An adaptive harmonic polynomial cell method with immersed boundaries: Accuracy, stability, and applications

Numerical analysis on the generation, propagation and interaction of solitary waves by a Harmonic Polynomial Cell Method

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

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 work, a virtual body-fitted grid is introduced and combined with the implicit velocity correction-based immersed boundary method (IBM) for simulation of incompressible flows with moving boundaries. The original implicit velocity correction-based IBM to this kind of problem requires the matrix inversion operation to be repeated at each time step, resulting in significant computational resources and time when the Gaussian elimination method is used for solution, whose computational complexity is $\mathcal{O}(M^3).$ The present method introduces a virtual body-fitted grid that moves together with the immersed boundary to overcome the above defect. As with the original implicit velocity correction-based IBM, the fractional step technique, which includes the prediction step and the correction step, is applied in the present method. Note that the correction step is implemented on the virtual grid in the present method instead of the Eulerian mesh in the original method. Since the relative positions between virtual grid points and Lagrangian points are changeless, the matrix in the correction step can be pre-calculated and stored, avoiding the need to update it at every time step. Although, within this approach, three additional steps including the marking virtual grid points and covered Eulerian points, and two interpolations between the Eulerian mesh and the virtual grid must be conducted at each time step, the computational effort is still greatly reduced as the computational complexity of these steps is $\mathcal{O}(M).$ A numerical experiment of flow around a transversely oscillating cylinder is first performed, demonstrating the improved efficiency, especially when the number of Lagrangian points is large. As validation, the flow over a flapping elliptical wing and a fluid-structure interaction (FSI) problem of vortex-induced vibrations of a circular cylinder are simulated. The numerical results are found to be in line with reference results, verifying the ability of the proposed method to simulate complex moving boundary problems.

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

An efficient semi-implicit immersed boundary method for the Navier–Stokes equations

A poroelastic immersed boundary method with applications to cell biology

In this work, the explicit boundary-condition-enforced immersed boundary method (EIBM) and the lattice Boltzmann flux solver (LBFS) are integrated into OpenFOAM to efficiently solve incompressible flows with complex geometries and moving boundaries. The EIBM applies the explicit technique to greatly improve the computational efficiency of the original boundary-condition-enforced immersed boundary method. In addition, the improved EIBM inherits the accurate interpretation of the no-slip boundary condition and the simple implementation from the original one. The LBFS uses the finite volume method to discretize the recovered macroscopic governing equations from the lattice Boltzmann equation. It enjoys the explicit relationship between the pressure and density, which avoids solving the pressure Poisson equation and thus saves much computational cost. Another attractive feature of the LBFS lies in its simultaneous evaluation of the inviscid and viscous fluxes. OpenFOAM, as an open-source CFD platform, has drawn increasing attention from the CFD community and has been proven to be a powerful tool for various problems. Thus, implementing the EIBM and LBFS into such a popular platform can advance the practical application of these two methods and may provide an effective alternative for complicated incompressible flow problems. The performance of the integrated solver in OpenFOAM is comprehensively assessed by comparing it with the widely used numerical solver in OpenFOAM, namely, the Pressure-Implicit with Splitting of Operators (PISO) algorithm with the IBM. A series of representative test cases with stationary and moving boundaries are simulated. Numerical results confirm that the present method does not have any streamline penetration and achieves the second-order accuracy in space. Therefore, the present method implemented in the open-source platform OpenFOAM may have good potential and can serve as a powerful tool for practical engineering problems.

In this paper, the in-house code based on the smoothed particle hydrodynamics is proposed to simulate a fluid-solid interaction (FSI) problem. This method is a Lagrangian, mesh-free method and it has a high ability to capture the free surface in two phase flows and also the interface in FSI problems. To compare ofweakly compressible SPH (WCSPH) and incompressible SPH (ISPH) schemes, fluid flow under a hypo-elastic gate is simulated in solid and fluid domains with both methods. At first fluid domain is simulated with ISPH method and solid domain is solved with WCSPH scheme. Another simulation is done with both fluid and solid parts solved with WCSPH method. The results of both methods are in a good agreement with each other and also with other researcher’s results. So it is concluded that it is easier to model the fluid flow with ISPH scheme and the solid part with WCSPH in coupling fluid-solid interaction problems with a good accuracy.

An immersed boundary-thermal lattice Boltzmann method for solid–liquid phase change

A novel ghost‐cell immersed boundary method for fully resolved simulation of char particle combustion has been developed. The boundary conditions at the solid particle surface, such as velocity, temperature, density, and chemical species concentration, are well enforced through the present method. Two semiglobal heterogeneous reactions and one homogeneous reaction are used to describe the chemical reactions in the domain, and the Stefan flow caused by the heterogeneous reactions is considered. A satisfactory agreement can be found between the present simulation results and experimental data in the literature. The method is then used to investigate the combustion property of a char particle and the interaction between CO2 gasification and O2 oxidation. Furthermore, combustion effect on the exchange of mass, momentum and energy between gas‐ and solid‐ phase is explored. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2851–2863, 2018

An Iterative Incompressible Immersed Boundary Method Applied to Biofluid-Structure Interaction Problems

Analysis of formation and slope stability in Caofeidian Channel in Bohai Bay

We present a consistent approach that allows to solve challenging general nonlinear fluid‐structure‐contact interaction (FSCI) problems. The underlying formulation includes both “no‐slip” fluid‐structure interaction as well as frictionless contact between multiple elastic bodies. The respective interface conditions in normal and tangential orientation and especially the role of the fluid stress within the region of closed contact are discussed for the general problem of FSCI. A continuous transition of tangential constraints from no‐slip to frictionless contact is enabled by using the general Navier condition with varying slip length. Moreover, the fluid stress in the contact zone is obtained by an extension approach as it plays a crucial role for the lift‐off behavior of contacting bodies. With the given continuity of the formulation, continuity of the discrete system of equations for any variation of the coupled system state (which is essential for the convergence of Newton's method) is reached naturally. As topological changes of the fluid domain are an inherent challenge in FSCI configurations, a noninterface fitted cut finite element method (CutFEM) is applied to discretize the fluid domain. All interface conditions, that is the “no‐slip” FSI, the general Navier condition, and frictionless contact are incorporated using Nitsche based methods, thus retaining the consistency of the model. To account for the strong interaction between the fluid and solid discretization, the overall coupled discrete system is solved monolithically. Numerical examples of varying complexity are presented to corroborate the developments. In a first example, the fundamental properties of the presented formulation such as the contacting and lift‐off behavior, the mass conservation, and the influence of the slip length for the general Navier interface condition are analyzed. Beyond that, two more general examples demonstrate challenging aspects such as topological changes of the fluid domain, large contacting areas, and underline the general applicability of the presented method.

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