On the discretized delta function and force calculation in the immersed boundary method

Signed distance field enhanced fully resolved CFD-DEM for simulation of granular flows involving multiphase fluids and irregularly shaped particles

On the application of immersed boundary, fictitious domain and body-conformal mesh methods to many particle multiphase flows

Implicit heat flux correction-based immersed boundary-finite volume method for thermal flows with Neumann boundary conditions

We present a 2D high‐order and easily accessible immersed‐boundary adaptive harmonic polynomial cell (IB‐AHPC) method to solve fully nonlinear wave‐structure interaction problems in marine hydrodynamics using potential‐flow theory. To reduce the total number of cells without losing accuracy, adaptive quad‐tree cell refinements are employed close to the free‐surface and structure boundaries. The present method is simpler to implement than the existing IB‐HPC alternatives, in that it uses standard square cells both in the fluid domain and at the boundaries, thus without having to use the more complex and expensive overlapping grids or irregular cells. The spurious force oscillations on moving structures, which is a known issue for immersed boundary methods (IBMs), are eliminated in this study by solving a separate boundary value problem (BVP) for a Lagrangian acceleration potential. We also demonstrate that solving a similar BVP for the corresponding Eulerian acceleration potential is far less satisfactory due to the involved second derivatives of the velocity potential in the body‐boundary condition, which are very difficult to calculate accurately in an IBM‐based approach. In addition, we present, perhaps for the first time since the HPC method was developed, a linear matrix‐based stability analysis for the time‐domain IB‐AHPC method. The stability analysis is also used in this study as a general guide to design robust and stable numerical algorithms, in particular related to the treatment of boundary conditions close to the intersection between a Dirichlet and a Neumann boundary, which is essential in time‐domain wave‐structure interaction analyses using IBMs. We confirm theoretically through the stability analysis that square cells have the best stability properties. The present method has been verified and validated satisfactorily by various cases in marine hydrodynamics, including a moving structure in an infinite fluid, fully nonlinear wave generation and propagation, and fully nonlinear diffraction and radiation of a ship cross section.

An immersed boundary method is improved and applied to 2-D flow fields involving a single stationary/moving object. The present immersed boundary method employs a body force proportional to a solid volume fraction for coupling the solid and fluid motions at the interface. A hyperbolic-tangent function is newly introduced as a surface digitiser for computing the volume fractions at the interface cells, and this improvement is proved to be efficient for problems involving arbitrary shape object. The present method is applied to a uniform flow field around a circular cylinder and an interaction problem of fluid and free-falling object. The computational results are found to agree with the results by the different methods of the present authors and the results reported in the literatures. Also the computation time is considerably cut down compared to the other methods by the series of improvements to the immersed boundary method.

In this paper, we propose an implicit Eulerian–Lagrangian model to resolve the fluid–structure interaction of submerged nets. The Reynolds-averaged Navier–Stokes equations are solved on an Eulerian grid using OpenFOAM and the geometry of the flexible net structures is tracked using Lagrangian points. The motion and deformation of the flexible net structures are advanced using an implicit scheme to avoid excessively small time intervals. The force acting on the net structures is calculated based on a mass–spring system. The screen model and the immersed boundary method are implemented to capture the interaction between the net structures and the surrounding fluid. We present a new drag coefficient formulation as based on a piecewise function for different net solidities to obtain a much improved drag force prediction. The numerical results are compared with a series of existing experiments showing excellent agreement and improved drag force predictions.

The present work proposes the application of a computational methodology based on the coupling of the Fourier Pseudospectral Method (FPSM) and the Immersed Boundary Method (IBM) for conducting flow simulations over slender airfoils. This methodology, termed IMERSPEC, leverages the benefits of both high accuracy and low computational cost inherent in pseudospectral methods, thanks to the utilization of the Fast Fourier Transform algorithm. IBM is employed to impose non-periodic boundary conditions in the Navier–Stokes equations, addressing the requirement of periodicity at boundaries for FPSM convergence and to accurately represent the immersed slender airfoil in the flow. The aerodynamic behavior of the analyzed profiles was assessed by calculating lift and drag coefficients, which were then compared with existing literature results. Consistently favorable outcomes were observed, particularly in flows at lower Reynolds numbers, demonstrating the effectiveness of the IMERSPEC methodology for simulating complex flows computationally. Additionally, weight functions, fundamental to IBM, are employed flexibly for aerodynamic force calculations. Specifically, within the same simulation, a Cubic function is utilized for drag calculation while a Hat function is employed for lift calculation, yielding results more closely aligned with the literature’s findings. This approach offers an alternative to previously proposed methods for IBM implementation.

Aeroelastic study of flexible flapping wings by a coupled lattice Boltzmann-finite element approach with immersed boundary method

A fast moving least squares approximation with adaptive Lagrangian mesh refinement for large scale immersed boundary simulations

Numerical modelling of hook and claw-type vacuum pump performance based on cut cell Cartesian method

Computational fluid dynamics (CFD) are at the forefront of computational mechanics in requiring large-scale computational resources associated with high performance computing (HPC). Many flows of practical interest also include moving and deforming boundaries. High fidelity computations of fluid-structure interactions (FSI) are amongst the most challenging problems in computational mechanics. Additionally, many FSI applications have different resolution requirements in different parts of the domain and therefore requirement adaptive mesh refinement (AMR) for computational efficiency. FLASH is a well established AMR code with an existing Lagrangian framework which could be augmented and exploited to implement an immersed boundary method for simulating fluid-structure interactions atop an existing infrastructure. This paper describes the augmentations to the Lagrangian framework, and the new parallel algorithms added to the FLASH infrastructure that enabled the implementation of immersed boundary method in FLASH. The paper also presents scaling behavior and performance analysis of the implementations.

Continuity constrained least-squares interpolation for SFO suppression in immersed boundary methods

A resolved CFDEM algorithm based on the immersed boundary for the simulation of fluid-solid interaction

An immersed boundary-lattice Boltzmann method is developed for fluid-structure interactions involving non-Newtonian fluids (e.g., power-law fluid). In this method, the flexible structure (e.g., capsule) dynamics and the fluid dynamics are coupled by using the immersed boundary method. The incompressible viscous power-law fluid motion is obtained by solving the lattice Boltzmann equation. The non-Newtonian rheology is achieved by using a shear rate-dependant relaxation time in the lattice Boltzmann method. The non-Newtonian flow solver is then validated by considering a power-law flow in a straight channel which is one of the benchmark problems to validate an in-house solver. The numerical results present a good agreement with the analytical solutions for various values of power-law index. Finally, we apply this method to study the deformation of a capsule in a power-law shear flow by varying the Reynolds number from 0.025 to 0.1, dimensionless shear rate from 0.004 to 0.1, and power-law index from 0.2 to 1.8. It is found that the deformation of the capsule increases with the power-law index for different Reynolds numbers and nondimensional shear rates. In addition, the Reynolds number does not have significant effect on the capsule deformation in the flow regime considered. Moreover, the power-law index effect is stronger for larger dimensionless shear rate compared to smaller values.

The ground effect of a hovering dragonfly was investigated through numerical simulations of both two-dimensional and three-dimensional dragonfly wings. An immersed boundary method, enhanced with a prediction-correction multi-direct forcing scheme and a smoothed discrete delta function, was employed. The inverse distance weighting interpolation was introduced to address the interpolation on a refined mesh. For two-dimensional simulation, the ground effect was divided into three regions: force enhancement, force reduction, and force recovery region. Various mechanisms, such as early or delayed vortex shedding, wall extrusion, vortex integration, and reattachment, were observed. Additionally, the vortex remained near the ground, altering the velocity difference between the wing and surrounding fluid through induced velocity. This led to a significant change in pressure on the windward side. A hysteresis phenomenon was discovered: in the force enhancement region, vertical force coefficient peaked at a later time. For three-dimensional simulation, the presence of ground resulted in a decrease in time-average vertical force coefficient. Additionally, the magnitude of this reduction diminished as the distance between the wing and ground increased. The influence of ground was primarily reflected in the more rapid growth of the vertical force coefficient during the initial stage of the downstroke, the magnitudes of its peak and trough values. These changes were attributed to alterations in the strength and state of the vortex near the wing, along with the induced effect of the rebounded vortex. It is more obvious during the downstroke that the downward velocity of the flow was enhanced, which causes the reduction of the relative inflow velocity to the wing.