High-order nite volume WENO schemes for the shallow water equations with dry states
- ORNL
- Brown University
The shallow water equations are used to model flows in rivers and coastal areas, and have wide applications in ocean, hydraulic engineering, and atmospheric modeling. These equations have still water steady state solutions in which the flux gradients are balanced by the source term. It is desirable to develop numerical methods which preserve exactly these steady state solutions. Another main difficulty usually arising from the simulation of dam breaks and flood waves flows is the appearance of dry areas where no water is present. If no special attention is paid, standard numerical methods may fail near dry/wet front and produce non-physical negative water height. A high-order accurate finite volume weighted essentially non-oscillatory (WENO) scheme is proposed in this paper to address these difficulties and to provide an efficient and robust method for solving the shallow water equations. A simple, easy-to-implement positivity-preserving limiter is introduced. One- and two-dimensional numerical examples are provided to verify the positivity-preserving property, well-balanced property, high-order accuracy, and good resolution for smooth and discontinuous solutions.
- Research Organization:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC); Work for Others (WFO)
- DOE Contract Number:
- DE-AC05-00OR22725
- OSTI ID:
- 1023850
- Journal Information:
- Advances in Water Resources, Vol. 34, Issue 8; ISSN 0309-1708
- Country of Publication:
- United States
- Language:
- English
Similar Records
Positivity-preserving high order well-balanced discontinuous Galerkin methods for the shallow water equations
High Order Well-Balanced Schemes and Applications to Non-Equilibrium Flow with Stiff Source Terms