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Title: Moving mesh methods for Boussinesq equation
Authors: Wan-Lung, L.
Tan, Z. 
Keywords: Boussinesq equation
Finite volume method
Moving mesh method
PDE evolution
WENO scheme
Issue Date: Dec-2009
Citation: Wan-Lung, L., Tan, Z. (2009-12). Moving mesh methods for Boussinesq equation. International Journal for Numerical Methods in Fluids 61 (10) : 1161-1178. ScholarBank@NUS Repository.
Abstract: The Boussinesq equation is a challenging problem both analytically and numerically. Owing to the complex dynamic development of small scales and the rapid loss of solution regularity, the Boussinesq equation pushes any numerical strategy to the limit. With uniform meshes, the amount of computational time is too large to enable us to obtain useful numerical approximations. Therefore, developing effective and robust moving mesh methods for these problems becomes necessary. In this work, we develop an efficient moving mesh algorithm for solving the two-dimensional Boussinesq equation. Our moving mesh algorithm is an extension of Tang and Tang (SIAM J. Numer. Anal. 2003; 41:487-515) for hyperbolic conservation laws and Zhang and Tang (Commun. Pure Appl. Anal. 2002; 1:57-73) for convection-dominated equations. Several numerical fluxes (Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction (2nd edn). Springer: Berlin, 1999; WASCOM 99": 10th Conference on Waves and Stability in Continuous Media, Porto Ercole, Italy, 1999; 257-264; High-order Methods for Computational Physics. Springer: Berlin, 1999; 439-582; J. Sci. Comput. 1990; 5:127-149; SIAM J. Numer. Anal. 2003; 41:487-515; Commun. Pure Appl. Anal. 2002; 1:57-73) are also discussed. Numerical results demonstrate the advantage of our moving mesh method in resolving the small structures. Copyright © 2009 John Wiley & Sons, Ltd.
Source Title: International Journal for Numerical Methods in Fluids
ISSN: 02712091
DOI: 10.1002/fld.2008
Appears in Collections:Staff Publications

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