Implementation of a Semi-implicit Time Integration Scheme in Non-Hydrostatic Euler Equations

[摘要] A semi-implicit time integration scheme is implemented in a non-hydrostatic Euler problem on the cubed-sphere grid. The semi-implicit time integration scheme is a 3-stage additive RungeKutta method, which is an Implicit-Explicit (IMEX) multi-stage single-step scheme. The system treats acoustic and gravity waves implicitly and advection explicitly. In the implicit part, we compute the linear system by defining a proper linear operator. Then, the numerical results are presented to compare the semi-implicit time integration scheme with the explicit RungeKutta time integration scheme in non-hydrostatic Euler equations. In terms of accuracy, we demonstrate that the proposed method performs better than other schemes.

[关键词] Semi-implicit time integration scheme;Additive Runge- Kutta method (ARK);Explicit Runge-Kutta method;Cubed-sphere grid;Non-hydrostatic Euler equations