A versatile sharp interface immersed boundary method for incompressible flows with complex boundaries

Abstract

A sharp interface immersed boundary method for simulating incompressible viscous flow past threedimensional immersed bodies is described. The method employs a multi-dimensional ghost-cell methodology to satisfy the boundary conditions on the immersed boundary and the method is designed to handle highly complex three-dimensional, stationary, moving and/or deforming bodies. The complex immersed surfaces are represented by grids consisting of unstructured triangular elements; while the flow is computed on non-uniform Cartesian grids. The paper describes the salient features of the methodology with special emphasis on the immersed boundary treatment for stationary and moving boundaries. Simulations of a number of canonical two-and three-dimensional flows are used to verify the accuracy and fidelity of the solver over a range of Reynolds numbers. Flow past suddenly accelerated bodies are used to validate the solver for moving boundary problems. Finally two cases inspired from biology with highly complex three-dimensional bodies are simulated in order to demonstrate the versatility of the method.

A Comparative Study on Evaluation Methods of Fluid Forces on Cartesian Grids

“…The forces evaluated by PS, MS1, MS2, and MS3 are shown in Figure 15. The result shows that the forces estimated by PS, MS2, and MS3 seem to converge to 1.09, which is consistent with the existing data obtained by the empirical relation derived from a number of experiments [15] and the numerical computations [7,16].…”

“…Note that the computation of both -and -derivatives requires quantities inside the solid region, in other words, in the ghost cells. For MS2, these quantities are estimated by the simplified version (avoiding recursive interpolation and extrapolation) of the ghost-cell method [7]. Concretely, the quantities in solid cells are computed by the fitting functions (see (6) and (7)) constructed in the normal probe approach illustrated in Figure 4(b):…”

“…For the PS, we have employed the ghost-cell approach described by Mittal et al [7]. For the MSs, we have tested three approaches that are often used in the studies of immersed boundary methods: a staircase approach, a ghost-cell approach, and a ghost-fluid approach, the details of which are described in Section 2.…”

A Lattice Boltzmann–Immersed Boundary method to simulate the fluid interaction with moving and slender flexible objects

“…Indeed an accurate prediction of the flow is dependent on capturing the fluid vorticity shed from the moving sharp tips of the plate, as well as the capability to deal with a one-dimensional object that behaves as a strip of finite thickness. We compare our results with the simulations performed by Mittal et al (2008), obtained by a direct-forcing method, and with the results of Koumoutsakos and Shiels (1996) who employed a vortex-particle method. The results obtained with our methodology are at a Reynolds number of Re h = U 0 h/ν = 1000, based on plate height.…”

Numerical Study on Hydrodynamic Performance of Bionic Caudal Fin

“…However, a large number of problems in biofluid dynamics involve interactions between deformable elastic bodies and incompressible viscous fluids. These fluid-structure interaction (FSI) problems involve the complicated interplay between a viscous fluid, deformable body, and free-moving boundary, making them difficult to discern [12][13][14][15][16][17][18][19][20][21][22][23].…”