Numerical method and analysis for fluid-structure model on unbounded domains

Abstract

Numerically solving the fluid-structure model on unbounded domains poses a challenge, due to the unbounded nature of the physical domain. To overcome this challenge, the artificial boundary method is specifically applied to numerically solve the fluid-structure model on unbounded domains, which can be used to analyze fluid-structure interactions in various scientific and engineering fields. Drawing inspiration from the artificial boundary method, we employ artificial boundaries to truncate the unbounded domain, subsequently designing the high order local artificial boundary conditions thereon based on the Padé approximation. Then, the initial value problem on the unbounded domain is reduced into an initial boundary value problem on the computational domain, which can be efficiently solved by adopting the finite difference method. Furthermore, a series of auxiliary variables is introduced specifically to address the issue of mixed derivatives arising in the artificial boundary conditions, and the stability, convergence and solvability of the reduced problem are rigorously analyzed. Numerical experiments are reported to demonstrate the effectiveness of artificial boundary conditions and theoretical analysis.