Multi-domain High-order Numerical Method for Shallow Water Equations on Cubed Sphere

• Main Authors: Ting-An Chen, 陳廷安
• Other Authors: 鄧君豪
• Format: Others
• Language: zh-TW
• Published: 2019
• Online Access: http://ndltd.ncl.edu.tw/cgi-bin/gs32/gsweb.cgi/login?o=dnclcdr&s=id=%22107NCHU5507031%22.&searchmode=basic

碩士 === 國立中興大學 === 應用數學系所 === 107 === In this paper, we find a skew-symmetry form of the shallow water equations on the cubed sphere, and construct the numerical scheme by the summation-by-parts finite difference method in the skew-symmetry form, and penalty method for implementation of the interface condition. We can use the energy estimation method to prove that the semi-discrete scheme is stable. To ensure that the nonlinear problem is still stable at full discrete level, we add an artificial dissipation term to the scheme. We valid our numerical scheme by simulating the steady state of a geostrophic flow and the zonal wavenumber-4 Rossby-Haurwitz problem. The simulation results of the steady state problem clearly show the expected convergence rate. Our simulation results for the Rossby-Haurwitz problem agree with results by other methods.