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      Fourth-Order Conservative Transport on Overset Grids Using Multi-Moment Constrained Finite Volume Scheme for Oceanic Modeling

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          With an increase in model resolution, compact high-order numerical advection scheme can improve its effectiveness and competitiveness in oceanic modeling due to its high accuracy and scalability on massive-processor computers. To provide high- quality numerical ocean simulation on overset grids, we tried a novel formulation of the fourth-order multi-moment constrained finite volume scheme to simulate continuous and discontinuous problems in the Cartesian coordinate. Utilizing some degrees of freedom over each cell and derivatives at the cell center, we obtained a two-dimensional (2D) cubic polynomial from which point values on the extended overlap can achieve fourth-order accuracy. However, this interpolation causes a lack of conservation because the flux between the regions are no longer equal; thus, a flux correction is implemented to ensure conservation. A couple of numerical experiments are presented to evaluate the numerical scheme, which confirms its approximately fourth-order accuracy in conservative transportation on overset grid. The test cases reveal that the scheme is effective to suppress numerical oscillation in discontinuous problems, which may be powerful for salinity advection computing with a sharp gradient.

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          Author and article information

          Journal of Ocean University of China
          Science Press and Springer (China )
          10 July 2020
          01 August 2020
          : 19
          : 4
          : 747-760
          1College of Global Change and Earth System Science, Beijing Normal University, Beijing 100875, China
          2State Key Laboratory of Severe Weather, Chinese Academy of Meteorological Sciences, Beijing 100081, China
          3College of Air Traffic Management, Civil Aviation Flight University of China, Guanghan 618307, China
          4School of Atmospheric Sciences, Sun Yat-Sen University, Guangzhou 510275, China
          5Plateau Atmosphere and Environment Key Laboratory of Sichuan Province, Chengdu University of Information Technology, Chengdu 610103, China
          6Department of Mechanical Engineering, Tokyo Institute of Technology, Tokyo 152-8550, Japan
          Author notes
          *Corresponding author: PENG Xindong, Tel: 0086-10-68409552 E-mail: pengxd@
          Copyright © Ocean University of China, Science Press and Springer-Verlag GmbH Germany 2020.

          The copyright to this article, including any graphic elements therein (e.g. illustrations, charts, moving images), is hereby assigned for good and valuable consideration to the editorial office of Journal of Ocean University of China, Science Press and Springer effective if and when the article is accepted for publication and to the extent assignable if assignability is restricted for by applicable law or regulations (e.g. for U.S. government or crown employees).

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