A Moving-Least-Square Immersed Boundary Method for Rigid and Deformable Boundaries in Viscous Flow (Communications in Computational Physics, 2017)
We present a moving-least-square immersed boundary method for solvingviscous incompressible flow involving deformable and rigid boundaries on a uniformCartesian grid. For rigid boundaries, no-slip conditions at the rigid interfaces are enforcedusing the immersed-boundary direct-forcing method. We propose a reconstructionapproach that utilizes moving least squares (MLS) method to reconstruct the velocityat the forcing points in the vicinity of the rigid boundaries. For deformableboundaries, MLS method is employed to construct the interpolation and distributionoperators for the immersed boundary points in the vicinity of the rigid boundariesinstead of using discrete delta functions. The MLS approach allows us to avoid distributingthe Lagrangian forces into the solid domains as well as to avoid using thevelocity of points inside the solid domains to compute the velocity of the deformableboundaries. The present numerical technique has been validated by several examplesincluding a Poiseuille flow in a tube, deformations of elastic capsules in shear flow anddynamics of red-blood cell in microfluidic devices.