A full Eulerian finite difference approach for solving fluid-structure coupling problems

TL;DR

This paper introduces a comprehensive Eulerian finite difference method for fluid-structure interaction problems, utilizing a fixed grid and volume-of-fluid approach to accurately simulate complex multiphase and deformable solid interactions.

Contribution

It presents a novel full Eulerian simulation framework combining finite difference and volume-of-fluid techniques for fluid-structure coupling on a fixed grid.

Findings

Validated the method through various tests.

Demonstrated numerical accuracy in fluid-structure problems.

Successfully simulated nonlinear Mooney-Rivlin materials.

Abstract

A new simulation method for solving fluid-structure coupling problems has been developed. All the basic equations are numerically solved on a fixed Cartesian grid using a finite difference scheme. A volume-of-fluid formulation (Hirt and Nichols (1981, J. Comput. Phys., 39, 201)), which has been widely used for multiphase flow simulations, is applied to describing the multi-component geometry. The temporal change in the solid deformation is described in the Eulerian frame by updating a left Cauchy-Green deformation tensor, which is used to express constitutive equations for nonlinear Mooney-Rivlin materials. In this paper, various verifications and validations of the present full Eulerian method, which solves the fluid and solid motions on a fixed grid, are demonstrated, and the numerical accuracy involved in the fluid-structure coupling problems is examined.