Second‐order scalar auxiliary variable Fourier‐spectral method for a liquid thin film coarsening model

Abstract

In this paper, we propose and analyze a second‐order accurate (in time) numerical scheme for the droplet liquid film coarsening model by using the scalar auxiliary variable (SAV) method, and the Fourier‐spectral method is used in space. The scheme is linear; thus, it could be solved very efficiently. Meanwhile, due to the application of SAV approach, the unconditional energy stability of the numerical scheme is also derived, without any restriction on the time step size. In addition, we also provide a rigorous error estimate that shows that our second‐order numerical scheme with Fourier‐spectral method in space converges with order , where and are time and space step sizes, respectively. Finally, a few numerical experiments are performed, which confirms the efficiency and accuracy of the proposed scheme, including the tests of the convergence, the mass conservation and the decrease of the energy. The simulation of coarsening process with time is also observed.