Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6928890 | Journal of Computational Physics | 2018 | 22 Pages |
Abstract
We consider a class of tumor growth models under the combined effects of density-dependent pressure and cell multiplication, with a free boundary model as its singular limit when the pressure-density relationship becomes highly nonlinear. In particular, the constitutive law connecting pressure p and density Ï is p(Ï)=mmâ1Ïmâ1, and when mâ«1, the cell density Ï may evolve its support according to a pressure-driven geometric motion with sharp interface along its boundary. The nonlinearity and degeneracy in the diffusion bring great challenges in numerical simulations. Prior to the present paper, there is lack of standard mechanism to numerically capture the front propagation speed as mâ«1. In this paper, we develop a numerical scheme based on a novel prediction-correction reformulation that can accurately approximate the front propagation even when the nonlinearity is extremely strong. We show that the semi-discrete scheme naturally connects to the free boundary limit equation as mââ. With proper spatial discretization, the fully discrete scheme has improved stability, preserves positivity, and can be implemented without nonlinear solvers. Finally, extensive numerical examples in both one and two dimensions are provided to verify the claimed properties in various applications.
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science Applications
Authors
Jian-Guo Liu, Min Tang, Li Wang, Zhennan Zhou,