A linearly implicit energy-stable scheme for critical dissipative surface quasi-geostrophic flows

Abstract

In this paper, we propose an effective linearly implicit unconditional energy-stable scheme for surface quasi-geostrophic flows based on the scalar auxiliary variable approach and the Fourier spectral Galerkin method. Compared with traditional numerical methods, our scheme has constant coefficient matrices at each time step, and the numerical solutions are consistent with the dissipation laws for modified energy. By treating linear terms implicitly and nonlinear terms explicitly, we derive the dissipation laws for discrete modified surface kinetic energy and Hamiltonian. To reduce the aliasing error induced by the Fourier spectral Galerkin method, we implement a 2/3 de-aliasing technique for the nonlinear terms. Furthermore, the integration concerning energy in our numerical scheme is exact due to the Fourier spectral Galerkin method. Numerical experiments are presented to verify the stability and efficiency of the proposed scheme.