Explicit staggered grid scheme for rotating shallow water equations on geostrophic flows Online publication date: Mon, 29-Jan-2018
by P.H. Gunawan; S.R. Pudjaprasetya
Progress in Computational Fluid Dynamics, An International Journal (PCFD), Vol. 18, No. 1, 2018
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.
Online publication date: Mon, 29-Jan-2018
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