SAV Fourier-spectral method for diffuse-interface tumor-growth model

The tumor-growth model, proposed by Oden et al., is a coupling system with high nonlinearity for the surface effects of the diffusion interface. In this paper, scalar auxiliary variable (SAV) method is introduced to handle nonlinear term in gradient flow. At the same time, semi-implicit difference scheme is adopted to discretize the time variable. To approximate the spatial variable, Fourier-spectral method for the first time is employed for the tumor-growth model whose merit is that high precision solution can be obtained without handling too many terms. Generally speaking, an efficient and robust energy stabilization scheme is constructed. It inherits the properties of energy dissipation and mass conservation related to continuous problems. The validity of our proposed numerical scheme is demonstrated by conducting some numerical experiments.