Title: Explicit staggered grid scheme for rotating shallow water equations on geostrophic flows

Authors: P.H. Gunawan; S.R. Pudjaprasetya

Addresses: School of Computing, Telkom University, Jalan, Telekomunikasi No. 1, Terusan Buah Batu, Bandung 40257, Indonesia ' Mathematics Department, Insitut Teknologi Bandung, Jalan, Ganesha No. 10, Bandung 40132, Indonesia

Abstract: This paper is devoted to the description of an explicit staggered grid scheme for the rotating shallow water equations in one and two-dimension. The shallow water equations is approximated using the momentum conservative scheme, and the Coriolis terms is calculated using the Crank-Nicolson method. The resulting scheme is implemented for simulating various rotating phenomena, such as, the interior gravity wave, oscillation in a paraboloid, coastal and equatorial Kelvin waves. Comparison with exact solution or other collocated scheme (Suliciu or HLLC scheme) give good agreement. The discrete L1 error and the convergence rate of the scheme are shown to be satisfied. Moreover, our numerical experiments satisfy entropy stability. Except from adjustment for the initial and boundary conditions, no special treatment are required for all simulations above. And these indicate the robustness of our explicit staggered grid scheme.

Keywords: finite volume method; explicit staggered scheme; rotating shallow water; Coriolis force; geostrophic flows.

DOI: 10.1504/PCFD.2018.089502

Progress in Computational Fluid Dynamics, An International Journal, 2018 Vol.18 No.1, pp.46 - 55

Received: 08 May 2021
Accepted: 12 May 2021

Published online: 25 Jan 2018 *

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