A Second-Order Well-Balanced Positivity Preserving Central-Upwind Scheme for the Saint-Venant System
نویسندگان
چکیده
منابع مشابه
A Second-order Well-balanced Positivity Preserving Central-upwind Scheme for the Saint-venant System
A family of Godunov-type central-upwind schemes for the Saint-Venant system of shallow water equations has been first introduced in [A. Kurganov and D. Levy, M2AN Math. Model. Numer. Anal., 36, 397-425, 2002]. Depending on the reconstruction step, the second-order versions of the schemes there could be made either well-balanced or positivity preserving, but fail to satisfy both properties simul...
متن کاملWell-Balanced Positivity Preserving Central-Upwind Scheme on Triangular Grids for the Saint-Venant System
We introduce a new second-order central-upwind scheme for the Saint-Venant system of shallow water equations on triangular grids. We prove that the scheme both preserves stationary steady states (lake at rest) and guarantees the positivity of the computed fluid depth. Moreover, it can be applied to models with discontinuous bottom topography and irregular channel widths. We demonstrate these fe...
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We develop a second-order central-upwind scheme for the non-hydrostatic version of the Saint-Venant system recently proposed in [M.-O. Bristeau and J. Sainte-Marie, Discrete Contin. Dyn. Syst. Ser. B, 10 (2008), pp. 733–759]. The designed scheme is both well-balanced (capable of exactly preserving the “lake-at-rest” steady state) and positivity preserving. We then use the central-upwind scheme ...
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Shallow water models are widely used to describe and study free-surface water flow. Even though, in many practical applications the bottom friction does not have much influence on the solutions, the friction terms will play a significant role when the depth of the water is very small. In this paper, we study the Saint-Venant system of shallow water equations with friction terms and develop a we...
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The paper is concerned with development of a new finite-volume method for a class of chemotaxis models and for a closely related haptotaxis model. In its simplest form, the chemotaxis model is described by a system of nonlinear PDEs: a convection-diffusion equation for the cell density coupled with a reaction-diffusion equation for the chemoattractant concentration. The first step in the deriva...
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ژورنال
عنوان ژورنال: Communications in Mathematical Sciences
سال: 2007
ISSN: 1539-6746,1945-0796
DOI: 10.4310/cms.2007.v5.n1.a6