Session F26: Computational Fluid Dynamics: Immersed Boundary Methods I

Approaching the efficiency of stationary-body methods in a strongly coupled immersed boundary framework for fluid-structure interaction

Strongly coupled immersed boundary (IB) methods strictly enforce the no-slip constraint on the body by solving the nonlinear fluid and structural equations of motion simultaneously. Handling this constraint requires solving several large dimensional systems that scale by the number of grid points in the flow domain even though the nonlinear constraints only scale by the small number of points used to represent the fluid-structure interface. In this talk, we will address the computational bottleneck of such strongly coupled IB methods wherein several costly large dimensional systems are solved for a small number of body variables. Our proposed approach is motivated by the efficient strategy employed in stationary-body IB methods---we precompute a matrix that encapsulates the large dimensional system so that the prohibitive large scale operations need not be performed at every time step. This precomputation process yields a small-dimensional system for the constraint equations which can solved at minimal computational cost while time advancing the equations. We also present a parallel implementation that scales favorably across multiple processors. The accuracy, computational efficiency and scalability of our approach are demonstrated on several two dimensional flow problems.   

A novel level-set-based immersed boundary method for simulating complex 3D fish-like swimming

The immersed boundary method (IBM) has been extensively applied to the modeling and simulation of three-dimensional fish-like swimming. The high Reynolds number, complex body morphology, or large computational domain often cause the immersed boundary reconstruction costly and introduce numerical difficulties during simulations. The level set (LS) method and adaptive mesh refinement (AMR) method partially solved the aforementioned problems, however, the high computational cost for immersed boundaries reconstruction in 3D fish-like swimming is still a problem, especially for a fish with a high Reynolds number and complex geometry, and fish school swimming. For example, even though, with the AMR technique, the computational load of simulation for fish school swimming has been distributed into separate nodes, the immersed boundary reconstruction in the AMR blocks with the finest mesh or the larger AMR blocks encompassing all fish bodies could also greatly increase the computational cost for the simulation. Thus, in this work, a narrow-band level-set-based immersed boundary method (NBLS-IBM) has been developed to improve the efficiency of simulating complex 3D fish-like swimming including shark-like body swimming and fish school swimming. This novel level-set-based immersed boundary method reduces the computational cost for boundary reconstruction from O(n³) to O(kn²).   

An Immersed Boundary Method for Compressible Viscous Flow with Heat Flux and Shear Stress Conditions

A new immersed boundary method for compressible viscous flow based on Peskin's approach is discussed. 

Arbitrary geometry is represented by boundary markers with two types of singular sources: (i) the usual Dirichlet-type sources and (ii) additional Neumann-type sources to incorporate heat flux and shear stress conditions. The formulation is applicable to regular geometries with finite thickness or extent as well as to infinitely thin surface-like geometries (in three-dimensional space). The added singular sources that modify the original Navier-Stokes equations are rigorously related to the jumps of flow variables. The strength of the added singular sources can be solved exactly from the provided boundary conditions under the framework of differential-algebraic equations with the half-explicit Runge-Kutta method without introducing additional stiffness into the system. This includes the Neumann case with two different values of the shear stress or heat flux across an infinitely thin surface. Accuracy is demonstrated analytically and numerically. Two- and three-dimensional examples are carried out to demonstrate convergence. The results are compared with previous numerical and experimental studies and analytical solutions.    

A subcycling/non-subcycling time advancement scheme-based sharp-interface immersed boundary method framework for solving fluid-structure interaction problems on dynamically adaptive grids

We present a fully Eulerian sharp-interface immersed boundary method to simulate fluid-structure interaction problems. The governing equations are solved using a finite-volume scheme on the blocked structured adaptive grids with both the subcycling and non-subcycling methods. A force-averaging technique is constructed to achieve excellent momentum conservation across the multiple levels of grid hierarchy. The geometry of the solid structure is described using a re-initialized level-set function, with which a novel local reconstruction of the solution near the immersed boundary is obtained based on the geometric information. Several numerical tests are presented to validate the accuracy and efficiency of the computational framework.   

Large-eddy simulation of a subaqueous cylindrical pendulum

The motion of pendulums has been long studied. As one of the first pioneers, Galileo Galilei found that the period of a pendulum is constant. This work regards the numerical study of subaqueous pendulums which are not fully understood yet, owing to the formation and, subsequently, dissipation of rich vortical flow structures around the pendulum geometry. Numerical simulations are done using large-eddy simulation (LES) to explore the evolution of the vortical structures and overall flow dynamics of the pendulum motion.

Recently, Mathai et al. (J. Fluid Mech., 2019) reported 2D PIV measurements of cylindrical pendulums in a water tank. We have investigated the 3D flow field around the cylinder by simulating the fluid-structure interaction (FSI) of the pendulums in the context of an immersed boundary model.

We employed the experimental data of Mathai et al. and Mongelli and Battista (Fluids, 2020) to validate our LES results for the angular velocity and the generated torque of the pendulums. The simulation results were used to elucidate the three-dimensional vortex dynamics of the flow around the subaqueous pendulum. Furthermore, we compared the effect of the wake correction proposed by Mathai et al. (2019) on the computed drag forces.