Hydrodynamic Instabilities in Well-Balanced Finite Volume Schemes for Frictional Shallow Water Equations. The Kinematic Wave Case

作者：Bohorquez Patricio^*; Rentschler Martin

来源：Journal of Scientific Computing, 2011, 48(1-3): 3-15.

DOI：10.1007/s10915-010-9444-4

• One layer shallow water
• Kinematic wave
• Roll waves
• WENO schemes
• Compact filter

We report the developments of hydrodynamic instabilities in several well-balanced finite volume schemes that are observed during the computation of the temporal evolution of an out-balance flow which is essentially a kinematic wave. The numerical simulations are based on the one-dimensional shallow-water equations for a uniformly sloping bed with hydraulic resistance. Subsequently, we highlight the need of low dissipative high-order well-balanced filter schemes for non-equilibrium flows with variable cut-off wavenumber to compute the out-balance flow under consideration, i.e. the kinematic wave.

• 出版日期2011-7