On thin gaps between rigid bodies two-way coupled to incompressible flow

Abstract

Two-way solid fluid coupling techniques typically calculate fluid pressure forces that in turn drive the solid motion. However, when solids are in close proximity (e.g. touching or in contact), the fluid in the thin gap region between the solids is difficult to resolve with a background fluid grid. Although one might attempt to address this difficulty using an adaptive, body-fitted, or ALE fluid grid, the size of the fluid cells can shrink to zero as the bodies collide. The inability to apply pressure forces in a thin lubricated gap tends to make the solids stick together, since collision forces stop interpenetration but vanish when the solids are separating leaving the fluid pressure forces on the surface of the solid unbalanced in regards to the gap region. We address this problem by adding pressure degrees of freedom onto surfaces of rigid bodies, and subsequently using the resulting pressure forces to provide solid fluid coupling in the thin gap region. These pressure degrees of freedom readily resolve the tangential flow along the solid surface inside the gap and are two-way coupled to the pressure degrees of freedom on the grid allowing the fluid to freely flow into and out of the gap region. The two-way coupled system is formulated as a symmetric positive-definite matrix which is solved using the preconditioned conjugate gradient method. Additionally, we provide a mechanism for advecting tangential velocities on solid surfaces in the gap region by extending semi-Lagrangian advection onto a curved surface mesh where a codimension-one velocity field tangential to the surface is defined. We demonstrate the convergence of our method on a number of examples, such as underwater rigid body separation and collision in both two and three spatial dimensions where typical methods do not converge. Finally, we demonstrate that our method not only works for the aforementioned "wet" contact, but also works in conjunction with "dry" contact where there is no fluid in the gap between the solids.

Preserving geometry and topology for fluid flows with thin obstacles and narrow gaps

“…Voxelization also leads the solid boundary velocity constraints to be applied at grid face centres rather than on the actual boundary itself. FEDKIW, 2015) proposed a two-way rigid-body-fluid coupling scheme that extends the voxelized approach to thin gaps using lower-dimensional advection and extra degrees of freedom, though it does not consider thin objects.…”

An adaptive discretization of compressible flow using a multitude of moving Cartesian grids

“…Each row ofĴ corresponds to one Voronoi face and is constructed by clipping surface triangles of nearby solids into the dual cell of the Voronoi face, computing weights as the orthogonally projected areas of the subpolygons resulting from clipping, normalizing weights, and assigning weights to related surface particles. We refer readers to [58] for a detailed description of this process. For rigid bodies, each row ofĴ is constructed by computing weights using the same method as was used for deformable bodies except that weights are assigned to rigid bodies instead of surface particles.…”

“…Here we briefly comment on our efforts to extend the gap flow formulation of [58] from incompressible flow to compressbile flow as well as from a single static grid to Chimera grids. We carried out a number of numerical tests in two and three spatial dimensions similar to those in [58].…”

“…We carried out a number of numerical tests in two and three spatial dimensions similar to those in [58]. Our two-way coupled gap flow solver passed all such tests for arbitrarily large fluid pressures, various overlapping fluid grids, various solid meshes, and various spatial configurations and geometries of rigid bodies.…”

“…We also demonstrate convergence for examples that two-way couple compressible flow with rigid and deformable solids where finer grids follow the motion of the solids. Furthermore, in the appendix, we briefly comment on our efforts to extend the method of [58] to handle compressible gap flow.…”