshizuka, S.; Oka, Y.; Togo, Y. (1986): Interpolating matrix method applied to fluid flows surrounded by complex boundaries. Proc. Int. Conf. Comput. Mech., Tokyo, VII-53∼58
Leonard, B. P. (1979): A stable and accurate convection modeling procedure based on quadratic upstream interpolation. Comput. Meths. Appl. Mech. Engrg. 19, 59–98
Miki, K.; Takagi, T. (1984): A domain decomposition and overlapping method for the generation of three-dimensional boundary-fitted coordinate system. J. Comput. Phys. 53, 319–330
Raithby, G. D. (1976): Skew upstream differencing schemes for problems involving fluid flow. Comput. Meths. Appl. Mech. Engrg. 9, 153–164
Roache, P. J. (1976): Computational fluid dynamics. Albuquerque: Hermosa
Thompson, J. F.; Warsi, Z. U. A.; Mastin, C. W. (1982): Boundary-fitted coordinate systems for numerical solution of partial differential equations—A review. J. Comput. Phys. 47, 1–108
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Communicated by G. Yagawa, January 4, 1989
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Koshizuka, S., Carrico, C.B., Lomperski, S.W. et al. Min-max truncation: An accurate and stable filtering method for difference calculation of convection. Computational Mechanics 6, 65–76 (1990). https://doi.org/10.1007/BF00373800
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DOI: https://doi.org/10.1007/BF00373800