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Explicit staggered grid scheme for rotating shallow water equations on geostrophic flows
Gunawan P.H.a, Pudjaprasetya S.R.b
a School of Computing, Telkom University, Bandung, 40257, Indonesia
b Mathematics Department, Insitut Teknologi Bandung, Bandung, 40132, Indonesia
[vc_row][vc_column][vc_row_inner][vc_column_inner][vc_separator css=”.vc_custom_1624529070653{padding-top: 30px !important;padding-bottom: 30px !important;}”][/vc_column_inner][/vc_row_inner][vc_row_inner layout=”boxed”][vc_column_inner width=”3/4″ css=”.vc_custom_1624695412187{border-right-width: 1px !important;border-right-color: #dddddd !important;border-right-style: solid !important;border-radius: 1px !important;}”][vc_empty_space][megatron_heading title=”Abstract” size=”size-sm” text_align=”text-left”][vc_column_text]Copyright © 2018 Inderscience Enterprises Ltd.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.[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Author keywords” size=”size-sm” text_align=”text-left”][vc_column_text]Crank-Nicolson methods,Geostrophic flow,Initial and boundary conditions,Rotating shallow water equations,Shallow water equations,Shallow waters,Staggered grid schemes,Staggered schemes[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Indexed keywords” size=”size-sm” text_align=”text-left”][vc_column_text]Coriolis force,Explicit staggered scheme,Finite volume method,Geostrophic flows,Rotating shallow water[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Funding details” size=”size-sm” text_align=”text-left”][vc_column_text]The second author gratefully acknowledge the financial support from RISET Desentralisasi ITB 2016 Nomor: 0056/E3.2/LT/2016.[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”DOI” size=”size-sm” text_align=”text-left”][vc_column_text]https://doi.org/10.1504/PCFD.2018.089502[/vc_column_text][/vc_column_inner][vc_column_inner width=”1/4″][vc_column_text]Widget Plumx[/vc_column_text][/vc_column_inner][/vc_row_inner][/vc_column][/vc_row][vc_row][vc_column][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][/vc_column][/vc_row]