Immersed Boundary Research Articles

Numerical study of aerodynamic roles of bridge railings by immersed boundary method

The roles of railings in determining the aerodynamic characteristics of bridge girders are investigated numerically. The Direct Forcing (DF) Immersed Boundary (IB) method is utilized to model the railings while the bridge girder is modeled by body-fitted mesh system. Two benchmark tests (flow around a circular cylinder at Re = 3900 and around an equipped bridge girder at 0 ° attack angle) are designed to validate the DF-IB method. It is shown that this method has sufficient accuracy to capture representative flow structures with fewer cells and little mesh topology change. The roles of railings are investigated at several wind attack angles up to ± 12°. Results show that railings mainly affect the upper surface of the girder section and their influence is sensitive to attack angle. For negative attack angles, only downstream railings influence the flow locally. For low positive attack angles, the separated vortex is suppressed by the railings and early reattachment is observed. When the attack angle is higher, separated flows generated from the highest horizontal bar and girder corner are mixed and transferred far from the upper surface, which results in a downstream boundary layer eruption. Thus, the upstream railing affects the flow over the entire upper surface, not just locally.

Wake modeling and simulation of an experimental wind turbine using large eddy simulation coupled with immersed boundary method alongside a dynamic adaptive mesh refinement

Accurate numerical models of the flow around wind turbines is highly relevant for optimizing the energy efficiency of wind farms. The main goal of this work is to apply large eddy simulation (LES) along with an immersed boundary (IB) method to generate spatial and temporal information of the velocity field and forces acting on a fully-resolved NREL S809 airfoil and NREL Phase VI wind turbine. The numerical framework used in the simulations performs LES under a Cartesian block-structured mesh that is dynamically refined via adaptive mesh refinement (AMR) to increase accuracy and reduce computational costs. The mesh refinement criteria is based on Lagrangian points and vorticity. Solid surfaces of the wind turbine are captured using the Lagrangian formulation of the IB method. The simulations are based on the NREL Phase VI wind turbine, where blade analysis of lift and drag coefficients were performed, followed by time-averaged streamwise velocity and vorticity evaluations. For different angles of attack, the wake centerline velocity analysis demonstrates high energy extraction in the near wake of the wind turbine blade. In terms of validation, the drag coefficient of the NREL S809 airfoil achieves better agreement with the experimental data than the lift coefficient. Validation from the NREL Phase VI shows that the power performance difference between the simulation and experiment is lower than 6%. Wake analysis of the wind turbine scenario are based on downstream profiles of the time-averaged streamwise velocity. The numerical simulation shows a higher loss of kinetic energy in the near wake region, mainly in the centerline, compared to benchmark data, but achieves very similar results to literature in the far-wake region.

Enthalpy-based immersed boundary-lattice Boltzmann model for solid-liquid phase change in porous media under local thermal non-equilibrium condition

Heat transfer enhancement structures are adopted to improve the performance of latent heat thermal energy storage (LHTES) systems, such as metallic porous matrix, multi-tube, and fin. The metallic porous matrix and complex geometries of the structures bring difficulties to the numerical studies of the solid-liquid phase transition in the enhanced LHTES system. In this work, an enthalpy-based immersed boundary (IB)-lattice Boltzmann (LB) model is proposed for solid-liquid phase change problems in porous media under the local thermal non-equilibrium (LTNE) condition. In this model, to reduce the numerical diffusion across the solid-liquid interface, a two-relaxation-time (TRT)-LB model is developed to obtain the temperature field of phase change material (PCM). Two single-relaxation-time (SRT)-LB equations (LBEs) are employed for the velocity field of the liquid PCM and the temperature field of the porous matrix, respectively. The partially saturated method is used for the non-slip boundary condition on the moving solid-liquid interface. Different discrete source term schemes are employed for source terms induced by surface heat transfer and IB. Based on the source term treatment, the multi-direct-forcing IB-LB method is employed for the implementation of velocity, enthalpy and temperature boundary conditions on the complex boundary. The proposed model is verified by four cases: one-dimensional conduction melting under the LTNE condition, natural convection in a metallic porous matrix-filled cavity, conduction melting in an annulus filled with metallic porous matrix, and constrained melting in an isothermal circular cylinder without porous media. As an example of application, a metallic porous matrix-enhanced LHTES system with different multi-tube arrangements at different Rayleigh numbers (Ra) and porosities is investigated.

A model predictive control (MPC)-integrated multiphase immersed boundary (IB) framework for simulating wave energy converters (WECs)

In this work, we present a novel MPC-integrated multiphase IB framework that can compute the optimal energy-maximizing control force “on-the-fly” by dynamically interacting with a high-fidelity numerical wave tank (NWT). The computational model closely mimics the working setup of the device at its site of operation. Due to the requirement of solving a constrained optimization problem at each time step of the IB simulation, the MPC algorithm utilizes a low-dimensional dynamical model of the device that is based on the linear potential theory (LPT). The multiphase IB solver, on the other hand, is based on the high-dimensional fictitious domain Brinkman penalization (FD/BP) method, which fully-resolves the hydrodynamic non-linearities associated with the wave–structure interaction (WSI). A time-series forecasting auto-regressive model is implemented that predicts wave heights (from the past NWT data) to estimate the future wave excitation/Froude–Krylov forces for the MPC algorithm. Moreover, we also experiment with non-linear Froude–Krylov (NLFK) forces for the first time in an MPC formulation. The NLFK forces are computed efficiently using a static Cartesian grid, in which the WEC geometry is implicitly represented by a signed distance function. Under varying sea conditions, the predictions of the MPC-integrated multiphase IB solver are compared to the widely popular LPT-based solvers. In agitated sea conditions and/or under aggressive control, the LPT-based WSI solvers produce too optimistic (and misleading) power output values. Overall, six WSI/MPC solver combinations are compared for a heaving vertical cylinder to determine the reasons for discrepancies between high- and low-fidelity predictions. We also determine the pathway of energy transfer from the waves to the power take-off (PTO) system and verify the relationships using IB simulations. Additionally, three different sea states are simulated within the IB simulation to test the adaptive capability of MPC for WECs. MPC is demonstrated to adapt to changing sea conditions and find the optimal solution for each sea state.The interaction between the distributed-memory parallel multiphase IB solver (written in C++) and the serial MPC solver (written in MATLAB) is fully described to facilitate reproducibility. A bespoke communication layer between the two solvers is developed, which can be easily modified by the WEC community to experiment with other optimal controllers and computational fluid dynamics (CFD) solvers. All codes for this work are made open-source for pedagogical and research purposes.

An analysis of the numerical stability of the immersed boundary method

We present a numerical stability analysis of the immersed boundary (IB) method for a special case which is constructed so that Fourier analysis is applicable. We examine the stability of the immersed boundary method with the discrete Fourier transforms defined differently on the fluid grid and the boundary grid. This approach gives accurate theoretical results about the stability boundary since it takes the effects of the spreading kernel of the immersed boundary method on the numerical stability into account. In this paper, the spreading kernel is the standard 4-point IB delta function. A three-dimensional incompressible viscous flow and a no-slip planar boundary are considered. The case of a planar elastic membrane is also analyzed using the same analysis framework and it serves as an example of many possible generalizations of our theory. We present some numerical results and show that the observed stability behaviors are consistent with what are predicted by the theory.

Numerical simulation for liquid sloshing with baffle by the CLSVOF/IB method

The liquid sloshing problem in a partially filled rectangular tank is numerically investigated by a Coupled Level Set and Volume Of Fluid (CLSVOF) method. In the present CLSVOF method, the Level Set (LS) equation needs to be solved to advect the LS function for calculating interface curvature; the re-distancing equation is also taken into account for the LS function being maintained as a distance function. For capturing the interface, the Tangent of Hyperbola for INterface Capturing (THINC) scheme with Weighted Linear Interface Calculation (WLIC) is implemented to advect the Volume of Fluid (VOF) function. To preserve mass conservation, the interface reconstruction procedure needs to be carried out on the basis of the connection between LS and VOF functions. Rectangular and prismatic tanks are used to validate the accuracy and mass conservation of the present CLSVOF method. Then, further simulations of the problem of partially filled liquid sloshing with baffle considered are conducted by combining the CLSVOF method and the Immersed Boundary (IB) method. Finally, the influence of different baffle lengths on the slapping pressure and free-surface is discussed.

An improved direct-forcing immersed boundary method for simulations of flow and heat transfer in particle-laden flows

In studies of particle-laden flow, the direct-forcing immersed boundary (IB) method is commonly utilized to fully resolve the flow around the particles. With the use of interpolation functions, the effective diameter of a particle is typically larger than the actual diameter, resulting in an erroneous flow field, an overestimated drag force, and an inaccurately estimated interphase heat transfer rate when the grid resolution is insufficient. Relatively high grid resolutions (typically dp/h > 20) are required to ensure accurate estimations of the momentum and heat transfer between fluid and particles, leading to high computational cost when simulating cases with numerous particles. To address these issues, we propose an improved direct-forcing IB method involving retraction of the Lagrangian points, which considers the interphase momentum and heat transfer simultaneously. The method establishes two sets of Lagrangian points for computing the drag force and heat transfer rate, respectively. Based on the optimal retraction distance of the two sets of Lagrangian points, two retraction functions of the Reynolds number and grid resolution are formulated. Using the developed retraction functions, we simulate the DKT process, non-isothermal flow past three in-line spheres, and gravitational settling of a sphere with variable temperature to validate the improved IB method. It is found that the drag force and Nusselt number can be accurately reproduced using the improved IB method with a relatively small grid resolution (dp/h = 10).

Temporary velocity correction-based immersed boundary–lattice Boltzmann method for incompressible flows in porous media at representative elementary volume scale

The immersed boundary (IB)–lattice Boltzmann (LB) method is an effective strategy for complex boundary condition treatment. By adding an extra body force term in the LB equation properly, the specific velocity boundary condition can be enforced in this method. However, when it comes to incompressible flows through porous media at the representative elementary volume (REV) scale, the conventional IB–LB method fails because the velocity and the force term induced by porous media are coupled. In order to solve this problem, a temporary velocity is used to construct the IB-induced force term with the enforcement of the velocity boundary condition. The temporary velocity is decomposed into the intermediate temporary velocity and the corresponding correction. By this treatment, the temporary velocity correction is the linear function of the IB-induced force term. Furthermore, to obtain the force term accounting for the IB, the velocity boundary condition is transformed to the temporary velocity. Consequently, a temporary velocity correction-based IB–LB method is established for the incompressible flows at the REV scale. To avoid the error of explicitly calculating the IB-induced force term, the multi-direct-forcing scheme is employed in which iteration is carried out in terms of the specific boundary condition. The proposed IB–LB method for REV-scale incompressible flows is applied for the Couette flow in a porous annulus and lid driven flow in a square cavity filled with porous matrix. Numerical results show the computational accuracy of the developed IB–LB method.

Performance of coastal circular bridge pier under joint action of solitary wave and sea current

As an important transportation infrastructure, coastal bridges are widely established in coastal areas, the piers of which are always subjected to waves and currents and are prone to damage, especially under extreme marine conditions. Since ocean waves and currents coexist and twist with each other, it is necessary to take both them and their interaction into account to better understand the interaction between the pier and the marine environment. To reveal the interaction mechanism among waves, currents and piers under extreme marine conditions caused by hurricanes or tsunamis, the joint action of solitary wave and sea current on the piers are studied based on a numerical model with the immersed boundary (IB) method in this paper. The calculation capability of this model is verified and a series of simulation cases are systematically carried out depending on this model. The prominent factors of the environmental conditions including current velocity and wave height and the piers with different diameters and arrangements are considered. The flow field, the wave run-up, the velocity, the pressure and the hydrodynamic load on the piers are investigated, the results of which indicate that the total force on the pier under the joint effect of solitary wave and sea current is several times the sum of the forces under solitary wave and current. The higher the velocity of the sea current is, the more significant the wave and current coupling effect is. When the tandem pier is with the small gap, the forces on the streamwise and transverse tandem piers are smaller and larger than those on the single pier, respectively, and with the increase of the gap, the force on the tandem pier tends to be that on the single pier. The small gap in the streamwise tandem piers and the large gap in the transverse tandem piers are beneficial to the stability of piers.

A subcycling/non-subcycling time advancement scheme-based DLM immersed boundary method framework for solving single and multiphase fluid–structure interaction problems on dynamically adaptive grids

In this paper, we present an adaptive implementation of the distributed Lagrange multiplier (DLM) immersed boundary (IB) method on multilevel collocated grids for solving single- and multiphase fluid–structure interaction (FSI) problems. Both a non-subcycling time advancement scheme and a subcycling time advancement scheme, which are applied to time-march the composite grid variables on a level-by-level basis, are presented; these schemes use the same time step size and a different time step size, respectively, on different levels. This is in contrast to the existing adaptive versions of the IB method in the literature, in which coarse- and fine-level variables are simultaneously solved and advanced in a coupled fashion. A force-averaging technique and a series of synchronization operations are constructed to achieve excellent momentum and mass conservation across multiple levels of grid hierarchy. We demonstrate the versatility of the present multilevel framework by simulating problems with various types of kinematic constraints imposed by structures on fluids, such as imposing a prescribed motion, free motion, and time-evolving shape of a solid body. The DLM method is also coupled to a robust level set method-based two-phase fluid solver to simulate challenging multiphase flow problems, including wave energy harvesting using a mechanical oscillator. The capabilities and robustness of the computational framework are validated against a variety of benchmarking single-phase and multiphase FSI problems from the literature, which include a three-dimensional swimming eel model to demonstrate the significant speedup and efficiency that result from employing the present multilevel subcycling FSI scheme.

Effect of porous media on wake-induced vibration (WIV) in tandem circular cylinder

In practical engineering, cylindrical structures are frequently arranged in tandem under different flow environments. In this study, wake-induced vibration (WIV) of a solid circular cylinder in the wake of a stationary porous cylinder is numerically investigated. A numerical model including the porous medium and vibration modules is established by using the Immersed Boundary (IB) method and the calculation accuracy of the model is verified by the experiment. Seven porosities of the upstream cylinder from 0.0 to 1.0 are considered and the downstream cylinder is allowed to oscillate in both streamwise and transverse directions. The effects of the gap between the two cylinders, the Reynolds number (Re) and the reduced velocity (Ur) on the upstream-stationary-downstream-vibrating tandem cylinders are investigated in terms of shear layer reattachment, vortex impingement and wake interference. The wake flow pattern and the vortex shed from the porous cylinder are vulnerable to the porosity of the cylinder. As a result, the vibration of the downstream cylinder caused by the wake changes at different porosities. Besides, the hydrodynamic force and vibration frequency are also tightly associated with the wake interaction. At different reduced velocities (Ur) and Reynolds numbers (Re), the WIV and the force on the cylinder change significantly.

On the Lagrangian-Eulerian coupling in the immersed finite element/difference method

The immersed boundary (IB) method is a non-body conforming approach to fluid-structure interaction (FSI) that uses an Eulerian description of the momentum, viscosity, and incompressibility of a coupled fluid-structure system and a Lagrangian description of the deformations, stresses, and resultant forces of the immersed structure. Integral transforms with Dirac delta function kernels couple the Eulerian and Lagrangian variables, and in practice, discretizations of these integral transforms use regularized delta function kernels. Many different kernel functions have been proposed, but prior numerical work investigating the impact of the choice of kernel function on the accuracy of the methodology has often been limited to simplified test cases or Stokes flow conditions that may not reflect the method's performance in applications, particularly at intermediate-to-high Reynolds numbers, or under different loading conditions. This work systematically studies the effect of the choice of regularized delta function in several fluid-structure interaction benchmark tests using the immersed finite element/difference (IFED) method, which is an extension of the IB method that uses a finite element structural discretization combined with a Cartesian grid finite difference method for the incompressible Navier-Stokes equations. Whereas the conventional IB method spreads forces from the nodes of the structural mesh and interpolates velocities to those nodes, the IFED formulation evaluates the regularized delta function on a collection of interaction points that can be chosen to be denser than the nodes of the Lagrangian mesh. This opens the possibility of using structural discretizations with wide node spacings that would produce gaps in the Eulerian force in nodally coupled schemes (e.g., if the node spacing is comparable to or broader than the support of the regularized delta function). Earlier work with this methodology suggested that such coarse structural meshes can yield improved accuracy for shear-dominated cases and, further, found that accuracy improves when the structural mesh spacing is increased. However, these results were limited to simple test cases that did not include substantial pressure loading on the structure. This study investigates the effect of varying the relative mesh widths of the Lagrangian and Eulerian discretizations in a broader range of tests. Our results indicate that kernels satisfying a commonly imposed even–odd condition require higher resolution to achieve similar accuracy as kernels that do not satisfy this condition. We also find that narrower kernels are more robust, in the sense that they yield results that are less sensitive to relative changes in the Eulerian and Lagrangian mesh spacings, and that structural meshes that are substantially coarser than the Cartesian grid can yield high accuracy for shear-dominated cases but not for cases with large normal forces. We verify our results in a large-scale FSI model of a bovine pericardial bioprosthetic heart valve in a pulse duplicator.

A simple and efficient parallel immersed boundary-lattice Boltzmann method for fully resolved simulations of incompressible settling suspensions

This study presents an efficient and parallel fully resolved direct numerical simulation (FR-DNS) of settling suspensions on multiple CPU cores based on the boundary-thickening direct forcing immersed boundary method (BTDF-IBM) and incompressible lattice Boltzmann method (LBM). The simple BTDF-IBM is used to meet the no-slip and no-penetration conditions on particle boundaries, and the incompressible LBM is used to achieve the capability of large pressure fluctuations in suspensions. In addition, a theoretical force model is used to compensate for the unresolved lubrication force between the two approaching particles. A swap strategy for the streaming step is used to reduce the memory storage of the LBM particle density functions to half. A distribution and communication strategy is proposed to handle the IBM computing and complete the immersed boundary (IB) force of the particles residing in the interface region between adjacent subdomains. The developed BTDF-IBM-LBM solver “PFlows” can simulate large particle-laden flows with more than O(106) particles and with a particle volume fraction of up to 0.4. An almost linear parallel speedup and efficiency of higher than 0.8 are obtained by testing three-dimensional (3D) cases (up to 1.0 billion fluid grids and 0.45 million particles) and two-dimensional (2D) cases (up to 1.2 billion fluid grids and 2.39 million particles). Finally, the framework is applied to three large-scale real simulations involving 50,000 particles settling in 2D and 3D bounded and unbounded domains for qualitative and quantitative validations. The particle settling behaviors and disturbed complex fluid flows in the vertical channel are demonstrated. The Boycott effect in the inclined channel is uncovered by a new mechanism that combines particle sliding at the lower sidewall with fluid convection in the upper region. The hindered settling of particles in the 3D periodic domain, which is affected by the strong particle-fluid hydrodynamic interactions and particle-particle many-body interactions at a high solid volume fraction, are analyzed. The complex behaviors and statistical characteristics of the suspensions are preliminarily revealed and analyzed, which demonstrates the prospective capability of the present framework for FR-DNS of large-scale 2D and 3D suspension flows that are relevant to many industrial applications by IB-LBM.

A Direct-Forcing Immersed Boundary Method for Incompressible Flows Based on Physics-Informed Neural Network

The application of physics-informed neural networks (PINNs) to computational fluid dynamics simulations has recently attracted tremendous attention. In the simulations of PINNs, the collocation points are required to conform to the fluid–solid interface on which no-slip boundary condition is enforced. Here, a novel PINN that incorporates the direct-forcing immersed boundary (IB) method is developed. In the proposed IB-PINN, the boundary conforming requirement in arranging the collocation points is eliminated. Instead, velocity penalties at some marker points are added to the loss function to enforce no-slip condition at the fluid–solid interface. In addition, force penalties at some collocation points are also added to the loss function to ensure compact distribution of the volume force. The effectiveness of IB-PINN in solving incompressible Navier–Stokes equations is demonstrated through the simulation of laminar flow past a circular cylinder that is placed in a channel. The solution obtained using the IB-PINN is compared with two reference solutions obtained using a conventional mesh-based IB method and an ordinary body-fitted grid method. The comparison indicates that the three solutions are in excellent agreement with each other. The influences of some parameters, such as weights for different loss components, numbers of collocation and marker points, hyperparameters in the neural network, etc., on the performance of IB-PINN are also studied. In addition, a transfer learning experiment is conducted on solving Navier–Stokes equations with different Reynolds numbers.

A strongly coupled immersed boundary method for fluid-structure interaction that mimics the efficiency of stationary body methods

Strongly coupled immersed boundary (IB) methods solve the nonlinear fluid and structural equations of motion simultaneously for strongly enforcing the no-slip constraint on the body. 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 scale only by the small number of points used to represent the fluid-structure interface. These costly large scale operations for determining only a small number of unknowns at the interface creates a bottleneck to efficiently time-advancing strongly coupled IB methods. In this manuscript, we present a remedy for this bottleneck that is motivated by the efficient strategy employed in stationary-body IB methods while preserving the favorable stability properties of strongly coupled algorithms—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 modified system of small-dimensional constraint equations that is 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. Although the demonstration problems consist of a combination of rigid and torsionally mounted bodies, the formulation is derived in a more general setting involving an arbitrary number of rigid, torsionally mounted, and continuously deformable bodies.

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.

A novel actuator line-immersed boundary (AL-IB) hybrid approach for wake characteristics prediction of a horizontal-axis wind turbine

The core idea of the actuator line (AL) model is to simplify the horizontal-axis wind turbine (HAWT) into a line with force distributed along the radial direction. The body force on the AL is employed to simulate the effect of the HAWT on the flow field, and the Navier-Stokes (N-S) equation is solved to obtain the aerodynamic and wake characteristics of the HAWT. Recently, the AL model has been comprehensively implemented in the investigation of wind turbine wakes. However, the existing standard AL model ignores or inaccurately describes the nacelle effects, which have been proven to considerably affect the accuracy of the near wake simulation. This paper develops an actuator line-immersed boundary (AL-IB) hybrid approach for the HAWT with high-accuracy and low-computational cost to address the physics problem underlying here. The wind turbine adopts the AL model instead of the body-fitted mesh method, and the nacelle is realized by the immersed boundary (IB) method. The large eddy simulation (LES) with a new localized dynamic Smagorinsky (LDS) sub-grid scale (SGS) model is adopted to model the turbulence to improve simulation accuracy of the near wake, thereby forming a set of high-fidelity numerical simulation framework of the HAWT wake. Firstly, the simulation accuracy of the AL-IB hybrid approach is validated by comparing the mean wake velocity profiles and turbulent kinetic energy (TKE) profiles of the HAWT with the experimental measurement results of the NTNU “Blind test 1”. Furthermore, the research is extended to the wake difference of the HAWT under two different numerical methods (AL and AL-IB). The results show that the solver developed based on AL-IB hybrid approach has higher accuracy than the standard AL model, which provides a feasible way for the refined numerical simulation of the large-scale wind farm.

IMMERSED BOUNDARY METHODS FOR THERMOFLUIDS PROBLEMS

We review the progress in the development and application of immersed boundary (IB) methods to thermofluids problems achieved in the last three decades. The implementation of different heat transfer boundary conditions, ranging from Dirichlet, Neumann, and Robin to conjugate heat transfer, are discussed for continuous as well as discrete forcing immersed boundary methods. We review several key studies that developed and employed IB methods with stationary boundaries for a variety of heat transfer scenarios such as forced convection, natural or mixed convection, radiation, and combustion. The computational challenges associated with the approaches employed for thermofluids problems with moving boundaries are discussed in detail. These include problems with rigid bodies that move under the influence of fluid dynamic forces as well as flow-induced deformation of compliant bodies. We conclude the article by briefly discussing the implementation of immersed boundary methods in two emerging areas: bioheat transfer and high-speed compressible flows.

Modeling rigid filament interaction under oscillatory flow using immersed boundary method

The thread-like biological filament structures can enhance many processes such as fluid transport, locomotion, defence against foreign bodies etc. Researchers have tried to mimic these filament movements to improve fluid transport, mixing, drug delivery for microfluidic applications. These biological filaments can be modelled as slender rigid filaments which can be either active or passive. Active filaments move on their own thus causing a disruption in the fluid domain in close vicinity while passive filaments undergo motion depending upon the fluid flow past them. The dynamics of both active and passive filaments in low Reynolds number flow has immense research potential. In the case of passive filament, the nature of the incoming flow field is an important factor that affects the flow physics around the filament. This paper studies the flow dynamics of vertical and inclined passive rigid filaments in an oscillatory flow. The effect of change in flow conditions is studied by varying the Reynolds and Strouhal numbers. The simulation involves fluid-structure interaction which is implemented with the help of continuous forcing based immersed boundary (IB) method using finite volume discretization. This is a preliminary work towards modelling active filaments under different fluid flow conditions in channel in the near future.

LES of Turbulent Flow through Square Duct with Rounded Corners

In the present study, large eddy simulation (LES) for turbulent flows through square ducts with four rounded corners is performed using immersed boundary (IB) method. The geometrical shape of the duct is determined by an equation |y|α+ |z|α= Rα with a deformation parameter α. The distribution and magnitude of the mean secondary flow with α≧4 is almost close to those of the square-duct case. The center position of secondary circulation flows with α≦4 approaches the square-side bisector in contrast to the square-duct case. The profiles of the Reynolds stress and behaviour of the instantaneous turbulent structures in case of α≧4 are similar with those in square duct case.