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Part of the book series: Notes on Numerical Fluid Mechanics and Multidisciplinary Design ((NNFM,volume 120))

Abstract

We develop an adaptive artificial viscosity method for the one-dimensional Saint-Venant system of shallow water equations. The proposed method is a semi-discrete finite-volume method based on an appropriate numerical flux and a high-order piecewise polynomial reconstruction. The latter is utilized without any computationally expensive nonlinear limiters, which are typically needed to guarantee nonlinear stability of the scheme. Instead, we enforce stability by adding an adaptive artificial viscosity, whose coefficients are proportional to the size of the weak local residual. Our method is capable to preserve the “lake at rest” steady state and the positivity of water depth. We test the proposed scheme on a number of benchmarks. The obtained numerical results clearly demonstrate that our method is well-balanced, positivity preserving and highly accurate.

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Correspondence to Yunlong Chen .

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Chen, Y., Kurganov, A., Lei, M., Liu, Y. (2013). An Adaptive Artificial Viscosity Method for the Saint-Venant System. In: Ansorge, R., Bijl, H., Meister, A., Sonar, T. (eds) Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 120. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33221-0_8

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  • DOI: https://doi.org/10.1007/978-3-642-33221-0_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33220-3

  • Online ISBN: 978-3-642-33221-0

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