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• W2057199138 abstract "We present a finite volume method for the numerical approximation of advection–diffusion problems in convection-dominated regimes. The method works on unstructured grids formed by convex polygons of any shape and yields a piecewise linear approximation to the exact solution which is second-order accurate away from boundary and internal layers. Basically, we define a constant approximation of the solution gradient in every mesh cell which is expressed by using the cell averages of the solution within the adjacent cells. A careful design of the reconstruction algorithm for cell gradients and the introduction in the discrete formulation of a special non-linear term, which plays the role of the artificial diffusion, allows the method to achieve shock-capturing capability. We emphasize that no slope limiters are required by this approach. Optimal convergence rates, as theoretically expected, and non-oscillatory behavior close to layers are confirmed by numerical experiments." @default.
• W2057199138 created "2016-06-24" @default.
• W2057199138 creator A5014223403 @default.
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• W2057199138 date "2008-02-01" @default.
• W2057199138 modified "2023-10-16" @default.
• W2057199138 title "A finite volume method for advection–diffusion problems in convection-dominated regimes" @default.
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• W2057199138 doi "https://doi.org/10.1016/j.cma.2007.11.014" @default.
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