High-Order Multirate Explicit Time-Stepping Schemes for the Baroclinic-Barotropic Split Dynamics in Primitive Equations

by   Rihui Lan, et al.

In order to treat the multiple time scales of ocean dynamics in an efficient manner, the baroclinic-barotropic splitting technique has been widely used for solving the primitive equations for ocean modeling. In this paper, we propose second and third-order multirate explicit time-stepping schemes for such split systems based on the strong stability-preserving Runge-Kutta (SSPRK) framework. Our method allows for a large time step to be used for advancing the three-dimensional (slow) baroclinic mode and a small time step for the two-dimensional (fast) barotropic mode, so that each of the two mode solves only need satisfy their respective CFL condition to maintain numerical stability. It is well known that the SSPRK method achieves high-order temporal accuracy by utilizing a convex combination of forward-Euler steps. At each time step of our method, the baroclinic velocity is first computed by using the SSPRK scheme to advance the baroclinic-barotropic system with the large time step, then the barotropic velocity is specially corrected by using the same SSPRK scheme with the small time step to advance the barotropic subsystem with a barotropic forcing interpolated based on values from the preceding baroclinic solves. Finally, the fluid thickness and the sea surface height perturbation is updated by coupling the predicted baroclinic and barotropic velocities. Temporal truncation error analyses are also carried out for the proposed schemes. Two benchmark tests drawn from the -MPAS-Ocean" platform are used to numerically demonstrate the accuracy and parallel performance of the proposed schemes.



There are no comments yet.


page 18

page 19

page 21

page 22


Stability and error analysis of IMEX SAV schemes for the magneto-hydrodynamic equations

We construct and analyze first- and second-order implicit-explicit (IMEX...

Adaptive PCA for Time-Varying Data

In this paper, we present an online adaptive PCA algorithm that is able ...

Exponential Time Differencing for the Tracer Equations Appearing in Primitive Equation Ocean Models

The tracer equations are part of the primitive equations used in ocean m...

Exact targeting of Gibbs distributions using velocity-jump processes

This work introduces and studies a new family of velocity jump Markov pr...

Study of instability of the Fourier split-step method for the massive Gross–Neveu model

Stability properties of the well-known Fourier split-step method used to...

Positivity-preserving finite difference WENO scheme for Ten-Moment equations with source term

We develop a positivity-preserving finite difference WENO scheme for the...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.