A mass conservative, well balanced, tangency preserving and energy decaying method for the shallow water equations on a sphere

Journal Article · 16 February 2022 · Journal of Computational Physics

DOI: https://doi.org/10.1016/j.jcp.2022.111067 · OSTI ID:1977279

Gunzburger, Max ^[1]; Li, Buyang ^[2]; Wang, Jilu ^[3]; Yang, Zongze  ^[2]

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1. Florida State Univ., Tallahassee, FL (United States); OSTI
2. Hong Kong Polytechnic University, Hung Hom (Hong Kong)
3. Beijing Computational Science Research Center (China)

Here a fully discrete surface finite element method is proposed for solving the viscous shallow water equations in a bounded Lipschitz domain on the sphere based on a general triangular mesh. The method consists of a modified Crank–Nicolson method in time and a Galerkin surface finite element method in space for the fluid thickness H and the fluid velocity u. A finite element space tangential to the sphere at all finite element nodes is proposed to approximate the fluid velocity u. The proposed method has second-order accuracy in time and first-order accuracy in space, and preserves mass conservation, well balancedness, tangency of velocity to the sphere, and energy decay. Numerical experiments are presented to illustrate the accuracy of the proposed method and the preservation of the physical properties, including mass conservation, well balancedness, and energy decay. A numerical simulation of ocean mesoscale activity on a circular basin with a continental shelf is provided.

• Research Organization: Florida State Univ., Tallahassee, FL (United States)
• Sponsoring Organization: USDOE Office of Science (SC); National Natural Science Foundation of China (NSFC)
• Grant/Contract Number: SC0020418
• OSTI ID: 1977279
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: C Vol. 457; ISSN 0021-9991
• Publisher: ElsevierCopyright Statement
• Country of Publication: United States
• Language: English