Asymptotic consistency of the rs-imex scheme for the low-froude shallow water equations: Analysis and numerics

Abstract

In the present work, we formally prove the asymptotic consistency of the recently presented Reference Solution IMplicit–EXplicit (RS-IMEX) scheme for the two-dimensional shallow water equations. The scheme has been analyzed extensively for the low-Froude one-dimensional shallow water equations in (Zakerzadeh IGPM report 455 (2016) [18]), and the present paper is going to discuss the asymptotic consistency analysis for the two-dimensional case, with the aid of some numerical experiments.