کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4526187 | 1323820 | 2010 | 18 صفحه PDF | دانلود رایگان |
Shallow water equations with a non-flat bottom topography have been widely used to model flows in rivers and coastal areas. An important difficulty arising in these simulations is the appearance of dry areas where no water is present, as standard numerical methods may fail in the presence of these areas. These equations also have still water steady state solutions in which the flux gradients are nonzero but exactly balanced by the source term. In this paper we propose a high order discontinuous Galerkin method which can maintain the still water steady state exactly, and at the same time can preserve the non-negativity of the water height without loss of mass conservation. A simple positivity-preserving limiter, valid under suitable CFL condition, will be introduced in one dimension and then extended to two dimensions with rectangular meshes. Numerical tests are performed to verify the positivity-preserving property, well-balanced property, high order accuracy, and good resolution for smooth and discontinuous solutions.
Journal: Advances in Water Resources - Volume 33, Issue 12, December 2010, Pages 1476–1493