Volume 25, Issue 5
A Highly Efficient Numerical Method for Rotating Oceanographic Flows Modeled by Saint-Venant System with Coriolis Forces

Xin Liu

Commun. Comput. Phys., 25 (2019), pp. 1394-1412.

Published online: 2019-01

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  • Abstract

In order to overcome the strong limitation of the computational cost for classic explicit schemes in quasi-geostrophic limit typically involved in oceanographic flows, in this study, a highly efficient numerical method for rotating oceanographic flows modeled by Saint-Venant system with Coriolis forces is developed. To efficiently deal with the rotating flows in the low Rossby and Froude number regime, the core idea is splitting fast varying flux terms into stiff and non-stiff parts, and implicitly approximating the fast dynamic waves using central difference method with an iteration algorithm and explicitly approximating slow dynamic waves using a finite-volume hyperbolic solver with minmod limiter. The proposed approach has a second order convergence rate in the quasi-geostrophic limit. The temporal evolution is approximated using a high-order implicit-explicit Runge-Kutta method. The proposed semi-implicit scheme is proved to be uniformly asymptotically consistent in the quasi-geostrophic limit when Froude and Rossby numbers→0. The proposed numerical methods are finally verified by numerical experiments of rotating shallow flows. The tests show that the proposed numerical scheme is stable and accurate with any grid size with low Rossby and Froude numbers, which leads to significant reduction of the computational cost comparing with classic explicit schemes.

  • Keywords

Saint-Venant system, implicit-explicit, Coriolis, low Rossby number, low Froude number, finite-volume method, quasi-geostrophic limit.

  • AMS Subject Headings

35Q35, 76U05, 76N99, 76M12, 65M06

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CiCP-25-1394, author = {}, title = {A Highly Efficient Numerical Method for Rotating Oceanographic Flows Modeled by Saint-Venant System with Coriolis Forces}, journal = {Communications in Computational Physics}, year = {2019}, volume = {25}, number = {5}, pages = {1394--1412}, abstract = {

In order to overcome the strong limitation of the computational cost for classic explicit schemes in quasi-geostrophic limit typically involved in oceanographic flows, in this study, a highly efficient numerical method for rotating oceanographic flows modeled by Saint-Venant system with Coriolis forces is developed. To efficiently deal with the rotating flows in the low Rossby and Froude number regime, the core idea is splitting fast varying flux terms into stiff and non-stiff parts, and implicitly approximating the fast dynamic waves using central difference method with an iteration algorithm and explicitly approximating slow dynamic waves using a finite-volume hyperbolic solver with minmod limiter. The proposed approach has a second order convergence rate in the quasi-geostrophic limit. The temporal evolution is approximated using a high-order implicit-explicit Runge-Kutta method. The proposed semi-implicit scheme is proved to be uniformly asymptotically consistent in the quasi-geostrophic limit when Froude and Rossby numbers→0. The proposed numerical methods are finally verified by numerical experiments of rotating shallow flows. The tests show that the proposed numerical scheme is stable and accurate with any grid size with low Rossby and Froude numbers, which leads to significant reduction of the computational cost comparing with classic explicit schemes.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0136}, url = {http://global-sci.org/intro/article_detail/cicp/12955.html} }
TY - JOUR T1 - A Highly Efficient Numerical Method for Rotating Oceanographic Flows Modeled by Saint-Venant System with Coriolis Forces JO - Communications in Computational Physics VL - 5 SP - 1394 EP - 1412 PY - 2019 DA - 2019/01 SN - 25 DO - http://doi.org/10.4208/cicp.OA-2018-0136 UR - https://global-sci.org/intro/article_detail/cicp/12955.html KW - Saint-Venant system, implicit-explicit, Coriolis, low Rossby number, low Froude number, finite-volume method, quasi-geostrophic limit. AB -

In order to overcome the strong limitation of the computational cost for classic explicit schemes in quasi-geostrophic limit typically involved in oceanographic flows, in this study, a highly efficient numerical method for rotating oceanographic flows modeled by Saint-Venant system with Coriolis forces is developed. To efficiently deal with the rotating flows in the low Rossby and Froude number regime, the core idea is splitting fast varying flux terms into stiff and non-stiff parts, and implicitly approximating the fast dynamic waves using central difference method with an iteration algorithm and explicitly approximating slow dynamic waves using a finite-volume hyperbolic solver with minmod limiter. The proposed approach has a second order convergence rate in the quasi-geostrophic limit. The temporal evolution is approximated using a high-order implicit-explicit Runge-Kutta method. The proposed semi-implicit scheme is proved to be uniformly asymptotically consistent in the quasi-geostrophic limit when Froude and Rossby numbers→0. The proposed numerical methods are finally verified by numerical experiments of rotating shallow flows. The tests show that the proposed numerical scheme is stable and accurate with any grid size with low Rossby and Froude numbers, which leads to significant reduction of the computational cost comparing with classic explicit schemes.

Xin Liu. (2020). A Highly Efficient Numerical Method for Rotating Oceanographic Flows Modeled by Saint-Venant System with Coriolis Forces. Communications in Computational Physics. 25 (5). 1394-1412. doi:10.4208/cicp.OA-2018-0136
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