ADirect-Forcing Immersed Boundary Projection Method for Thermal Fluid-Solid Interaction Problems

In this paper,we develop a direct-forcing immersed boundary projection method for simulating the dynamics in thermal fluid-solid interaction problems.The underlying idea of the method is that we treat the solid as made of fluid and introduce two virtual forcing terms.First,a virtual fluid force distributed only on the solid region is appended to the momentum equation to make the region behave like a real solid body and satisfy the prescribed velocity.Second,a virtual heat source located inside the solid region near the boundary is added to the energy transport equation to impose the thermal boundary condition on the solid boundary.We take the implicit second-order backward differentiation to discretize the time variable and employ the Choi-Moin projection scheme to split the coupled system.As for spatial discretization,second-order centered differences over a staggered Cartesian grid are used on the entire domain.The advantages of this method are its conceptual simplicity and ease of implementation.Numerical experiments are performed to demonstrate the high performance of the proposed method.Convergence tests show that the spatial convergence rates of all unknowns seem to be super-linear in the 1-norm and 2-norm while less than linear in the maximum norm.

Combination of direct-forcing fictitious domain method and sharp interface method for dielectrophoresis of particles

In this paper, we combine the direct-forcing fictitious domain （DF/FD） method and the sharp interface method to resolve the problem of particle dielectrophoresis in two dimensions. The flow field and the motion of particles are solved with the DF/FD method, the electric field is solved with the sharp inter- face method, and the electrostatic force on the particles is computed using the Maxwell stress tensor method. The proposed method is validated via three problems： effective conductivity of particle compos- ite between two planar plates, cell trapping in a channel, and motion of particles due to both conventional and traveling wave dielectrophoretic forces.

A LB-DF/FD Method for Particle Suspensions

In this paper, we propose a lattice Boltzmann (LB) method coupled with adirect-forcing fictitious domain (DF/FD) method for the simulation of particle suspensions. This method combines the good features of the LB and the DF/FD methodsby using two unrelated meshes, namely, an Eulerian mesh for the flow domain and aLagrangian mesh for the solid domain, which avoids the re-meshing procedure anddoes not need to calculate the hydrodynamic forces at each time step. The non-slipboundary condition is enforced by introducing a forcing term into the lattice Boltzmann equation, which preserves all remarkable advantages of the LBM in simulatingfluid flows. The present LB-DF/FD method has been validated by comparing its results with analytical results and previous numerical results for a single circular particleand two circular particles settling under gravity. The interaction between particle andwall, the process of drafting-kissing-tumbling (DKT) of two settling particles will bedemonstrated. As a manifestation of the efficiency of the present method, the settlingof a large number (128) of circular particles is simulated in an enclosure.

Hydrodynamics characterization of a choanoid fluidized bed bioreactor used in the bioartificial liver system： Fully resolved simulation with a fctitious domain method

Choanoid fluidized bed bioreactors （CFBBs） are newly developed core devices used in bioartificial liver- support systems to detoxify blood plasma of patients with microencapsulated liver cells. Direct numerical simulations （DNS） with a direct-forcing/fictitious domain （DF/FD） method were conducted to study the hydrodynamic performance of a CFBB. The effects of particle-fluid density ratio, particle number, and fil- ter screens preventing particles flowing out of the reactor were investigated. Depending on density ratio, two flow patterns are evident： the circulation mode in which the suspension rises along one sidewall and descends along the other sidewall, and the non-circulation mode in which the whole suspension roughly flows upward. The circulation mode takes place under non-neutral-buoyancy where the particle sedimentation dominates, whereas the non-circulation mode occurs under pure or near-neutral buoy- ancy with particle-fluid density ratios of unity or near unity. With particle-fluid density ratio of 1.01, the bioartificial liver reactor performs optimally as the significant particle accumulation existing in the non-circulation mode and the large shear forces on particles in the circulation mode are avoided. At higher particle volume fractions, more particles accumulate at the filter screens and a secondary counter circulation to the primary flow is observed at the top of the bed. Modelled as porous media, the filter screens play a negative role on particle fluidization velocities; without screens, particles are fluidized faster because of the higher fluid velocities in the jet center region. This work extends the DF/FD-based DNS to a fluidized bed and accounts for effects from inclined side walls and porous media, providing some hydrodynamics insight that is important for CFBB design and operation optimization.