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구면 천수방정식계에서 불연속 갤러킨 기법의 수치 플럭스 비교
이태형(T.H. Yi),최석진(S.J. Choi),강신후(S.H. Kang) 한국전산유체공학회 2013 한국전산유체공학회 학술대회논문집 Vol.2013 No.5
In developing the dynamic core of a numerical weather prediction model with the discontinuous Galerkin method, a numerical flux at the boundaries of grid elements plays a vital role since it preserves the local conservation properties and has a significant impact on the accuracy and stability of numerical solutions. Due to these reasons, we implemented approximate Riemann fluxes such as Lax-Friedrichs and Roe fluxes for spherical shallow water equations in order to figure out the stability and accuracy of these fluxes. For the comparison, some of two- and three-dimensional test cases are performed on both a plane and a cubed-sphere with various numbers of element and polynomial orders. The detailed numerical studies include the Gaussian bell on a plane, and the zonal flow over an isolated mountain and the Rossby-Haurwitz wave on a cubed-sphere. It was shown that the Lax-Friedrichs flux is relatively dissipative than the Roe at low grid resolutions and has a weak numerical stability.