Abstract
The paper is devoted to a new efficient numerical method for fluid dynamics applications. The method is of the second order of approximation and has a very compact numerical stencil. It combines traditional merits of finite-volume and finite-difference approaches such as shock capturing and linear Fourier accuracy on coarse grids. Possible applications of the method include gas dynamics and geophysical flow modelling
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References
Colonius T, Lele S K. Computational aeroacoustics: progress on nonlinear problems of sound generation. Progress in Aerospace Sciences, 2004; 40: 345–416
Karabasov S A, Goloviznin V M, Kozubskaya T K, Abalakin I A. A new high-resolution balance-characteristic method for aeroacoustics. In: 12th AIAA/CEAS Aeroacoustics Conference (27th AIAA Aeroacoustics Conference), Cambridge, Massachusetts, May 8–10, 2006. AIAA paper-2006-2415
Goloviznin V M, Semenov V N, Korortkin I A, Karabasov S A. A novel computational method for modelling stochastic advection in heterogeneous media. Transport in Porous Media, 2007; 6(2): 439–456
Lele S K. Compact finite-difference scheme with spectral-like resolution. J Comp Phys, 1992; 103: 16–42
Harten A, Engqist B, Osher S, Chakravarthy S. Uniformly high order accurate essentially non-oscillatiry schemes III. J Comput Phys, 1987; 71: 231–303
Titarev V A, Toro E F. ADER: Arbitrary high order Godunov approach. J Sci Comput, 2002; 17: 609–618
Iserles A. Generalized leapfrog methods. IMA Journal of Numerical Analysis, 1986; 6(2): 381–392
Thomas J P, Roe P L. Development of non-dissipative numerical schemes for computational aeroacoustics. AIAA Paper 93-3382
Goloviznin V M, Samarskii A A. Difference approximation of convective transport with spatial splitting of time derivative. Mathematical Modelling, 1998; 10(1): 86–100
Goloviznin VM. Balancing characteristic method for systems of hyperbolic conservation laws. Doklady Mathematics, 2005; 72(1): 619–623
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Karabasov, S.A., Goloviznin, V.M. (2007). A New Efficient High-Resolution Method for Non-Linear Problems in Fluid Mechanics. In: Zhuang, F.G., Li, J.C. (eds) New Trends in Fluid Mechanics Research. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75995-9_77
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DOI: https://doi.org/10.1007/978-3-540-75995-9_77
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-75994-2
Online ISBN: 978-3-540-75995-9
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