Numerical Simulation of the Ripa Model using the Upwind CE/SE Scheme (European Journal of Pure and Applied Mathematics, 2025)
This paper focuses on the numerical investigation of the shallow water equations (SWEs) with temperature gradients, commonly referred to as the Ripa system, using the finite volume upwind Conservation Element Solution Element (CE/SE) scheme. The inclusion of source-term on the right-hand side of the model introduces additional complexity, making the equations non-conservative and challenging to solve numerically. The primary objective is to develop a numerical scheme that effective ly handles non-conservative differential terms with accuracy and efficiency. To address these challenges, a finite volume upwind CE/SE technique is proposed. The method is tested on several numerical problems to evaluate its effectiveness, robustness, and stability, particularly in resolving discontinuities and shocks. The results of the proposed scheme are compared with those obtained using the standard CE/SE scheme.
Keywords: Ripa model; Non-conservative systems; Horizontal temperature gradient; Bottom topography; Upwind CE/SE scheme \sep CE/SE scheme \sep Smart grid