TY - JOUR

T1 - A mixed mimetic spectral element model of the rotating shallow water equations on the cubed sphere

AU - Lee, D.

AU - Palha, A.

PY - 2018/12/15

Y1 - 2018/12/15

N2 - In a previous article [J. Comp. Phys. 357 (2018) 282–304] [4], the mixed mimetic spectral element method was used to solve the rotating shallow water equations in an idealized geometry. Here the method is extended to a smoothly varying, non-affine, cubed sphere geometry. The differential operators are encoded topologically via incidence matrices due to the use of spectral element edge functions to construct tensor product solution spaces in H(rot), H(div) and L2. These incidence matrices commute with respect to the metric terms in order to ensure that the mimetic properties are preserved independent of the geometry. This ensures conservation of mass, vorticity and energy for the rotating shallow water equations using inexact quadrature on the cubed sphere. The spectral convergence of errors are similarly preserved on the cubed sphere, with the generalized Piola transformation used to construct the metric terms for the physical field quantities.

AB - In a previous article [J. Comp. Phys. 357 (2018) 282–304] [4], the mixed mimetic spectral element method was used to solve the rotating shallow water equations in an idealized geometry. Here the method is extended to a smoothly varying, non-affine, cubed sphere geometry. The differential operators are encoded topologically via incidence matrices due to the use of spectral element edge functions to construct tensor product solution spaces in H(rot), H(div) and L2. These incidence matrices commute with respect to the metric terms in order to ensure that the mimetic properties are preserved independent of the geometry. This ensures conservation of mass, vorticity and energy for the rotating shallow water equations using inexact quadrature on the cubed sphere. The spectral convergence of errors are similarly preserved on the cubed sphere, with the generalized Piola transformation used to construct the metric terms for the physical field quantities.

KW - Cubed sphere

KW - Mimetic

KW - Shallow water

KW - Spectral convergence

UR - http://www.scopus.com/inward/record.url?scp=85052734016&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2018.08.042

DO - 10.1016/j.jcp.2018.08.042

M3 - Article

AN - SCOPUS:85052734016

VL - 375

SP - 240

EP - 262

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

ER -