Abstract
Hydrodynamic problems often feature geometrical configurations that allow a suitable dimensional model reduction. One-dimensional models may be sometimes accurate enough for describing a dynamic of interest. In other cases, localized relevant phenomena require more precise models. To improve the computational efficiency, geometrical multiscale models have been proposed, where reduced (1D) and complete (2D–3D) models are coupled in a unique numerical solver. In this paper we consider an adaptive geometrical multiscale modeling: the regions of the computational domain requiring more or less accurate models are automatically and dynamically selected via a heuristic criterion. To the best of our knowledge, this is a first example of automatic geometrical multiscale model reduction.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Colella, P.: Multidimensional upwind methods for hyperbolic conservation laws. J. Comput. Phys. 87, 171–200 (1990)
Cardiovascular Mathematics, Modeling and Simulation of the Circulatory System. Formaggia, L., Quarteroni, A., Veneziani, A. (eds.), Springer, Milano (2009)
Krámer, T., Józsa, J.: Solution-adaptivity in modelling complex shallow flows. Computers & Fluids 36, 562–577 (2007)
LeVeque, R.J.: Finite Volume Methods for Hyperbolic Problems. Cambridge, (2001).
LeVeque, R.J.: Clawpack, Version 4.3. http://depts.washington.edu/clawpack/clawpack-4.3/
Mauri, L., Perotto, S., Veneziani, A.: An adaptive geometrical multiscale model for the shallow water equations. In preparation (2012)
Miglio, E., Perotto, S., Saleri, F.: Model coupling techniques for free-surface flow problems. Part I. Nonlinear Analysis, 63, 1885–1896 (2005)
Roe, P.L.: Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys. 43, 357–372 (1981)
Sleigh, P.A., Berzins, M., Gaskell, P.H., Wright, N.G.: An unstructured finite volume algorithm for predicting flow in rivers and estuaries. Computers & Fluids 27, 479–508 (1998)
Vreugdenhil, C.B.:Numerical Methods for Shallow-Water Flow. Springer, (1994).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mauri, L., Perotto, S., Veneziani, A. (2013). Adaptive Geometrical Multiscale Modeling for Hydrodynamic Problems. In: Cangiani, A., Davidchack, R., Georgoulis, E., Gorban, A., Levesley, J., Tretyakov, M. (eds) Numerical Mathematics and Advanced Applications 2011. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33134-3_76
Download citation
DOI: https://doi.org/10.1007/978-3-642-33134-3_76
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-33133-6
Online ISBN: 978-3-642-33134-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)