Direct-forcing Immersed Boundary Method Research Articles

Direct numerical simulation of a stationary spherical particle in fluctuating inflows

Fully resolved direct numerical simulations are conducted to study the effects of fluctuating freestream flow on the drag force and wake characteristics of a stationary spherical particle. Sinusoidal fluctuation around a mean value is adopted as the freestream velocity. The interaction between the particle and fluctuating flow is computed by the direct-forcing immersed boundary method. We principally consider the relative difference between the computed mean drag and the drag law of a uniform flow past the particle and the properties of drag fluctuation in different freestream fluctuation directions. For the influence of streamwise fluctuating inflow, the relative mean drag difference increases with the particle Reynolds number. At small or intermediate particle scale ratios, the relative mean drag difference is very close to zero, indicating that the classical drag law can be used in these cases, while a large particle scale ratio can induce a notable increase in the relative mean drag difference at a large particle Reynolds number and high fluctuation intensity. For the transverse fluctuating inflow, generally, there is an evident increase in the mean drag coefficient when the particle scale ratio is small. Compared with the streamwise fluctuation case, the drag fluctuation intensity is a little smaller with the transverse fluctuating inflow. An explicit empirical drag fluctuation law is obtained by fitting the data for streamwise fluctuating inflow. The wake characteristics are also analyzed, and they are found to be strongly dependent on the direction of inflow fluctuation.

A novel interpolation-free sharp-interface immersed boundary method

This paper describes a novel 2nd order direct forcing immersed boundary method designed for simulation of 2D and 3D incompressible flow problems with complex immersed boundaries. In this formulation, each cell cut by the immersed boundary (IB) is reshaped to conform to the shape of the IB. IBs are modeled as a series of 2D planes in 3D space that connect seamlessly at the edges of the cut cells, in a way that mimics conformal grid. IBs are represented in a continuous and consistent fashion from one cell to another, thus eliminating spatial pressure oscillations originating from inconsistent description of the IB as well as the traditional stair-step problem, leading to a more accurate resolution of the boundary layer. Boundary conditions are enforced at the exact location of the IB devoid of interpolation, which guarantees sound simulations even on grids with high aspect ratio, and enables simulations of flow packed with multiple IBs in close proximity. Boundary conditions for each phase across the IB are enforced independently, yielding a unique capability to solve flows with zero-thickness IBs. Simulations of a large number of 2D and 3D test cases confirm the prowess of the devised immersed boundary method in solving flows over multiple loosely/closely-packed IBs; stationary, moving and highly morphing IBs; as well as IBs with zero-thickness. Results show that predictions from the proposed scheme agree remarkably well with theoretical models and experimental data for both integral variables and local flow fields and they are often with less than 1% deviation from solutions obtained by conformal grid of similar resolution.

Utilization of direct forcing immersed boundary methods for the optimization of inertial focusing microfluidics

Inertial focusing microfluidics have gained significant momentum in the last decade for their ability to separate and filter mixtures of particles and cells based on size [1-3]. However, the most important feature is that the separation is passive, without the need for external forces. At the heart of inertial focusing is the balance between counteracting lift forces: shear and wallinduced lift. Shear-induced lift is a product of the curvature of the fluid flow and the rotation of the particle in the flow, while wall-induced lift is generated by the disturbance of the fluid by the particle near a wall. This phenomenon was first observed by Segre and Silberberg for the focusing of particles in a pipe, and was later extended to the focusing of cells and particle in rectangular channels [4]. Taking advantage of inertial focusing we explore particle capture utilizing an expanded channel microfluidics chip design. By expanding a small region of the straight channel microvortices form in the well, which allows for size selective trapping of particles.

Aeroacoustic simulation of a cross-flow fan using lattice Boltzmann method with a RANS model

The present study developed an unsteady RANS approach based on the lattice Boltzmann method (LBM), which can perform direct aeroacoustic simulations of low-speed fans at lower computational cost compared with the conventional LBM-LES approach. In this method, the k-ω turbulence model is incorporated into the LBM flow solver, where the transport equations of k and ω are also computed by the lattice Boltzmann method, similar to the Navier-Stokes equations. In addition, moving boundaries such as fan rotors are considered by a direct-forcing immersed boundary method. This numerical method was validated in a two-dimensional simulation of a cross-flow fan. As a result, the simulation was able to capture an eccentric vortex structure in the rotor, and the pressure rise by the work of the rotor can be reproduced. Also, the peak sound of the blade passing frequency can be successfully predicted by the present method. Furthermore, the simulation results showed that the peak sound is generated by the interaction between the rotor blade and the flow around the tongue part of the casing.

A direct forcing immersed boundary method for cavitating flows

AbstractIn the current study, an immersed boundary method for simulating cavitating flows with complex or moving boundaries is presented, which follows the discrete direct forcing approach. Although the immersed boundary methods are widely used in various applications of single phase, multiphase, and particulate flows, either incompressible or compressible, and numerous alternative formulations exist, to the best of the authors' knowledge, a handful of computational works employ such methodologies on cavitating flows. The herein proposed method, following previous works of the author's group, tries to fill this gap and to solidify the development of a computational tool of a simple formulation capable to tackle complex numerical problems of cavitation modeling. The method aims to be used in a wide range of applications of industrial interest and treat flows of engineering scales. Therefore, a validation of the method is performed by numerous benchmark test‐cases, of progressively increasing complexity, from incompressible low Reynolds number to compressible and highly turbulent cavitating flows.

Turbulent flow simulation of a single-blade Magnus rotor

This paper presents numerical studies of the Magnus effect for a kinetic turbine on a horizontal axis. To focus on the Magnus blade, a single self-spinning cylindrical blade is assumed. An iterative direct-forcing immersed boundary method is employed within the Eulerian-Lagrangian framework due to its capability to treat complex and moving geometries. The Eulerian fluid domain is discretized using the finite volume method while the Magnus rotor is represented by a set of discrete points/markers. The aim of the numerical studies is to provide insights for the design process and predict aerodynamic performances under various operating conditions. Results for stationary and self-spinning cylinders in turbulent flows are found to be in good agreement with published data. By increasing the aspect ratio of the cylinder (simulated segment length over its diameter) from 3 to 10, a 30% drop in lift coefficient and a 22% increase in drag coefficient were observed, which is believed to be attributed to an enhancement of the three-dimensionality of the near-wake. For the Magnus rotor, key parameters such as dynamic forcing and frequency, distribution of pressure coefficient and torque have been produced for two cases with different structural designs and working conditions. With increase of the aspect ratio from 3 to 10, stable forces are observed from the root side of the blade and the torque coefficient increases from 0.68 to 2.1, which indicates a superior performance in terms of power extraction.

A one-sided direct forcing immersed boundary method using moving least squares

This paper presents a one-sided immersed boundary (IB) method using kernel functions constructed via a moving least squares (MLS) method. The resulting kernels effectively couple structural degrees of freedom to fluid variables on only one side of the fluid-structure interface. This reduces spurious feedback forcing and internal flows that are typically observed in IB models that use isotropic kernel functions to couple the structure to fluid degrees of freedom on both sides of the interface. The method developed here extends the original MLS methodology introduced by Vanella and Balaras (2009) [27]. Prior IB/MLS methods have used isotropic kernel functions that coupled fluid variables on both sides of the boundary to the interfacial degrees of freedom. The original IB/MLS approach converts the cubic spline weights typically employed in MLS reconstruction into an IB kernel function that satisfies particular discrete moment conditions. This paper shows that the same approach can be used to construct one-sided kernel functions (kernel functions are referred to as generating functions in the MLS literature). We also examine the performance of the new approach for a family of kernel functions introduced by Peskin. It is demonstrated that the one-sided MLS construction tends to generate non-monotone interpolation kernels with large over- and undershoots. We present two simple weight shifting strategies to construct generating functions that are positive and monotone, which enhances the stability of the resulting IB methodology. Benchmark cases are used to test the order of accuracy and verify the one-sided IB/MLS simulations in both two and three spatial dimensions. This new IB/MLS method is also used to simulate flow over the Ahmed car model, which highlights the applicability of this methodology for modeling complex engineering flows.

A resolved CFD-DEM method based on the IBM for sedimentation of dense fluid-particle flows

Motivated by the interest in accurate simulation of dense fluid-particle flows, a resolved CFD-DEM method is developed by incorporating computational fluid dynamics and discrete element method (CFD-DEM) with the immersed boundary method (IBM). In this approach, the fluid phase is simulated by the CFD while the individual particles are analyzed by means of the DEM. The direct-forcing IBM, which satisfies the no-slip boundary condition and the divergence-free condition simultaneously, is introduced to handle the interactions between rigid boundaries and fluid with inherent ease of tracking drastically moving geometries by a set of Lagrangian points. The strongly coupled system is then achieved through the successive iterative procedure. A significant advantage of the proposed method is that the fluid phase is fully resolved around the particle phase and as a result, for dense particulate flows where the interaction effects on either phase is considerably strong, the essential influence of the wake flow on particles could be reflected truthfully. The gravity-induced sedimentations of particles are performed to demonstrate the accuracy of the presented resolved method, and the comparison with the results obtained by the conventional unresolved CFD-DEM method is also performed which reveals that the proposed method shows a superiority of the precise description of the fluid-particle interactions over the conventional method especially when the dense particulate flows are involved.

Direct forcing immersed boundary methods: Improvements to the ghost-cell method

The ghost-cell immersed boundary methods (IBMs) are widely used to implement boundary conditions on non-body fitted grids. It has been previously shown that they have two major drawbacks. Firstly, these methods tend to have a maximum stencil size larger than 1, yielding non-band matrices. Secondly, for a maximum stencil size of 2 the ghost-cell linear IBM [1] have a first-order convergence rate for Neumann immersed boundary conditions. To address these two shortcomings and in the pursuit of increased accuracy and increased order of convergence the current article proposes the linear/quadratic square shifting methods for the ghost-cell IBM for Cartesian grids. The linear square shifting method guarantees a maximum stencil size of 1 and also improves the accuracy and convergence while the quadratic square shifting method improves the accuracy and convergence while maintaining the same stencil size of 2 as the original linear method [1]. The quadratic ghost-cell method [2,3] further improves the accuracy and convergence whilst maintaining a maximum stencil size of 3 while the currently proposed quadratic square shifting method makes it possible to increase the Lagrange polynomial interpolation order whilst maintaining a maximum stencil of 2 resulting in an improved order of convergence for Neumann immersed boundary conditions. The proposed methods are evaluated by considering their accuracy and convergence thanks to a comprehensive verification and validation process. Firstly, the canonical verification 2D and 3D Poisson test problems for various analytical solutions and immersed boundaries are considered and are followed by various verification and validation test cases for the Navier-Stokes governing equations, with and without heat transfer, in 2D and 3D.

Direct-forcing immersed-boundary method: A simple correction preventing boundary slip error

The boundary slip error resulting from the interpolation/spreading non-reciprocity of the direct-forcing immersed-boundary method is analyzed based on a simple and generic theoretical framework. In explicit implementations, the slip error scales with the Courant number, as predicted by the analysis and confirmed by lattice-Boltzmann simulation results. Using an analytical approximation of the non-reciprocity error, the immersed-boundary force can be corrected in order to prevent boundary slip and flow penetration. This a priori correction leads to a major improvement of the no-slip condition while avoiding any additional computational time or implementation effort.

A Multi-Fidelity Framework for Wildland Fire Behavior Simulations over Complex Terrain

A method for the large-eddy simulation (LES) of wildfire spread over complex terrain is presented. In this scheme, a cut-cell immersed boundary method (CC-IBM) is used to render the complex terrain, defined by a tessellation, on a rectilinear Cartesian grid. Discretization of scalar transport equations for chemical species is done via a finite volume scheme on cut-cells defined by the intersection of the terrain geometry and the Cartesian cells. Momentum transport and heat transfer close to the immersed terrain are handled using dynamic wall models and a direct forcing immersed boundary method. A new “open” convective inflow/outflow method for specifying atmospheric wind boundary conditions is presented. Additionally, three basic approaches have been explored to model fire spread: (1) Representing the vegetation as a collection of Lagrangian particles, (2) representing the vegetation as a semi-porous boundary, and (3) representing the fire spread using a level set method, in which the fire spreads as a function of terrain slope, vegetation type, and wind speed. Several test and validation cases are reported to demonstrate the capabilities of this novel wildfire simulation methodology.

A structured adaptive mesh refinement strategy with a sharp interface direct-forcing immersed boundary method for moving boundary problems

We develop a versatile and accurate structured adaptive mesh refinement (S-AMR) strategy with a moving least square sharp-direct forcing immersed boundary method (IBM) for incompressible fluid-structure interaction (FSI) simulations. The computational grid consists of several nested blocks in different refinement levels. While blocks with the coarsest grid cover the entire computational domain, the computational domain is locally refined at the location of solid boundary (moving or fixed) by bisecting selected blocks in every coordinate direction. The grid topology and data structure is managed by an extended version of Afivo toolkit (Teunissen and Ebert, 2018), where a novel technique is introduced for conservative data transfer between the coarser and the finer blocks, particularly in velocity transformation for which the mass conservation plays a crucial role. In the present study, the continuity and Navier-Stokes equations for incompressible flows are spatially discretized with a second order central finite difference method using a collocated arrangement and are time-integrated using a semi-implicit second order fractional step method, although the proposed S-AMR strategy can be used with different discretization schemes. An IBM using a moving least square approach is utilized to impose boundary conditions. To handle FSI problems, all the governing equations for the dynamics of fluid and structure are simultaneously advanced in time by a predictor-corrector strategy. Several test cases of increasing complexity are solved in order to demonstrate the robustness and accuracy of the proposed method as well as its capability in simulation-driven mesh adaptivity.

A sharp interface direct-forcing immersed boundary method using the moving least square approximation

Based on the Moving Least Square (MLS) approximation, we propose a sharp interface direct-forcing immersed boundary method for incompressible fluid flows with fixed and moving boundaries. Since the domain of definition for the interpolation is highly flexible and the MLS approximation provides an accurate reconstructed approximation of the solution, the proposed method serves the precision and versatility required for a numerical framework to study the fluid-structure interaction problems. To alleviate the inherent spurious numerical oscillation that occurs in the calculated forces on moving boundary embedded objects, we use a two step predictor-corrector method in which the direct forcing terms are calculated after the predictor step and imposed on the whole solid domain as well as at the immediate vicinity of the solid boundary inside the fluid domain. To represent the arbitrary geometries, we adopt a signed distance function representation of the rigid body and an interpolation strategy to considerably reduce the computational cost of the re-initialization of the distance function at every time step. The potential capability of the method is demonstrated for both fixed and moving boundary problems. We also solve a sedimentation of a single cylinder to demonstrate the ability of the present method in solving fluid-structure interaction problems. These numerical experiments show that the proposed moving least square immersed boundary method can handle relatively complex moving problems while enjoying a versatile interpolation strategy and keeping the boundary conditions sharp with remarkable accuracy.

Vertical-Axis Wind Turbine Blade-Shape Optimization Using a Genetic Algorithm and Direct-Forcing Immersed Boundary Method

The aim of this study was to prove that an optimization method combining genetic algorithms with a direct-forcing immersed boundary method as a distinguished numerical method could improve the performance of vertical-axis wind turbine blades. The proposed direct-force immersed boundary (DFIB) flow solver was tested using the benchmark laminar flow problems (lid-driven flow, flow over a stationary cylinder, and vortex-induced vibration of the circular cylinder). Two cases were analyzed, one of a stationary airfoil and another of a rotating airfoil in a vertical-axis wind turbine. The analysis was carried out using two-dimensional flow simulations in a laminar flow regime. A NACA 0012 airfoil was used as the original airfoil cross section of the vertical-axis wind turbine. The proposed method successfully simulated the moving blade in the flow field, and the results revealed that the optimized wind turbine blade designed using the proposed method had an efficiency improvement of 5.61% compared to the original airfoil.

A coupled polygonal DEM-LBM technique based on an immersed boundary method and energy-conserving contact algorithm

This work presents a framework of coupling polygonal discrete elements and the lattice Boltzmann method using a direct forcing immersed boundary scheme. In this technique, an energy-conserving contact algorithm is utilized to handle the interactions between convex and concave polygonal particles. The surface of a polygon is represented by discrete boundary points which includes vertices of polygonal particles and/or points interpolated from vertices. The fluid-particle coupling is obtained through the interactions of the boundary points and the imaginary fluid particles using a direct forcing immersed boundary method. Validations of the proposed technique are made by single particle and multiple arbitrarily-shaped particle sedimentation tests, and the effect of particle shape is illustrated using a drafting-kissing-tumbling benchmark.

A numerical framework for modelling the dynamics of open ocean aquaculture structures in viscous fluids

This paper presents a complete numerical framework for modelling open ocean aquaculture structures in waves and current using Computational Fluid Dynamics (CFD). A structural dynamics model is incorporated to account for the motions and deformations of the net. It is based on the lumped mass method, a non-linear material law and implicit time step advancing. The presence of the porous net is considered in the momentum equations of the fluid using a forcing term based on Lagrangian-Eulerian coupling and the acting forces on the net. The proposed framework is suitable for simulating the interaction of nets of arbitrary geometry and under large motion with fluids including complex free surfaces. This is in contrast to existing models which either neglect important non-linearities, the physical interaction with the fluid or are limited to certain net geometries. In addition, the fluid-structure interaction of floating objects with mooring lines, nets and fluid is accounted for in the model. A new floating algorithm is presented for the interaction of the fluid and the rigid structure. It is based on a continuous direct forcing immersed boundary method and a level set representation of the object in the Eulerian fluid domain. This effectively avoids computationally expensive reconstruction processes of existing approaches and enables the application to large three-dimensional structures. The complete numerical framework is first validated against existing measurements for forces on rigid and flexible nets, net deformations and moored-floating structures with and without a net in waves. Then, a semi-submersible and a mobile floating open ocean aquaculture structure are investigated, and the possibilities of the numerical approach are highlighted.

A semi-implicit direct forcing immersed boundary method for periodically moving immersed bodies: A Schur complement approach

An extended immersed boundary methodology utilizing a semi-implicit direct forcing approach was formulated for the simulation of incompressible flows in the presence of periodically moving immersed bodies. The methodology utilizes a Schur complement approach to enforce no-slip kinematic constraints for immersed surfaces. The methodology is split into an “embarrassingly” parallel pre-computing stage and a time integration stage, both of which take advantage of the general parallel file system (GPFS) for efficient writing and reading of large amounts of data. The methodology can be embedded straight forwardly into the whole family of pressure–velocity segregated solvers of incompressible Navier–Stokes equations based on projection or fractional step approaches. The methodology accurately meets the no-slip kinematic constraints on the surfaces of immersed oscillating bodies. In this study, it was extensively verified by applying it for the simulation of a number of representative flows developing in the presence of an oscillating sphere. The capabilities of the methodology for the simulation of incompressible flow generated by a number of bodies whose motion is governed by general periodic kinematics were demonstrated by simulation of the flow developing in the presence of two out-of-phase oscillating spheres. The physical characteristics of the generated flows in terms of the time evolutions of the total drag coefficients were presented as a function of Reynolds values. The vortical structures inherent in the generated flows were visualized by presenting the isosurfaces of the λ2 criterion.

Numerical Simulation of Dam-Break Flood Impacting Buildings by a Volume of Fluid and Immersed Boundary Method

A three-dimensional hydrodynamic model is developed to study the propagation of dam-break-induced flood and the interaction between floods and buildings. In the proposed mathematic model, the volume of fluid (VOF) method and the immersed boundary (IB) method are used to address the air/water interface and fluid/structure interface respectively. Barely a limited number of publications focus on 3D simulations of the dam-break flood impacting buildings in the long flume heretofore, for researching the dam-break flood impacting buildings involves some hard issues like a wave breaking phenomena, flood-building interaction, and computational efficiency. Therefore, the highlights to this paper are: (1) The THINC/SW (THINC with Slope Weighting), which is extremely simple and efficient and meanwhile can also solve the wave breaking process, is adopted in the paper. Furthermore, its numerical accuracy is comparable to the conventional VOF schemes that use geometrical reconstructions. (2) The direct forcing IB method, which can be easily applied to three-dimensional simulation, is adopted to promote the computational efficiency of the three-dimensional numerical model and handle flood-building interaction interface treatment. The proposed VOF/IB model is validated by the physical experiment results and is also compared with the two-dimensional depth-averaged Shallow-Water Equations (SWEs), and Coupled Level Set/Volume of Fluid and Immersed Boundary (CLSVOF/IB) models in terms of accuracy and efficiency.

Numerical investigation of particle lateral migration in straight channel flows using a direct-forcing immersed boundary method

Inertia-induced cross-stream migration has been recently exploited for precise position of particles in confined channel flows. In this work, a three-dimensional finite volume based immersed boundary method has been developed to study the lateral migration and hydrodynamic self-assembly of neutrally-buoyant particles in pressure-driven flows. Simulation results show that, in 2D channel flows, the equilibrium position for a circular particle is closer to the centreline for larger particle Reynolds number due to the increasing flow rate, while in 3D square duct flow, the equilibrium position for a spherical particle is near a face centre and is closer to the wall for larger particle Reynolds number. Self-assembly of a pair of particles is observed in 3D square duct flows but not in 2D channel flows. Mechanisms for the self-assembly are discussed.

A scalable parallel algorithm for direct-forcing immersed boundary method for multiphase flow simulation on spectral elements

In this work, we propose a highly scalable parallel double binned ghost particle (DBGP) algorithm for direct-forcing immersed boundary spectral element method for multiphase flow simulations. In particular, the DBGP algorithm is designed to obtain fully distributed data storage and scalable data transfer across hundreds of thousands of processors. The proposed algorithm uses a queen and worker data structure for fully resolved particles to demarcate particle-level and marker-level quantities and communication. In the DBGP algorithm, each particle’s centroid is represented by a queen marker and the particle surface is covered with a uniform distribution of surface worker markers. The queen marker contains information on the translational and rotational motion of a particle and integrates the force and torque computed at all the worker markers, while the worker marker implements the fluid–particle interaction. Ghost queen and ghost worker markers are generated for each real queen and real worker marker during computation for particle-level and marker-level communications, respectively. A double Cartesian binning process is introduced that divides the physical domain into a coarse queen-bin and a fine worker-bin structure in three dimensions. The queen-bin and worker-bin sizes are determined by their zone of influence at the particle-level and marker-level communication, respectively. Bin-to-rank maps that relate each queen-bin and worker-bin to all the MPI ranks that they interact with are created. By using the queen/worker marker representation and two-layer bin-to-rank maps, data communication across very large number of MPI ranks is efficiently carried out. A scaling analysis has been conducted, showing excellent performance of the DBGP algorithm for up to 16,384 MPI ranks in both weak and strong scaling studies. The proposed method has been demonstrated to accurately predict sedimentation of particle clouds. The simulated correlation between the mean settling velocity and volume fraction is in good agreement with empirical correlations from previous studies.