Squirmers are models of a class of microswimmers that self-propel in fluids without significant deformation of their body shape, such as ciliated organisms and phoretic particles. Available techniques for their simulation are based on the boundary element method and do not contemplate nonlinearities such as those arising from the inertia of the fluid or non-Newtonian rheology. This article describes a methodology to simulate squirmers that overcomes these limitations by using volumetric numerical methods, such as finite elements or finite volumes. It deals with interface conditions at the surface of the squirmer that generalize those in the published literature, which are generally restricted to the imposition of slip velocities. The actual procedures to be performed on a fluid solver to implement the proposed methodology are provided, including the treatment of metachronal surface waves. Among the several numerical examples, a two-dimensional simulation is shown of the hydrodynamic interaction of two individuals of Opalina ranarum.
A three dimensional parallel implementation of Multiscale Mixed Methods based on non-overlapping domain decomposition techniques is proposed for multi-core computers and its computational performance is assessed by means of numerical experimentation. As a prototypical method, from which many others can be derived, the Multiscale Robin Coupled Method is chosen and its implementation explained in detail. Numerical results for problems ranging from millions up to more than 2 billion computational cells in highly heterogeneous anisotropic rock formations based on the SPE10 benchmark are shown. The proposed implementation relies on direct solvers for both local problems and the interface coupling system. We find good weak and strong scalalability as compared against a state-of-the-art global fine grid solver based on Algebric Multigrid preconditioning in single and two-phase flow problems.
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