Abstract

A new multi-moment global shallow water model on the cubed sphere is proposed by adopting a two-stage fourth-order Runge-Kutta time integration. Through calculating the values of predicted variables at half time step t=tn+12Δt by a second-order formulation, a fourth-order scheme can be derived using only two stages within one time step. This time integration method is implemented in our multi-moment global shallow water model proposed in Chen and Xiao (2008) to build and validate a new and more efficient numerical integration framework for dynamical cores. As the key task, the numerical formulation for evaluating the derivatives in time has been developed through the Cauchy-Kowalewski procedure and the spatial discretization of the multi-moment finite volume method, which ensures fourth-order accuracy in both time and space. Several major benchmark tests are used to verify the proposed numerical framework in comparison with the existing four-stage fourth-order Runge-Kutta method which is based on the method of lines framework. The two-stage fourth-order scheme saves about 30% computational cost in comparison with the four-stage Runge-Kutta scheme for global advection and shallow water models. The proposed two-stage fourth-order framework offers a new option to develop high-performance time marching strategy of practical significance in dynamical cores for atmospheric and oceanic models.

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