A stable fluid-structure-interaction solver for low-density rigid particles using the immersed boundary projection method
(English)Manuscript (preprint) (Other academic)
Dispersion of particles with complex geometries and very low or close to unity density ratios are ubiquitous in both natural and industrial environments. We show that while explicit methods for coupling the incompressible Navier-Stokes equations and Newton's equations of motion are often sufficient to solve for motion of cylindrical and spherical particles with low density ratios, for more complex particles they become unstable. For example, the critical density ratio, for which numerical method becomes unstable, is significantly increased for an explicit coupling, compared to implicit coupling, in simulations of the flow around cylinder with a splitter plate. We present an implicit formulation of the coupling between rigid body dynamics and fluid dynamics within the framework of the immersed boundary projection method. In addition to the Navier-Stokes equations, we solve Newton's equations of motion for a rigid body. In a similar manner to previous work on the immersed boundary projection method, the resulting matrix equation in the present approach is solved using a block-LU decomposition. Each step of the block-LU decomposition is modified to incorporate the rigid body dynamics. We ensure that our method preserve the efficiency and second-order accuracy in space and third-order accuracy in time of the original method, only with small additional computational cost. We find that implicit coupling yields stable solution for density ratios as low as .
Immersed boundary method, Newton's equations of motion, Implicit coupling, Numerical stability, Low density ratios, Complex particles
IdentifiersURN: urn:nbn:se:kth:diva-158316OAI: oai:DiVA.org:kth-158316DiVA: diva2:776156
FunderSwedish Research Council, VR-2010-3910
QS 20152015-01-072015-01-072015-01-19Bibliographically approved