An immersed boundary method based on discrete stream function formulation for two- and three-dimensional incompressible flows

Abstract

a b s t r a c tAn immersed boundary method is proposed in the framework of discrete stream function formulation for incompressible flows. In order to impose the non-slip boundary condition, the forcing term is determined implicitly by solving a linear system. The number of unknowns of the linear system is the same as that of the Lagrangian points representing the body surface. Thus the extra cost in force calculation is negligible if compared with that in the basic flow solver. In order to handle three-dimensional flows at moderate Reynolds numbers, a parallelized flow solver based on the present method is developed using the domain decomposition strategy. To verify the accuracy of the immersed-boundary method proposed in this work, flow problems of different complexity (decaying vortices, flows over stationary and oscillating cylinders and a stationary sphere, and flow over low-aspect-ratio flat-plate) are simulated and the results are in good agreement with the experimental or computational data in previously published literatures.

Numerical Simulation of a Three-Dimensional Fish-like Body Swimming with Finlets

“…The direct forcing IB method is used to enforce the non-slip boundary condition on the complex surface of the fish. For the technical details of this numerical methodology and some benchmark validations, please refer to [20].…”

Underlying principle of efficient propulsion in flexible plunging foils

“…Extensive validations of the immersed boundary solver can be found in Ref. [14] (on flows past rigid objects) and [15] (on FSI problems). For the simulations of this work, a rectangular computational domain of size 20L × 12L used, with the grid width being 0.02L.…”

Numerical study on hydrodynamic effect of flexibility in a self-propelled plunging foil

“…More specifically, we use a variant of the direct-forcing immersed boundary methods which is based on the discrete stream function formulation for incompressible Navier-Stokes equations [40].…”

“…where d is the regularized delta function (in this work, a 3-point regularized delta function is used [40]); U b is the desired velocity at the Lagrangian points. If the motion of the immersed body is prescribed, U b is known beforehand; while for FSI problems, U b is a priori unknown and must be obtained by solving the structural equation.…”

“…For the details of the numerical method, including the determination of forcing term FðX; tÞ, spatial discretization and time advancing scheme, please refer to [40]. Systematic validations of the flow solver on flows over stationary and moving obstacles can also be found in [40], e.g., flows past a circular cylinder (at Re = 40, 100, 200), an in-line oscillating cylinder in fluid at rest, and flow past a three-dimensional low-aspect-ratio flat-plate of zero-thickness (at Re = 100). The predictions of lift, drag or velocity profiles were in excellent agreement with those from other literature.…”