Open Collections

A Simple Solver for Simulating Fluid-Structure Interactions in 2D

Banff International Research Station for Mathematical Innovation and Discovery

We propose a fully eulerian model for simulating the interaction of fluid-fluid and fluid-solid structures for incompressible fluids and a black-box type numerical scheme for computing its solution. The physical model consists of two Hamilton-Jacobi type PDEs: the fluid-fluid and fluid-solid interfaces are implicitly tracked by a level set equation, and the fluid motion is modeled by the vorticity formulation of Navier-Stokes equation, also of Hamilton-Jacobi type. This approach simplifies the task by allowing us to implement a single numerical scheme for solving both equations. We present the proposed scheme along with several numerical experiments simulating the coalescence of gas bubbles and the oscillations of an elastic membrane that demonstrate the simplicity and robustness of this approach.

Mathematics; Numerical analysis; Partial differential equations

video/mp4

Author affiliation: California State University-Northridge

2019-03-17

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/68829

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/