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报告人： 田纳西大学数学系 邢雨龙教授
报告题目：High order accurate numerical methods for the shallow-water equations
报告时间：2012年6月6日，星期三 16:00 pm - 17:00pm
报告地点：B703
学院联系人：邱建贤教授
报告摘要：
Shallow-water equations with a non-flat bottom topography have been widely used to model flows in rivers and coastal areas. These equations have steady-state solutions in which the flux gradients are non-zero but exactly balanced by the source term. Therefore extra care must be paid to approximate the source term numerically. Another important difficulty arising in these simulations is the appearance of dry areas, and standard numerical methods may fail in the presence of these areas.
In this presentation, we propose some recently developed high-order discontinuous Galerkin and weighted essentially non-oscillatory methods, which can preserve the steady-state exactly, and at the same time are positivity preserving without loss of mass conservation. Some numerical tests are performed to verify the positivity, well-balanced property, high-order accuracy, and good resolution for smooth and discontinuous solutions.