|Preprint-No.:||< 352 >||Published in:||December 2012||PDF-File:||IGPM352_k.pdf|
|Title:||An Asymptotic Preserving Scheme for Low Froude Number Shallow Flows|
|Authors:||Koottungal Revi Arun and Sebastian Noelle|
We present an asymptotic preserving (AP), large time-step scheme for the shallow water equations in the low Froude number limit. Based on a multiscale asymptotic expansion, the momentum fluxes are split into a nonstiff and a stiff part. A semi-implicit discretisation, where the nonstiff terms are treated explicitly and stiff terms implicitly in time, is crucial to achieve the AP property. A combination of the semi-discrete mass and momentum equations leads to an elliptic equation for the water height at the new time-level. With the aid of this, the momentum can be update explicitly using a large time- step which solely determined by the nonstiff characteristic speeds. The second order accuracy of the scheme is based on Runge-Kutta and Crank-Nicolson time-stepping procedures and MUSCL-type reconstructions. The numerical results clearly demonstrate the accuracy and robustness of the scheme and its efficacy to compute very low Froude number flows.
|Keywords:||shallow water equations, low Froude number limit, stiffness, semi–implicit time discretisation, flux decomposition, asymptotic preserving schemes|