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
SN - 0021-9991
VL - 375
SP - 240
EP - 262
JO - Journal of Computational Physics
JF - Journal of Computational Physics
ER -