Abstract

We develop an energy-stable scheme for simulating fluid-particle interaction problems governed by a coupled system consisting of the incompressible Navier-Stokes (NS) equations defined in a time-dependent fluid domain and Newton's second law for particle motion. A modified temporary arbitrary Lagrangian-Eulerian (tALE) method is designed based on a bijective mapping between the fluid regions at different time steps. In the proposed numerical scheme, the tALE mesh velocity, the incompressible NS equations, and Newton's second law are solved simultaneously. We prove that under certain conditions, the new time discretization scheme satisfies an energy law. For the space discretization, the extended finite element method (XFEM) is used to solve the problem on a fixed Cartesian mesh. The developed method is first-order accurate in time and space without being momentum conservative. To verify the accuracy and stability of our numerical scheme, we present numerical experiments including the fitting of the Jeffery orbit by rotating of an ellipse and the free-falling of an elliptic particle in water.

Full Text
Paper version not known

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.