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Jellyfish are one of the earliest example of animal that actively regulate swimming, but the mechanisms governing the locomotion are still a matter of research. Jellyfish obtain locomotion by activating the subumbrellar muscle layer. Sensory inputs trigger the contraction of the bell and the fluid-structure interaction effects driving locomotion. These have been extensively studied, whereas a representation of the full neuro-mechanical locomotion chain, with focus on the actuation-locomotion dynamics, has not been proposed yet. A model of such a complex multi-physical phenomenon would be informative for several purposes, ranging from the comprehension of behavioral aspects to the design of soft actuators and bio-inspired devices. In this regard, we propose a computational framework to address the coupled electrophysiological, elastic, and fluid aspects of the locomotion of the Scyphozoan group. This relies on the sequential coupling of segregated solvers, such that each sub-problem can be addressed with the most computationally effective technique. The spatial discretization is addressed by isogeometric analysis for the electrophysiological and elastic sub-problems, and by finite differences for the fluid sub-problem. The active strain approach allows to distribute the active contraction of radial and coronal muscle fibers following the biological architecture. The inherent multi-scale nature of the model is addressed by means of a nested grid approach and multiple time-advancement lines. In view of a reasonable computational effort, we enforce the hypothesis of axial symmetry limiting the number of degrees of freedom used in the simulations. The effectiveness of the scheme employed for each sub-problem is verified against different test-cases of engineering and biologic inspiration. Finally, we carry out an extensive comparison between the simulation output and the in-vivo measurements on a 3-cm specimen of Aurelia Aurita. • Formulation of an axisymmetric model for the straight propulsion of jellyfish. • Coupling of a neuronal excitation model with a fluid-structure computational framework. • Flexible handling of coupled sub-problems by staggered time schemes and nested grids. • Tuning an active-strain approach to replicate high-fidelity muscle contractions. [ABSTRACT FROM AUTHOR]

This paper proposes a 2D particle inertial focusing model by the immersed boundary–lattice Boltzmann method (IB-LBM), aiming to study the effects of particle shapes on their focusing state. First, as the validation, we investigated the inertial focusing of circular particles and got consistent focus positions with other previous reports. Then, the inertial focusing of the circle, rectangle, ellipse, and capsule particles were studied in detail. The results revealed that the particle shapes significantly influence the focusing positions, self-rotation, and running speed. At a given Reynolds number, the circular particle has a minimum average distance to the pipe center in the focus state, then follows the elliptical, capsular, and rectangular particles. The elliptical particle's self-rotation cycle is in approximately the cubed relation to the long-short axis ratio. Moreover, the rectangle particle runs fastest at the same Reynolds number, followed by capsule, ellipse, and circle particles. Our study and the above results can provide a significant reference for screening or separating particles with different shapes in microfluidic devices. [ABSTRACT FROM AUTHOR]

A 3-D simulation of red blood cells (RBCs) described as deformable cells in plasma flow is an indispensable element of blood flow analysis in the human vessels. To numerically investigate RBC motion in shear and Poiseuille flow, a mesoscale low dimensional-RBC method based on dissipative particle dynamics method has been successfully combined with a hybrid lattice Boltzmann method-immersed boundary method. This new model decreases the computational cost compared to the low dimensional RBC method and models the deformation of red blood cell accurately. To evaluate and validate the present numerical method, the relationship between the RBC diameter and the force value derived by the low dimensional-RBC method is compared with numerical and experimental data. In addition, as a benchmark test, the deformation index as the function of the capillary number of RBC motion through a narrow cylindrical tube has been performed. The behaviour of RBC in a shear flow and Poiseuille flow has been investigated. The present results demonstrated that this model is applied to reduce the computational cost, while maintaining the model precision. [ABSTRACT FROM AUTHOR]

Currently, most wind turbine performance analyses and simulations are performed assuming constant pitch and yaw angles during each rotation. Nevertheless, induced vibration or rotor imbalance can affect the pitch or yaw angle within each rotation. In this study, the effects of low-amplitude sinusoidal pitch angle oscillations of the blade on the performance of a wind turbine was investigated numerically by comparing it against the baseline (without pitch variations). Large eddy simulations were performed in which the motion of blades was handled by the curvilinear immersed boundary (CURVIB) method. The grid resolution was increased near the moving immersed boundaries using dynamic overset grids to resolve rotating blades. It was found that low-amplitude (up to 3 degrees) sinusoidal oscillations in the pitch angle negligibly affected the mean torque but increased its fluctuations and created distinct features in the wake of the turbine. In fact, the turbine's mean torque at wind speed of 15 m/s decreases from 1245 N.m to 1223 N.m, while its fluctuation (standard deviation) increases from 2.85 N.m to 7.94 N.m, with a dynamic pitch of 0.5 degrees and frequency of 3.6 Hz. [ABSTRACT FROM AUTHOR]

The Immersed Boundary (IB) method has been widely used to solve fluid-structure interaction problems, including those where the structure interacts with polymeric fluids. In this paper, we examine the convergence of one such scheme for a well known two-dimensional benchmark flow for the Oldroyd-B constitutive model, and we show that the traditional IB-based scheme fails to adequately capture the polymeric stress near to embedded boundaries. We analyze the reason for such failure, and we argue that this feature is not specific to the case study chosen, but a general feature of such methods due to lack of convergence in velocity gradients near interfaces. In order to remedy this problem, we build a different scheme for the Oldroyd-B system using the Immersed Boundary Smooth Extension (IBSE) scheme, which provides convergent viscous stresses near boundaries. We show that this modified scheme produces convergent polymeric stresses through the whole domain, including on embedded boundaries, and produces solutions in good agreement with known benchmarks.

The Immersed Boundary (IB) method has been widely used to solve fluid-structure interaction problems, including those where the structure interacts with polymeric fluids. In this paper, we examine the convergence of one such scheme for a well known two-dimensional benchmark flow for the Oldroyd-B constitutive model, and we show that the traditional IB-based scheme fails to adequately capture the polymeric stress near to embedded boundaries. We analyze the reason for such failure, and we argue that this feature is not specific to the case study chosen, but a general feature of such methods due to lack of convergence in velocity gradients near interfaces. In order to remedy this problem, we build a different scheme for the Oldroyd-B system using the Immersed Boundary Smooth Extension (IBSE) scheme, which provides convergent viscous stresses near boundaries. We show that this modified scheme produces convergent polymeric stresses through the whole domain, including on embedded boundaries, and produces solutions in good agreement with known benchmarks.

A non-equilibrium scheme and an optimized approximate force are proposed for the immersed boundary–lattice Boltzmann method (IB-LBM) to solve the fluid–structure interaction (FSI) equations. This new IB-LBM uses the discrete velocity distribution function and non-equilibrium distribution function to establish the interpolation operator and the spread operator at the mesoscopic scale. In the interpolation operator, we use the force model of LBM to derive a direct force with a simple form. In the spread operator, we give a theoretical proof with local second-order accuracy of the spread process using the non-equilibrium theory from the LBM. A non-iterative explicit force approximation scheme optimizes the direct force in that the streamlines have no penetration phenomenon, and the no-slip condition is strictly satisfied. Different from other schemes for the IB-LBM, we try to apply the non-equilibrium theory from the LBM to the IB-LBM and obtain good results. The explicit force obtained using the non-equilibrium scheme and then optimized via the non-iterative streamline correction equation simplifies the explicit direct force scheme and the original implicit scheme previously proposed but obtains a similar streamline correction result compared with the implicit method. Numerical tests prove the applicability and accuracy of this method in the simulation of complex conditions such as moving rigid bodies and deforming flexible bodies. [ABSTRACT FROM AUTHOR]

In this work, we employed the Immersed Boundary-Lattice Boltzmann Method (IB-LBM) to simulate the motion of a microparticle in a microchannel under the influence of a standing surface acoustic wave (SSAW). To capture the response of the target microparticle in a straight channel under the effect of the SSAW, in-house code was built in C language. The SSAW creates pressure nodes and anti-nodes inside the microchannel. Here, the target particle was forced to traverse toward the pressure node. A mapping mechanism was developed to accurately apply the physical acoustic force field in the numerical simulation. First, benchmarking studies were conducted to compare the numerical results in the IB-LBM with the available analytical, numerical, and experimental results. Next, several parametric studies were carried out in which the particle types, sizes, compressibility coefficients, and densities were varied. When the SSAW is applied, the microparticles (with a positive acoustic contrast factor) move toward the pressure node locations during their motion in the microchannel. Hence, their steady-state locations are controlled by adjusting the pressure nodes to the desired locations, such as the centerline or near the microchannel sidewalls. Moreover, the geometric parameters, such as radius, density, and compressibility of the particles affect their transient response, and the particles ultimately settle at the pressure nodes. To validate the numerical work, a microfluidic device was fabricated in-house in the cleanroom using lithographic techniques. Experiments were performed, and the target particle was moved either to the centerline or sidewalls of the channel, depending on the location of the pressure node. The steady-state placements obtained in the computational model and experiments exhibit excellent agreement and are reported. [ABSTRACT FROM AUTHOR]

Estimating the wind velocity field in an urban area is important for pedestrian comfort and safety, as the local wind velocities dictate the transport of heat and air pollution in urban environments. Therefore, it is an essential requirement to assess wind patterns when designing urban areas. Computational Fluid Dynamics (CFD) numerical solvers are usually employed to estimate the wind comfort in an urban area under different wind intensities and directions. However, CFD simulations are expensive in terms of time, especially when many scenarios are addressed to ensure safety and comfort for multiple conditions. Here, a CFD framework based on an immersed boundary approach to discretize the urban topography is developed and validated against experimental data in a wind tunnel and two different standard body-fitted mesh codes. The new solver employs a structured cartesian octree grid automatically generated from Lidar data of urban topographies. The advantages are eliminating the complex and time-consuming pre-processing of urban topographies and making the framework accessible to urban planners without CFD expertise. Furthermore, the code is equipped with GPU parallelization that further reduces the computational time. Provided that the best practice guidelines for urban simulations are satisfied, in particular at least 10 cells between two buildings, the code shows very good agreement in all the tests comprising of a simplified and real urban neighborhood highlighting the importance of accurately solving the complex terrain topography of an urban region when non-negligible elevation changes of the order of 20/40 meters are present. • Developing an advanced CFD model for urban design using immersed boundary methodology. • Eliminating the complex and time-consuming pre-processing of urban to pographies. • Validating of the model against independent experimental measures in wind tunnel. • Detailed comparison between IBM and two body-fitted mesh solvers. • Importance of including local elevation changes in the order of 20/40 m. [ABSTRACT FROM AUTHOR]

The density and viscosity ratios on partially liquid-filled sloshing with baffle have been investigated numerically in this study. As the key to success in the present simulation, the Coupled Level Set and the Volume of Fluid (CLSVOF) method and the Immersed Boundary (IB) method are used to capture gas/liquid and fluid/structure interfaces, respectively. Within the CLSVOF method, surface normal in weighting factors is calculated by the level set function, resulting in a more accurate solution. Furthermore, the Tangent of Hyperbola for INterface Capturing (THINC) coupled with the Weighted Linear Interface Calculation (WLIC) scheme is used for capturing moving interface. As a standard practice, we first validate the code by comparing it with experimental results of liquid sloshing, which involves large deformation of interface. In addition to the validation study of the present method, the problems of liquid sloshing with baffle are investigated to understand kinematics and dynamics behaviors under different density and viscosity ratios. [ABSTRACT FROM AUTHOR]

Currently, most wind turbine performance analyses and simulations are performed assuming constant pitch and yaw angles during each rotation. Nevertheless, induced vibration or rotor imbalance can affect the pitch or yaw angle within each rotation. In this study, the effects of low-amplitude sinusoidal pitch angle oscillations of the blade on the performance of a wind turbine was investigated numerically by comparing it against the baseline (without pitch variations). Large eddy simulations were performed in which the motion of blades was handled by the curvilinear immersed boundary (CURVIB) method. The grid resolution was increased near the moving immersed boundaries using dynamic overset grids to resolve rotating blades. It was found that low-amplitude (up to 3 degrees) sinusoidal oscillations in the pitch angle negligibly affected the mean torque but increased its fluctuations and created distinct features in the wake of the turbine. In fact, the turbine’s mean torque at wind speed of 15 m/s decreases from 1245 N.m to 1223 N.m, while its fluctuation (standard deviation) increases from 2.85 N.m to 7.94 N.m, with a dynamic pitch of 0.5 degrees and frequency of 3.6 Hz.

We propose and analyze computationally a new fictitious domain method, based on higher order space‐time finite element discretizations, for the simulation of the nonstationary, incompressible Navier–Stokes equations on evolving domains. The physical domain is embedded into a fixed computational mesh such that arbitrary intersections of the moving domain's boundaries with the background mesh occur. The potential of such cut finite element techniques for higher order space‐time finite element methods has rarely been studied in the literature so far and deserves further elucidation. The key ingredients of the approach are the weak formulation of Dirichlet boundary conditions by Nitsche's method, the flexible and efficient integration over all types of intersections of cells by moving boundaries and the spatial extension of the discrete physical quantities to the entire computational background mesh including fictitious (ghost) subdomains of fluid flow. Thereby, an expensive remeshing and adaptation of the sparse matrix data structure are avoided and the computations are accelerated. To prevent spurious oscillations caused by irregular intersections of mesh cells, a penalization, defining also implicitly the extension to ghost domains, is added. These techniques are embedded in an arbitrary order, discontinuous Galerkin discretization of the time variable and an inf‐sup stable discretization of the spatial variables. The parallel implementation of the matrix assembly is described. The optimal order convergence properties of the algorithm are illustrated in a numerical experiment for an evolving domain. The well‐known 2d benchmark of flow around a cylinder as well as flow around moving obstacles with arising cut cells and fictitious domains are considered further. [ABSTRACT FROM AUTHOR]

An immersed boundary fast integration methodology featured by a consistent weight learning is proposed to accelerate Galerkin meshfree computation. In the proposed approach, the problem domain is embedded in a rectangular spatial domain discretized by regular distributions of meshfree nodes and integration sampling points with virtual integration cells. A trimming operation of the rectangular spatial domain by the physical problem boundary with nodal discretization yields the discrete model for meshfree computation, where the integration sampling points are grouped into the interior sampling points and the near boundary sampling points which form a training set. For the interior sampling points, a natural alignment between the influence domains of meshfree shape functions and virtual integration cells can be easily realized through employing integer support sizes, which ensures a satisfactory accuracy for the basis degree correspondent normal order Gauss integration. The background cells for the domain integration are completely avoided, which greatly simplifies the preprocessing for numerical integration. Meanwhile, a machine learning module is devised to optimize the weights of near boundary integration sampling points. The key step to construct this machine learning module for weight optimization is the selection of the variational integration consistency condition as the loss function, which guarantees the convergence of Galerkin meshfree formulation. The accuracy and efficiency of the proposed weight learning immersed boundary fast integration methodology is thoroughly validated through numerical results. [ABSTRACT FROM AUTHOR]

[Display omitted] • The new modification of wall boundary condition in the IB method to improve the accuracy of numerical simulations. • Investigation of unequal fiber sizes on the collection efficiency and quality factor and comparing it with equal fiber sizes. • Investigation of the number of rows on collection efficiency and quality factor in the filter with equal and unequal fibers. • Finding the optimal approach to enhance filter performance at different Stokes numbers. Fibrous filters are widely used to remove particles from gas-solid flows. In the present research, the potential to enhance the collection efficiency of fibrous filters was investigated by increasing the number of filter rows and using varying sizes of square fibers. A two dimensional model was used to simulate the transport and deposition of particles, employing the developed Eulerian-Lagrangian solver coupled with the Immersed Boundary (IB) method. Several structures of filter fibers including the equal and unequal fibers in the arrangement of two, four and six rows were investigated. The results showed increasing the size difference between large and small fibers in the filter media increases the collection efficiency and pressure drop simultaneously. To find the effective structure of enhancing the filter performance, the quality factor was considered. The results of quality factor showed that using unequal fibers has an advantage over increasing the number of rows in an equal-fiber structure to increase the collection efficiency. Therefore, using the unequal fibers with the growth rate of 1.2 to 1.4, are more effective than increasing the number of rows in equal fiber structures. [ABSTRACT FROM AUTHOR]

Red blood cells (RBCs) are able to undergo significant shape changes when they flow in the microcirculation thanks to their ability to withstand large deformations. In this context, particular attention should be dedicated to the role of RBC deformability and membrane viscosity on the RBC fluid dynamics at the microscale. Experimentally investigating the impact of the RBC viscoelastic properties is challenging due to the overlapping effects of multiple viscous dissipation sources, making high-fidelity cell-resolved simulations crucial. This work focuses on (i) developing a fluid–structure interaction framework to predict the RBC dynamics at the microscale and (ii) evaluating the impact of the cell viscoelastic properties such as deformability, viscosity contrast and membrane viscosity on the RBC transport in bounded shear flow. An incompressible Lattice Boltzmann method (LBM) is adopted to resolve the fluid dynamics inside and outside the RBCs, alongside with a tagging procedure to assign a viscosity contrast between the cytoplasm and the plasma. A finite-element model coupled with the Standard-Linear-Solid model describes the viscoelastic behavior of the RBC membrane. The interaction between the fluid and the RBCs is enforced by means of an immersed-boundary (IB) technique. Benchmark tests are performed to simulate the deformation of a purely elastic capsule, a viscoelastic capsule, and a viscoelastic RBC subjected to a bounded shear flow. A good agreement is found between the present results and literature data obtained with similar IB-LBM methods. The analysis of the impact of the cell viscoelasticity on the RBC dynamics highlights the importance of including the membrane viscosity and a physiological viscosity contrast in the RBC model, especially when investigating the RBC time-dependent behavior. Overall, our findings revealed that adding a viscous term in the RBC model significantly impacts the migration timescale but has a minor effect on the RBC final equilibrium position. • A Lattice Boltzmann-Finite Element framework for red blood cell transport is proposed. • A method is used to tag the outer plasma and the RBC inner cytoplasm viscosity. • The Standard-Linear-Solid model is adapted to account for the RBC membrane viscosity. • The framework predicts RBC stretching, motion and migration in bounded shear flow. • Physiological viscoelastic properties are needed to predict the RBC migration. [ABSTRACT FROM AUTHOR]

Solid–fluid force models are essential to efficiently model multiple industrial apparatuses such as fluidized beds, spouted beds, and slurry transport. They are generally built using strong hypotheses (e.g. fully developed flow and no relative motion between particles) that affect their accuracy. We study the effect of these hypotheses on particle dynamics using the sedimentation of a pair of particles. We develop new induced drag, lift and torque models for pairs of particles based on an artificial neural network (ANN) regression. The fluid force model covers a range of Reynolds numbers of 0.1 to 100 and particle centroid distance of up to 9 particle diameters. The ANN model uses 3475 computational fluid dynamics (CFD) simulation results as the training data set. Using this fluid force model, we develop a reduced-order model (ROM), which includes the virtual mass force, the Meshchersky force, the history force, the lubrication force, and the Magnus force. Using the results of a resolved computational fluid dynamics coupled with a discrete element method (CFD-DEM) model as a reference, we analyze the discrepancies between the ROM and CFD-DEM results for a series of sedimentation cases that cover particle Archimedes number from 20 to 2930 and particle to fluid density ratio of 1.5 to 1000. The errors primarily stem from particle history interactions that are not accounted for by the fully developed flow hypothesis. The importance of this effect on the dynamic of two particles is isolated and it is shown that it is more pronounced in cases with a lower particle-to-fluid density ratio (such as solid–liquid cases). This work underscores the need for more research on these effects to increase the precision of solid–fluid force models for small particle-to-fluid density ratios (1.5). [Display omitted] • ANN pairwise hydrodynamic force model for Reynolds number ∈ [ 1 , 100 ] used in a ROM. • Compare ROM's performance with resolved CFD-DEM for 16 sedimentation cases. • Analyze sedimentation dynamics across density ratios of 1.5 to 1000. • Demonstrate the importnace of the particle interaction history's effect on their dynamics. • Emphasize interaction history's importance at lower particle-to-fluid density ratios. [ABSTRACT FROM AUTHOR]

Qualitative description of stressing energies between grinding beads/media in wet stirred media mills at different operation settings could provide a comprehensive understanding of the process parameter influence. In the current work, a modeling approach for wet stirred media mills is described, employing a coupled CFD-DEM framework. This study employs an immersed boundary methodology to emulate the pin-type stirrer rotation in CFD and utilizes a hydrodynamic lubrication force to model the squeezing out and sucking in of fluid between two grinding bead surfaces. The results indicate the influence of process parameters such as the stirrer rotation speed, bead diameter, and bead filling degree. Key findings include the necessity of coupled CFD-DEM with lubrication (i.e., comparison of results from DEM, and coupled CFD-DEM simulations). Dependence of system dynamics on the fluid properties is numerically analyzed using the properties of water–glycerol mixtures. [Display omitted] • A coupled CFD-DEM framework to model the wet stirred media mills is presented. • An immersed boundary methodology is used to emulate the stirrer rotation in CFD. • Fluid interaction between grinding bead surfaces is modeled using lubrication force. • The effect of process parameters on the system behavior is described. • Water-glycerol mixture properties are used to analyze the fluid effect. [ABSTRACT FROM AUTHOR]

Bridge pier scour was simulated by a coupled fully 3D hydro-morphodynamic model and validated against 24 experimental datasets for a combination of different pier shapes, approach velocities and sediment bed material. The proposed numerical model adopts an Eulerian multi-fluid model to account for rolling and saltating particles and computes bed shear stresses from implicit wall functions. ANSYS Fluent solved the continuity and Navier-Stokes equations, closed by the RSM turbulence model, which were coupled with sediment transport submodels by source terms. Numerical instabilities were addressed in the sediment transport submodels which were ascribed to the fine mesh resolution required to resolve the crucial horseshoe vortex and the diffusion resulting from the discretization of the Immersed Boundary method. [ABSTRACT FROM AUTHOR]

We revisit the Partially-Saturated-Cells method (PSC) in the context of incompressible single-phase flows past stationary and moving bodies. This methodology adds a solid collision operator to the Lattice Boltzmann Equation, resulting in a unified evolution equation everywhere in the domain that suitably accounts for the boundary conditions. The unified evolution equation, which also allows for a smooth transition from solid cells to fluid cells, is dictated by the solid volume fraction, obtained using a simple geometric approach. We prove that the PSC approach exhibits nominal second-order accuracy in presence of straight and curved boundaries for pressure, although spatial order of accuracy in velocity degrades to first-order. Our analysis also reveals that PSC is approximately discretely conservative in the incompressible limit with the mass conservation errors being dependent on the lattice size and relaxation time. For simulations involving moving body problems, the method is found to introduce acceptable level of spurious force oscillations, which rapidly decrease with increasing grid resolution. To the best of the authors' knowledge, the present investigations pertaining to discrete conservation and spurious force oscillations in the PSC approach have never been discussed in literature. Extensive numerical experiments are performed involving both stationary and moving bodies, with imposed and induced motion, to assess the applicability of the PSC approach. Our findings illustrate that the inclusion of added mass effects are important for accurate force and torque computations in case of accelerating solids. Numerical investigations, that include unsteady flows featuring three degrees-of-freedom fluid-particle interactions clearly highlight the ability of the PSC approach in resolving complex hydrodynamical phenomena. This in-depth evaluation of the PSC approach conclusively demonstrates its efficacy as a promising computational framework for efficient and robust computations of incompressible fluid flows over a range of flow scenarios. [ABSTRACT FROM AUTHOR]

We present a formulation for the weak enforcement of continuity conditions at material interfaces in high‐order problems by means of Nitsche's method, which is particularly suited for unfitted discretizations. This formulation is extended to impose generalized periodicity conditions at the unit cell boundaries of periodic structures. The formulation is derived for flexoelectricity, a high‐order electromechanical coupling between strain gradient and electric field, mathematically modeled as a coupled system of fourth‐order PDEs. The design of flexoelectric devices requires the solution of high‐order boundary value problems on complex material architectures, including general multimaterial arrangements. This can be efficiently achieved with an immersed boundary B‐splines approach. Furthermore, the design of flexoelectric metamaterials also involves the analysis of periodic unit cells with generalized periodicity conditions. Optimal high‐order convergence rates are obtained with an unfitted B‐spline approximation, confirming the reliability of the method. The numerical simulations illustrate the usefulness of the proposed approach toward the design of functional electromechanical multimaterial devices and metamaterials harnessing the flexoelectric effect. [ABSTRACT FROM AUTHOR]

A non-equilibrium scheme and an optimized approximate force are proposed for the immersed boundary–lattice Boltzmann method (IB-LBM) to solve the fluid–structure interaction (FSI) equations. This new IB-LBM uses the discrete velocity distribution function and non-equilibrium distribution function to establish the interpolation operator and the spread operator at the mesoscopic scale. In the interpolation operator, we use the force model of LBM to derive a direct force with a simple form. In the spread operator, we give a theoretical proof with local second-order accuracy of the spread process using the non-equilibrium theory from the LBM. A non-iterative explicit force approximation scheme optimizes the direct force in that the streamlines have no penetration phenomenon, and the no-slip condition is strictly satisfied. Different from other schemes for the IB-LBM, we try to apply the non-equilibrium theory from the LBM to the IB-LBM and obtain good results. The explicit force obtained using the non-equilibrium scheme and then optimized via the non-iterative streamline correction equation simplifies the explicit direct force scheme and the original implicit scheme previously proposed but obtains a similar streamline correction result compared with the implicit method. Numerical tests prove the applicability and accuracy of this method in the simulation of complex conditions such as moving rigid bodies and deforming flexible bodies.

In this work, we employed the Immersed Boundary-Lattice Boltzmann Method (IB-LBM) to simulate the motion of a microparticle in a microchannel under the influence of a standing surface acoustic wave (SSAW). To capture the response of the target microparticle in a straight channel under the effect of the SSAW, in-house code was built in C language. The SSAW creates pressure nodes and anti-nodes inside the microchannel. Here, the target particle was forced to traverse toward the pressure node. A mapping mechanism was developed to accurately apply the physical acoustic force field in the numerical simulation. First, benchmarking studies were conducted to compare the numerical results in the IB-LBM with the available analytical, numerical, and experimental results. Next, several parametric studies were carried out in which the particle types, sizes, compressibility coefficients, and densities were varied. When the SSAW is applied, the microparticles (with a positive acoustic contrast factor) move toward the pressure node locations during their motion in the microchannel. Hence, their steady-state locations are controlled by adjusting the pressure nodes to the desired locations, such as the centerline or near the microchannel sidewalls. Moreover, the geometric parameters, such as radius, density, and compressibility of the particles affect their transient response, and the particles ultimately settle at the pressure nodes. To validate the numerical work, a microfluidic device was fabricated in-house in the cleanroom using lithographic techniques. Experiments were performed, and the target particle was moved either to the centerline or sidewalls of the channel, depending on the location of the pressure node. The steady-state placements obtained in the computational model and experiments exhibit excellent agreement and are reported.

Simulation of the dynamic behavior of mitral valve closure could improve clinical treatment by predicting surgical procedures outcome. We propose here a method to achieve this goal by using the immersed boundary method. In order to go towards patient-based simulation, we tailor our method to be adapted to a valve extracted from medical image data. It includes investigating segmentation process, smoothness of geometry, case setup and the shape of the left ventricle. We also study the influence of leaflet tissue anisotropy on the quality of the valve closure by comparing with an isotropic model. As part of the anisotropy analysis, we study the influence of the principal material direction by comparing methods to obtain them without dissection. Results show that our method can be scaled to various image-based data. We evaluate the mitral valve closure quality based on measuring bulging area, contact map, and flow rate. The results show also that the anisotropic material model more precisely represents the physiological characteristics of the valve tissue. Furthermore, results indicate that the orientation of the principal material direction plays a role in the effectiveness of the valve seal., Competing Interests: Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2024 Elsevier B.V. All rights reserved.)

We use computational fluid dynamics (CFD) to simulate blood flow in intracranial aneurysms (IAs). Despite ongoing improvements in the accuracy and efficiency of body‐fitted CFD solvers, generation of a high quality mesh appears as the bottleneck of the flow simulation and strongly affects the accuracy of the numerical solution. To overcome this drawback, we use an immersed boundary method. The proposed approach solves the incompressible Navier–Stokes equations on a rectangular (box) domain discretized using uniform Cartesian grid using the finite element method. The immersed object is represented by a set of points (Lagrangian points) located on the surface of the object. Grid local refinement is applied using an automated algorithm. We verify and validate the proposed method by comparing our numerical findings with published experimental results and analytical solutions. We demonstrate the applicability of the proposed scheme on patient‐specific blood flow simulations in IAs. [ABSTRACT FROM AUTHOR]

A highly accurate and fully implicit algorithm for analyses of transient effects in heated grooved channels, including chaotic responses and transition to secondary states, has been developed. The algorithm can handle pattern interaction problems arising from combinations of geometric and heating patterns which are expected to be beneficial in the development of energy efficient stirring systems. The algorithm uses spectral spatial discretization and up to sixth‐order temporal discretization, providing the means to deliver machine accuracy. The spatial discretization relies on a combination of Chebyshev and Fourier expansions, guaranteeing very good resolution in the vicinity of the grooved walls. The enforcement of boundary conditions along the irregular boundaries is carried out using the immersed boundary conditions. The overall discretization leads to a gridless algorithm and provides the geometric flexibility required for efficient analyses of multitude of topography patterns. Extensive testing demonstrates that the algorithm achieves the theoretically predicted accuracy. [ABSTRACT FROM AUTHOR]

SUMMARY: Cable subsystems characterized by long, slender, and flexible structural elements are featured in numerous engineering systems. In each of them, interaction between an individual cable and the surrounding fluid is inevitable. Such a fluid‐structure interaction has received little attention in the literature, possibly due to the inherent complexity associated with fluid and structural semidiscretizations of disparate spatial dimensions. This article proposes an embedded boundary approach for filling this gap, where the dynamics of the cable are captured by a standard finite element representation 𝒞 of its centerline, while its geometry is represented by a discrete surface ∑h that is embedded in the fluid mesh. The proposed approach is built on master‐slave kinematics between 𝒞 and ∑h, a simple algorithm for computing the motion/deformation of ∑h based on the dynamic state of 𝒞, and an energy‐conserving method for transferring to 𝒞 the loads computed on ∑h. Its effectiveness is demonstrated for two highly nonlinear applications featuring large deformations and/or motions of a cable subsystem and turbulent flows: an aerial refueling model problem, and a challenging supersonic parachute inflation problem. The proposed approach is verified using numerical data and validated using real flight data. [ABSTRACT FROM AUTHOR]

We adopt a numerical method to solve Poisson's equation on a fixed grid with embedded boundary conditions, where we put a special focus on the accurate representation of the normal gradient on the boundary. The lack of accuracy in the gradient evaluation on the boundary is a common issue with low-order embedded boundary methods. Whereas a direct evaluation of the gradient is preferable, one typically uses post-processing techniques to improve the quality of the gradient. Here, we adopt a new method based on the discontinuous-Galerkin (DG) finite element method, inspired by the recent work of [A.J. Lew and G.C. Buscaglia. A discontinuous-Galerkin-based immersed boundary method. International Journal for Numerical Methods in Engineering, 76:427-454, 2008]. The method has been enhanced in two aspects: firstly, we approximate the boundary shape locally by higher-order geometric primitives. Secondly, we employ higher-order shape functions within intersected elements. These are derived for the various geometric features of the boundary based on analytical solutions of the underlying partial differential equation. The development includes three basic geometric features in two dimensions for the solution of Poisson's equation: a straight boundary, a circular boundary, and a boundary with a discontinuity. We demonstrate the performance of the method via analytical benchmark examples with a smooth circular boundary as well as in the presence of a singularity due to a re-entrant corner. Results are compared to a low-order extended finite element method as well as the DG method of [1]. We report improved accuracy of the gradient on the boundary by one order of magnitude, as well as improved convergence rates in the presence of a singular source. In principle, the method can be extended to three dimensions, more complicated boundary shapes, and other partial differential equations.

This work extends the characteristic-based volume penalization method, originally developed and demonstrated for compressible subsonic viscous flows in (J. Comput. Phys. 262, 2014), to a hyperbolic system of partial differential equations involving complex domains with moving boundaries. The proposed methodology is shown to be Galilean-invariant and can be used to impose either homogeneous or inhomogeneous Dirichlet, Neumann, and Robin type boundary conditions on immersed boundaries. Both integrated and non-integrated variables can be treated in a systematic manner that parallels the prescription of exact boundary conditions with the approximation error rigorously controlled through an a priori penalization parameter. The proposed approach is well suited for use with adaptive mesh refinement, which allows adequate resolution of the geometry without over-resolving flow structures and minimizing the number of grid points inside the solid obstacle. The extended Galilean-invariant characteristic-based volume penalization method, while being generally applicable to both compressible Navier-Stokes and Euler equations across all speed regimes, is demonstrated for a number of supersonic benchmark flows around both stationary and moving obstacles of arbitrary shape. [ABSTRACT FROM AUTHOR]

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.

This paper presents a new stabilized form of incompressible Navier–Stokes equations for weak enforcement of Dirichlet boundary conditions at immersed boundaries. The boundary terms are derived via the Variational Multiscale (VMS) method which involves solving the fine-scale variational problem locally within a narrow band along the boundary. The fine-scale model is then variationally embedded into the coarse-scale form that yields a stabilized method which is free of user defined parameters. The derived boundary terms weakly enforce the Dirichlet boundary conditions along the immersed boundaries that may not align with the inter-element edges in the mesh. A unique feature of this rigorous derivation is that the structure of the stabilization tensor which emerges is naturally endowed with the mathematical attributes of area-averaging and stress-averaging. The method is implemented using 4-node quadrilateral and 8-node hexahedral elements. A set of 2D and 3D benchmark problems is presented that investigate the mathematical attributes of the method. These test cases show that the proposed method is mathematically robust as well as computationally stable and accurate for modeling boundary layers around immersed objects in the fluid domain. [ABSTRACT FROM AUTHOR]

A spectrally accurate and very efficient algorithm suitable for prediction of pressure losses in heated grooved channels has been developed. Heating and topography patterns are used to create spatial flow modulations resulting in a pattern interaction problem. Search for combinations of patterns resulting in the reduction of pressure losses requires development of a very accurate and efficient algorithm. The proposed algorithm uses a combination of the Fourier expansions in the horizontal directions and the Chebyshev expansions in the vertical direction to provide a very good resolution of the near wall regions. The immersed boundary conditions (IBC) method is used to enforce flow boundary conditions at the geometrically irregular boundaries. The resulting gridless discretization can be easily adapted to handle a wide range of topography patterns. Various tests demonstrate that the algorithm delivers spectral accuracy and can provide machine level accuracy. Comparisons with the standard open‐source codes based either on the finite volume or on the spectral element discretization demonstrate several orders of magnitude better efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this article, high‐order finite difference solutions of the exact potential‐flow problem for nonlinear water waves are developed which treat both the free surface and the uneven sea bottom boundary conditions using an immersed boundary method (IBM). The convergence, accuracy, and stability of this approach is first established for the linear problem, using various orders of scheme and different grid discretization strategies. The nonlinear wave problem on a flat bottom is then considered, and the solutions are compared with the highly accurate stream function theory solution. The convergence performance of the numerical solution for this nonlinear wave problem is established. Finally, linear wave shoaling and nonlinear wave propagation over a submerged bar are also tested. A preconditioned iterative solution strategy is also developed and shown to provide optimal scaling of the solution effort with increasing number of unknowns. Compared with existing free surface tracking methods, the IBM retains the same level of accuracy and stability when solving the linear problem. For the nonlinear problem, the IBM behaves reasonably in terms of accuracy, but generally with slightly higher computational effort. When it comes to the wave–body interaction problem, it is expected that the IBM will be advantageous compared with the σ‐transform method, since it removes the necessity of constructing an artificial continuous free‐surface inside the body. [ABSTRACT FROM AUTHOR]

A CFD-DEM-IBM method with high resolution is proposed based on the immersed boundary method（IBM） to describe the sedimentation phenomenon accurately and to investigate the underlying influence mechanism between fluid and particles in dense fluid-particle systems. The fluid phase is analyzed by the computational fluid dynamics（CFD） while the discrete element method（DEM） is utilized to simulate the motion of individual particles. The IBM is introduced to tackle the moving boundaries of particles and the interaction forces between fluid and particles are considered by an extra body force added to the Navier-Stokes momentum equation. The strongly coupled fluid-solid system is then achieved through the successive iterative scheme where several iterations are required within each time step until the convergence conditions are exactly satisfied. Sedimentations of one, two and multiple particles are simulated, which reveal that the proposed method could obtain the accurate interaction forces among discrete particles and fluid along with the fully resolved fluid phase around the particles compared with the conventional unresolved CFD-DEM method. The agreement between present results and previous work demonstrates the accuracy and validity of the presented method, and the applicability together with the superiority of the CFD-DEM-IBM method is also proved when the dense particulate flows occur. [ABSTRACT FROM AUTHOR]

We recently developed the open-source library tIGAr, which extends the FEniCS finite element automation framework to isogeometric analysis. The present contribution demonstrates the utility of tIGAr in complex problems by applying it to immersogeometric fluid–structure interaction (FSI) analysis. This application is implemented as the new open-source library CouDALFISh (Coupling, via Dynamic Augmented Lagrangian, of Fluids with Immersed Shells, pronounced "cuttlefish"), which uses the dynamic augmented Lagrangian (DAL) method to couple fluid and shell structure subproblems. The DAL method was introduced previously, over a series of papers largely focused on heart valve FSI, but an open-source implementation making extensive use of automation to compile numerical routines from high-level mathematical descriptions brings newfound transparency and reproducibility to these earlier developments on immersogeometric FSI analysis. The portions of CouDALFISh that do not use code generation also illustrate how a framework like FEniCS remains useful even when some functionality is outside the scope of its standard workflow. This paper summarizes the workings of CouDALFISh and documents a variety of benchmarks demonstrating its accuracy. Although the implementation emphasizes transparency and extensibility over performance, it is nonetheless demonstrated to be sufficient to simulate 3D FSI of an idealized aortic heart valve. Source code will be maintained at https://github.com/david-kamensky/CouDALFISh. [ABSTRACT FROM AUTHOR]