کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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499541 | 863049 | 2008 | 20 صفحه PDF | دانلود رایگان |
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.
Journal: Computer Methods in Applied Mechanics and Engineering - Volume 197, Issues 13–16, 15 February 2008, Pages 1242–1261