Unified momentum equation approach for fluid–structure interaction problems involving linear elastic structures

Abstract

In this article, we present a fully Eulerian monolithic numerical method for simulating fluid–structure interaction problems. This method is based on the unified momentum equation approach, where the elastodynamic equation for linear elastic solids and the incompressible Navier–Stokes equation are unified into a single velocity-based momentum equation that can be solved using a proper numerical method for computational fluid dynamics. The level set method combined with a displacement field extension procedure was employed to capture the moving interfaces. Owing to the formulation scheme applied to the unified momentum equation, both the velocity and stress fields are computed for both the structure and the fluid. Therefore, this method is capable of not only simulating the dynamic interactions of a fluid and structure, but also computing the stress fields in both phases. Three problems were simulated as test examples, a falling disk in a fluid, the oscillation of a flexible rod in a channel, and a bouncing ball, and the results obtained were found to be physically realistic and in good agreement with the published data.