High-order compact finite difference schemes for the spherical shallow water equations
2013 (English)Report (Other academic)
This work is devoted to the application of the super compact finite difference (SCFDM) and the combined compact finite difference (CCFDM) methods for spatial differencing of the spherical shallow water equations in terms of vorticity, divergence and height. Five high-order schemes including the fourth-order compact, the sixth-order and eighth-order SCFDM and the sixth-order and eighth-order CCFDM schemes are used for spatial differencing of the spherical shallow water equations. To advance the solution in time, a semi-implicit Runge-Kutta method is used. In addition, to control the nonlinear instability and avoiding the polar problem a high-order spatial filter is proposed. An unstable barotropic mid-latitude zonal jet is employed as an initial condition. For the numerical solution of the elliptic equations in the problem, a direct hybrid method which consists of using a high-order compact scheme for spatial differencing in the latitude coordinate and a fast Fourier transform in longitude coordinate is utilized. The convergence rate for all methods is studied and veried. Qualitative and quantitative assessment of the results, such as measures of maximum vorticity gradient, power spectrum of total energy, relative change in potential enstrophy and potential palinstrophy, reveal that the sixth-order and eighth-order CCFDM and the sixth-order and eighth-order SCFDM methods lead to a remarkable improvement of the solution over the fourth-order compact method. It is also shown that the performance of the sixth-order and eighth-order CCFDM methods are superior to the sixth-order and eighth-order SCFDM methods. Copyright c 2013 John Wiley & Sons, Ltd.
Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2013. , 27 p.
LiTH-MAT-R, ISSN 0348-2960 ; 9
Compact finite difference; High-order methods; Spherical shallow water equations; Numerical accuracy
IdentifiersURN: urn:nbn:se:liu:diva-96371ISRN: LiTH-MAT-R--2013/09--SEOAI: oai:DiVA.org:liu-96371DiVA: diva2:641060