Geodesic
Balance-characteristic schemes with separated conservative and flux variables
Matematičeskoe modelirovanie, Tome 15 (2003) no. 9, pp. 29-48.

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The new approach is proposed for the development of difference methods with high resolution for the equation of convection with regard to diffusion. It based on the introduction of two different types of variables – “conservative” and “flux”, corresponding to the realization of the conservation law and correct calculation of characteristic region of influence respectively. The process of creation of new algorithms consists of two stages. At the first stage, linear uniform conservative difference schemes with improved dissipative and dispersion characteristics are constructed on the minimal computing stencil. At the second stage, conservative algorithm of minimal correction of the calculated values is used for the realization of the sufficient conditions of the principle of maximum. Explicit monotone algorithms were developed, that are stable in the case of the Courant number is less than unit and have the second order of accuracy on the smooth solutions. It is shown that new algorithms have noticeable advantages in comparison with the well-known TVD-schemes, based on the limitation of fluxes. 
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V. M. Goloviznin; S. A. Karabasov; I. M. Kobrinskii. Balance-characteristic schemes with separated conservative and flux variables. Matematičeskoe modelirovanie, Tome 15 (2003) no. 9, pp. 29-48. http://geodesic.mathdoc.fr/item/MM_2003_15_9_a2/

[1] B. L. Rozhdestvenskii, N. N. Yanenko, Sistemy kvazilineinykh uravnenii, Nauka, M., 1978 | MR | Zbl

[2] J. P. Boris, D. L. Book, K. Hain, “Flux-corrected transport: Generalization of the method”, J. Comput. Physics, 31 (1975), 335–350

[3] Van Leer B., “Towards the ultimate conservative difference scheme. V: A second-order sequel to Godunov's method”, J. Comput. Physics, 32 (1979), 101–137 | DOI | MR

[4] Harten A., “High resolution schemes for hyperbolic conservation laws”, J. Comput. Phys., 49 (1983), 357–393 | DOI | MR | Zbl

[5] Harten, S. Osher, “Uniformly high-order accurate non-oscillatory schemes, I”, SIAM. J. Numer. Anal., 24:2 (1987) | DOI | MR | Zbl

[6] Harten, B. Engqist, S. Osher, S. Chakravarthy, “Uniformly High Order Accurate Essentially Non-Oscillatiry Schemes, III”, J. Comput. Physics, 71 (1987), 231–303 | DOI | MR | Zbl

[7] Kolgan V. P., “Konechno-raznostnaya skhema dlya rascheta dvumernykh razryvnykh reshenii nestatsionarnoi gazovoi dinamiki”, Uch. Zap. TsAGI, 3:6 (1972), 68–77

[8] Vyaznikov K. V., Tishkin V. F., Favorskii A. P., Shashkov M. Yu., Kvazimonotonnye raznostnye skhemy povyshennogo poryadka tochnosti, Preprint IPM AN SSSR im. M. V. Keldysha, 1983, No 36, M.

[9] V. M. Goloviznin, A. A. Samarskii, “Raznostnaya approksimatsiya konvektivnogo perenosa s prostranstvennym rasschepleniem vremennoi proizvodnoi”, Matem. modelirovanie, 10:1 (1998), 86–100 | MR

[10] B. M. Goloviznin, A. A. Samarskii, “Nekotorye svoistva raznostnoi skhemy “Kabare””, Matem. modelirovanie, 10:1 (1998), 101–116 | MR

[11] R. Rouch, Vychislitelnaya gidrodinamika, Mir, M., 1976

[12] A. A. Samarskii, Teoriya raznostnykh skhem, Nauka, M., 1977 | MR | Zbl

[13] A. Tolstych, “The response of a variable resolution semi-Lagrangian NWP model to changes in horizontal interpolation”, Q. J. Meteorol. Sos., 122 (1996), 765–778 | DOI

[14] A. Iserles, “Generalized leapfrog methods”, IMA Journal of Numerical Analysis, 6 (1986) | MR

[15] Thomas J. P., Roe P. L., “Development of non-dissipative numerical schemes for computational aeroacoustics”, AIAA, 1995, 3382, 11-th Computational Fluid Dynamics Conference