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We give a weak formulation for solving the wave equation ( u ̈ = ∇ 2 u + f ) on a 2-dimensional immersed domain. In the spatial finite element discretization, boundaries do not conform to element boundaries. Dirichlet and Neumann boundary conditions are enforced weakly by Nitsche’s method. Additional penalty terms act on the gradient jumps over the interior faces of the elements cut by the boundary. These terms ensure a non-stiff temporal system, which makes it possible to perform explicit time stepping. We give optimal a priori error estimates: second order accuracy for u − u h and u ̇ − u ̇ h , and first order accuracy for ∇ ( u − u h ) in L 2 -norm. Numerical results verify this. [ABSTRACT FROM AUTHOR]

A computational tool is developed to capture the interaction of solid object with two-phase flow. The full two-dimensional Navier–Stokes equations are solved on a regular structured grid to resolve the flow field. The level set and the immersed boundary methods are used to capture the free surface of a fluid and a solid object, respectively. A two-step projection method along with Multi-Processing (OpenMP) is employed to solve the flow equations. The computational tool is verified based on numerical and experimental data with three scenarios: a cylinder falling into a rectangular domain due to gravity, transient vertical oscillation of a cylinder by releasing above its equilibrium position, and a dam breaking in the presence of a fixed obstacle. In the first two validation simulations, the accuracy of the immersed boundary method is verified. However the accuracy of the level set method while the computational tool can model the high density ratio is confirmed in the dam breaking simulation. The results obtained from the current method are in good agreement with experimental data and other numerical studies. The applicability of the current computational tool for the interaction of a buoy in a water wave tank with two types of waves; symmetrical and asymmetrical waves; has also been studied. [ABSTRACT FROM AUTHOR]

The immersed boundary method(IBM)was rapid developed in recent years because of its flexibility for complex configurations and moving bodies. Up to date, most of the resear-ches on IB method focused on the incompressible flow due to the limitation of the interpolation method. The current research applied the Choi’s power-law interpolation and the Crocce-Buse-mann relationship for the velocity and temperature approximation in the objective cells. The ghost cell method was also used for computing the variables at the cells in the body. The subson-ic/transonic NACA0012 airfoil compressible cases and 2D supersonic cylinder benchmark cases were chosen for method validation. The numerical result of these benchmark cases with proper parameter k compared well with the experimental data. The mesh convergence of the new method has also been proved. The analysis and discussion show that the method is suitable for compressi-ble flow simulation. [ABSTRACT FROM AUTHOR]

Complex fluid–structure interactions between elastic filaments, or cilia, immersed in viscous flows are commonplace in nature and bear important roles. Some biological systems have evolved to interpret flow-induced motion into signals for the purpose of feedback response. Given the challenges associated with extracting meaningful experimental data at this scale, there has been particular focus on the numerical study of these effects. Porous models have proven useful where cilia arrangements are relatively dense, but for more sparse configurations the dynamic interactions of individual structures play a greater role and direct modelling becomes increasingly necessary. The present study reports efforts towards explicit modelling of regularly spaced wall-mounted cilia using a lattice Boltzmann-immersed boundary method. Both steady and forced unsteady 2D channel flows at different Reynolds numbers are investigated, with and without the presence of a periodic array of elastic inextensible filaments. It is demonstrated that the structure response depends significantly on Reynolds number. For low Reynolds flow, the recirculation vortex aft of successive filaments is small relative to the cilia spacing and does not fully bridge the gap, in which case the structure lags the flow. At higher Reynolds number, when this gap is fully bridged the structure and flow move in phase. The trapping of vortices between cilia is associated with relatively lower wall shear stress. At low to intermediate Reynolds, vortex bridging is incomplete and large deflection is still possible, which is reflected in the tip dynamics and wall shear stress profiles. [ABSTRACT FROM AUTHOR]

This paper presents large-scale parallel computational fluid dynamics simulations for the Stratospheric Observatory for Infrared Astronomy (SOFIA). SOFIA is an airborne, 2.5-m infrared telescope mounted in an open cavity in the aft fuselage of a Boeing 747SP. These simulations focus on how the unsteady flow field inside and over the cavity interferes with the optical path and mounting structure of the telescope. A temporally fourth-order accurate Runge–Kutta, and a spatially fifth-order accurate WENO-5Z scheme were used to perform implicit large eddy simulations. An immersed boundary method provides automated gridding for complex geometries and natural coupling to a block-structured Cartesian adaptive mesh refinement framework. Strong scaling studies using NASA's Pleiades supercomputer with up to 32 k CPU cores and 4 billion computational cells show excellent scaling. Dynamic load balancing based on execution time on individual adaptive mesh refinement (AMR) blocks addresses irregular numerical cost associated with blocks containing boundaries. Limits to scaling beyond 32 k cores are identified, and targeted code optimisations are discussed. [ABSTRACT FROM AUTHOR]

This paper presents a two-dimensional coupled bonded particle and lattice Boltzmann method (BPLBM) developed to simulate the fluid-solid interactions in geomechanics. In this new technique, the bonded particle model is employed to describe the inter-particle movement and forces, and the bond between a pair of contacting particles is assumed to be broken when the tensile force or tangential force reaches a certain critical value. As a result the fracture process can be delineated based on the present model for the solid phase comprising particles, such as rocks and cohesive soils. In the meantime, the fluid phase is modelled by using the LBM, and the immersed moving boundary scheme is utilized to characterize the fluid-solid interactions. Based on the novel technique case studies have been conducted, which show that the coupled BPLBM enjoys substantially improved accuracy and enlarged range of applicability in characterizing the mechanics responses of the fluid-solid systems. Indeed such a new technique is promising for a wide range of application in soil erosion in Geotechnical Engineering, sand production phenomenon in Petroleum Engineering, fracture flow in Mining Engineering and fracture process in a variety of engineering disciplines. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

An embedded formulation for the simulation of immiscible multi-fluid problems is proposed. The method is particularly designed for handling gas-liquid systems. Gas and liquid are modeled using the Eulerian and the Lagrangian formulation, respectively. The Lagrangian domain (liquid) moves on top of the fixed Eulerian mesh. The location of the material interface is exactly defined by the position of the boundary mesh of the Lagrangian domain. The individual fluid problems are solved in a partitioned fashion and are coupled using a Dirichlet-Neumann algorithm. Representation of the pressure discontinuity across the interface does not require any additional techniques being an intrinsic feature of the method. The proposed formulation is validated, and its potential applications are shown. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The shock-capturing, non-hydrostatic, three-dimensional (3D) finite-volume model NHWAVE was originally developed to simulate wave propagation and landslide-generated tsunamis in finite water depth (Ma, G., Shi, F., Kirby, J. T., 2012. Ocean Model. 43-44, 22-35). The model is based on the incompressible Navier-Stokes equations, in which the z-axis is transformed to a σ -coordinate that tracks the bed and surface. As part of an ongoing effort to simulate waves in polar marginal ice zones (MIZs), the model has now been adapted to allow objects of arbitrary shape and roughness to float on or near its water surface. The shape of the underside of each floating object is mapped onto an upper σ -level slightly below the surface. In areas without floating objects, this σ -level continues to track the surface and bed as before. Along the sides of each floating object, an immersed boundary method is used to interpolate the effects of the object onto the neighboring fluid volume. Provided with the object’s shape, location, and velocity over time, NHWAVE determines the fluid fluxes and pressure variations from the corresponding accelerations at neighboring cell boundaries. The system was validated by comparison with analytical solutions and a VOF model for a 2D floating box and with laboratory measurements of wave generation by a vertically oscillating sphere. A steep wave simulation illustrated the high efficiency of NHWAVE relative to a VOF model. In a more realistic MIZ simulation, the adapted model produced qualitatively reasonable results for wave attenuation, diffraction, and scattering. [ABSTRACT FROM AUTHOR]

In this work, an approach is proposed for solving the 3D shallow water equations with embedded boundaries that are not aligned with the underlying horizontal Cartesian grid. A hybrid cut-cell/ghost-cell method is used together with a direction-splitting implicit solver: Ghost cells are used for the momentum equations in order to prescribe the correct boundary condition at the immersed boundary, while cut cells are used in the continuity equation in order to conserve mass. The resulting scheme is robust, does not suffer any time step limitation for small cut cells, and conserves fluid mass up to machine precision. Moreover, the solver displays a second-order spatial accuracy, both globally and locally. Comparisons with analytical solutions and reference numerical solutions on curvilinear grids confirm the quality of the method. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We model the three-dimensional interaction of compressible materials separated by sharp interfaces. We simulate fluid and hyperelastic solid flows in a fully Eulerian framework. The scheme is the same for all materials and can handle large deformations and frictionless contacts. Necessary conditions for hyperbolicity of the hyperelastic neohookean model in three dimensions are proved thanks to an explicit computation of the characteristic speeds. We present stiff multimaterial interactions including air–helium and water–air shock interactions, projectile-shield impacts in air and rebounds. [ABSTRACT FROM AUTHOR]

The effect of reducing submergence depth at a low and moderate Reynolds number flow is investigated using large eddy simulation (LES) around a matrix of cubes. The submerged body is modeled using an immersed boundaiy method, while the free-surface is accounted for using a moving mesh. Results show that for reducing the submergence depth, the forces acting on the cube reduce as the force variation increased. Variation in depth is also found to influence the level of damping and redistribution of turbulence near the free-surface boundaiy. Both submergence depth and Reynolds number are also found to influence the dominant free-surface signature and shedding frequencies from the cube. In the interobstacle region (IOR), the variation of Reynolds number and submergence depth is found to have little effect. [ABSTRACT FROM AUTHOR]

A Cartesian cut-cell method for viscous flows interacting with freely moving boundaries is presented. The method enables a sharp resolution of the embedded boundaries and strictly conserves mass, momentum, and energy. A new explicit Runge–Kutta scheme ( PC-RK ) is introduced by which the overall computational time is reduced by a factor of up to 2.5. The new scheme is a predictor–corrector type reformulation of a popular class of Runge–Kutta methods which substantially reduces the computational effort for tracking the moving boundaries and subsequently reinitializing the solver impairing neither stability nor accuracy. The structural motion is computed by an implicit scheme with good stability properties due to a strong-coupling strategy and the conservative discretization of the flow solver at the material interfaces. A new formulation for the treatment of small cut cells is proposed with high accuracy and robustness for arbitrary geometries based on a weighted Taylor-series approach solved via singular-value decomposition. The efficiency and the accuracy of the new method are demonstrated for several three-dimensional cases of laminar and turbulent particulate flow. It is shown that the new method remains fully conservative even for large displacements of the boundaries leading to a fast convergence of the fluid–solid coupling while spurious force oscillations inherent to this class of methods are effectively suppressed. The results substantiate the good stability and accuracy properties of the scheme even on relatively coarse meshes. [ABSTRACT FROM AUTHOR]

The present numerical study aims to identify the instability modes in the wake behind a transversely oscillating sphere with amplitude A =0.5 at Reynolds number Re =300. The governing equations are solved in the non-inertial frame using the immersed boundary method. The longitudinal thread-like structure is accompanied by asymmetric shedding before the onset of a “lock-in” regime. The wake is found to exhibit symmetric vortex shedding and organized chain like structures in the synchronized regime. Lesser flow inertia at a relatively low Re is dominated by the externally applied motion of the sphere resulting in negative energy transfer by the fluid to the sphere. In the synchronous regime different timing of vortex shedding and phases of coefficient of vortex with sphere motion demarcate two wake modes which have close resemblance with the modes found in induced vibration of a sphere. [ABSTRACT FROM AUTHOR]

Hydrodynamic focusing of particles is numerically studied by the immersed boundary – lattice Boltzmann method. Particle focusing entropy is proposed to quantitatively characterize processing performance and final results of hydrodynamic focusing. Simulations of hydrodynamic focusing in several straight microchannels are carried out to evaluate versatility of the focusing entropy. Time evolutions of focusing entropies and particle trajectories are analyzed contrastively. The results demonstrate that the focusing entropy is an effective scale to measure particles ordering degree and hydrodynamic focusing performance. Higher ordering degree determines lower focusing entropy, which indicates better focusing performance. Channel cross section, particle rigidness and channel Reynolds number are three major factors influencing focusing dynamics and final results. Rectangular microchannel is more advantageous than circular and square ones in hydrodynamic focusing. Particles of different rigidness in rectangular microchannel can be separated significantly with the flow mediation. Increasing channel Reynolds numbers can lead to higher efficiency and better focusing performance. [ABSTRACT FROM AUTHOR]

A new way of handling, simultaneously, porosity and bending resistance of a massive filament is proposed. Our strategy extends the previous methods where porosity was taken into account in the absence of bending resistance of the structure and overcomes related numerical issues. The new strategy has been exploited to investigate how porosity affects the stability of slender elastic objects exposed to a uniform stream. To understand under which conditions porosity becomes important, we propose a simple resonance mechanism between a properly defined characteristic porous time-scale and the standard characteristic hydrodynamic time-scale. The resonance condition results in a critical value for the porosity above which porosity is important for the resulting filament flapping regime, otherwise its role can be considered of little importance. Our estimation for the critical value of the porosity is in fairly good agreement with our DNS results. The computations also allow us to quantitatively establish the stabilizing role of porosity in the flapping regimes. [ABSTRACT FROM AUTHOR]

Efficient and profitable oil production is subject to make reliable predictions about reservoir performance. However, restricted knowledge about reservoir rock and fluid properties and its geometrical structure calls for history matching in which the reservoir model is calibrated to emulate the field observed history. Such an inverse problem yields multiple history-matched models, which might result in different predictions of reservoir performance. Uncertainty quantification narrows down the model uncertainties and boosts the model reliability for the forecasts of future reservoir behaviour. Conventional approaches of uncertainty quantification ignore large-scale uncertainties related to reservoir structure, while structural uncertainties can influence the reservoir forecasts more significantly compared with petrophysical uncertainty. Quantification of structural uncertainty has been usually considered impracticable because of the need for global regridding at each step of history matching process. To resolve this obstacle, we develop an efficient methodology based on Cartesian cut cell method that decouples the model from its representation onto the grid and allows uncertain structures to be varied as a part of history matching process. Reduced numerical accuracy due to cell degeneracies in the vicinity of geological structures is adequately compensated with an enhanced scheme of a class of locally conservative flux continuous methods (extended enriched multipoint flux approximation method or extended EMPFA). The robustness and consistency of the proposed hybrid Cartesian cut cell/extended EMPFA approach are demonstrated in terms of true representation of geological structures influence on flow behaviour. Significant improvements in the quality of reservoir recovery forecasts and reservoir volume estimation are presented for synthetic model of uncertain structures. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The immersed boundary method is extended to a diffuse solid–fluid interface alleviating the need of reconstruction near a solid wall. The scope of a solid surface, felt through a non zero volume fraction, is limited within one grid cell. The no-slip condition is realized in the limit of sufficiently finer mesh. A single universal equation is approximated in the entire domain using geometrically constructed volume fraction. A predictor–corrector type of time marching algorithm is used to solve the conservation equations where variables are defined in non-staggered arrangement. Second order approximation of volume integrals results in linear systems that are only a weak function of the object geometry. A Heaviside function based triangulation of the interfacial cells is found to produce highly accurate volume fractions. The computed data shows second order convergence with grid spacing while linearized body resolution does not have appreciable effect on the solution. The method is tested in problems that involve three modes of convective heat transfer with single/multiple, stationary/dynamic objects. Comparison with reported data reveals the accuracy, versatility and promise of the method for heat transfer on complex geometries. [ABSTRACT FROM AUTHOR]

The Immersed Boundary method is a simple, efficient, and robust numerical scheme for solving PDE in general domains, yet it only achieves first-order spatial accuracy near embedded boundaries. In this paper, we introduce a new high-order numerical method which we call the Immersed Boundary Smooth Extension (IBSE) method. The IBSE method achieves high-order accuracy by smoothly extending the unknown solution of the PDE from a given smooth domain to a larger computational domain, enabling the use of simple Cartesian-grid discretizations (e.g. Fourier spectral methods). The method preserves much of the flexibility and robustness of the original IB method. In particular, it requires minimal geometric information to describe the boundary and relies only on convolution with regularized delta-functions to communicate information between the computational grid and the boundary. We present a fast algorithm for solving elliptic equations, which forms the basis for simple, high-order implicit-time methods for parabolic PDE and implicit–explicit methods for related nonlinear PDE. We apply the IBSE method to solve the Poisson, heat, Burgers', and Fitzhugh–Nagumo equations, and demonstrate fourth-order pointwise convergence for Dirichlet problems and third-order pointwise convergence for Neumann problems. [ABSTRACT FROM AUTHOR]

We present a new method for the geometric reconstruction of elastic surfaces simulated by the immersed boundary method with the goal of simulating the motion and interactions of cells in whole blood. Our method uses parameter-free radial basis functions for high-order meshless parametric reconstruction of point clouds and the elastic force computations required by the immersed boundary method. This numerical framework allows us to consider the effect of endothelial geometry and red blood cell motion on the motion of platelets. We find red blood cells to be crucial for understanding the motion of platelets, to the point that the geometry of the vessel wall has a negligible effect in the presence of RBCs. We describe certain interactions that force the platelets to remain near the endothelium for extended periods, including a novel platelet motion that can be seen only in 3-dimensional simulations that we term "unicycling." We also observe red blood cell-mediated interactions between platelets and the endothelium for which the platelet has reduced speed. We suggest that these behaviors serve as mechanisms that allow platelets to better maintain vascular integrity. • R radial basis function-based modeling of blood cells in 3-dimensional immersed boundary whole blood simulations. • R simulations of blood flow over physiologically inspired endothelium. • R observation and characterization of novel interactions between red blood cells, platelets, and endothelium. [ABSTRACT FROM AUTHOR]

A novel membrane resonant droplet ejector (MRDE) for viscous industrial liquids is proposed in the paper. In MRDE, a vibrating nozzle is built to generate micro-droplets and the nozzle clogging could be reduced. The droplet jetting mechanism is studied by a three-dimensional (3D) lattice Boltzmann (LB) model. The effects of voltage amplitude and driving frequency on droplet volume and velocity are explored. Experimental Results show that low-viscosity water and viscous glycol could be jetted stably in parameters of 30 V/16 kHz and 60 V/20 kHz, respectively. Moreover, the droplet jetting of MRDE and in-situ observation is set up to analysis the droplet jetting characteristics. The critical thresholds for MRDE are 9.340 ≤ R e ≤ 17.65 , 3.653 ≤ W e ≤ 8.846 and 0.014 ≤ o h ≤ 0.411 , which has a wider printable range than traditional piezoelectric printheads. With the compact structure, MRDE is easy of integration for mass industrial applications compared with the pneumatic and needle-based ejectors. [Display omitted] • A novel membrane resonant droplet ejector (MRDE) is proposed for viscous industrial liquid. • The vibrating nozzle could reduce nozzle clogging. • The critical thresholds for MRDE is presented which extends the traditional printable range. • MRDE is easy of integration for mass industrial applications. [ABSTRACT FROM AUTHOR]

In the context of numerical simulations of multiphysics flows, accurate tracking of an interface and consistent computation of its geometric properties are crucial. In this paper, we investigate a level set technique that satisfies these requirements and ensures local third-order accuracy on the level set function (near the interface) and first-order accuracy on the curvature, even for long-time computations. The method is developed in a finite differences framework on Cartesian grids. As in usual level set strategies, reinitialization steps are involved. Several reinitialization algorithms are reviewed and mixed to design an accurate and fast reinitialization procedure. When coupled with a time evolution of the interface, the reinitialization procedure is performed only when there are too large deformations of the isocontours. This strategy limits the number of reinitialization steps and shows a good balance between accuracy and computational cost. Numerical results compare well with usual level set strategies and confirm the necessity of the reinitialization procedure, together with a limited number of reinitialization steps. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

We present a conservative method for the three-dimensional coupling between an inviscid compressible flow and a moving rigid solid. We consider an inviscid Euler fluid in conservative form discretized using a high-order monotonicity-preserving finite volume method with a directional operator splitting. An immersed boundary technique is employed through the modification of the finite volume fluxes in the vicinity of the solid. The method yields exact conservation of mass, momentum, and energy of the system, and also exhibits important consistency properties, such as conservation of uniform movement of both fluid and solid as well as the absence of numerical roughness on a straight boundary. The coupling scheme evaluates the fluxes on the fluid side and the forces and torques on the solid side only once every time step, ensuring the computational efficiency of the coupling. We present numerical results assessing the robustness of the method in the case of rigid solids with large displacements. [ABSTRACT FROM AUTHOR]

The method of regularized Stokeslets (MRS) is a numerical approach using regularized fundamental solutions to compute the flow due to an object in a viscous fluid where inertial effects can be neglected. The elastic object is represented as a Lagrangian structure, exerting point forces on the fluid. The forces on the structure are often determined by a bending or tension model, previously calculated using finite difference approximations. In this paper, we study spherical basis function (SBF), radial basis function (RBF), and Lagrange-Chebyshev parametric models to represent and calculate forces on elastic structures that can be represented by an open curve, motivated by the study of cilia and flagella. The evaluation error for static open curves for the different interpolants, as well as errors for calculating normals and second derivatives using different types of clustered parametric nodes, is given for the case of an open planar curve. We determine that SBF and RBF interpolants built on clustered nodes are competitive with Lagrange-Chebyshev interpolants for modeling twice-differentiable open planar curves. We propose using SBF and RBF parametric models within the MRS for evaluating and updating the elastic structure. Results for open and closed elastic structures immersed in a 2D fluid are presented, showing the efficacy of the RBF-Stokeslets method. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In the present paper we study a finite element method for the incompressible Stokes problem with a boundary immersed in the domain on which essential constraints are imposed. Such type of methods may be useful to tackle problems with complex geometries, interfaces such as multiphase flow and fluid–structure interaction. The method we study herein consists in locally refining elements crossed by the immersed boundary such that newly added elements, called subelements, fit the immersed boundary. In this sense, this approach is of a fitted type, but with an original mesh given independently of the location of the immersed boundary. We use such a subdivision technique to build a new finite element basis, which enables us to represent accurately the immersed boundary and to impose strongly Dirichlet boundary conditions on it. However, the subdivision process may imply the generation of anisotropic elements, which, for the incompressible Stokes problem, may result in the loss of inf–sup stability even for well-known stable element schemes. We therefore use a finite element approximation, which appears stable also on anisotropic elements. We perform numerical tests to check stability of the chosen finite elements. Several numerical experiments are finally presented to illustrate the capabilities of the method. The method is presented for two-dimensional problems. [ABSTRACT FROM AUTHOR]

The objective of this work is to present a conservative coupling method between an inviscid compressible fluid and a deformable structure undergoing large displacements. The coupling method combines a cut-cell Finite Volume method, which is exactly conservative in the fluid, and a symplectic Discrete Element method for the deformable structure. A time semi-implicit approach is used for the computation of momentum and energy transfer between fluid and solid, the transfer being exactly balanced. The coupling method is exactly mass-conservative (up to round-off errors in the geometry of cut-cells) and exhibits numerically a long-time energy-preservation for the coupled system. The coupling method also exhibits consistency properties, such as conservation of uniform movement of both fluid and solid, absence of numerical roughness on a straight boundary, and preservation of a constant fluid state around a wall having tangential deformation velocity. The performance of the method is assessed on test cases involving shocked fluid flows interacting with two and three-dimensional deformable solids undergoing large displacements. [ABSTRACT FROM AUTHOR]

Deterministic lateral displacement (DLD) arrays containing shaped pillars have been found to be more effective in biomedical sample separation. This study aims to numerically investigate the interplay between particles and microfluidic arrays, and to find out the key factors in determining the critical size of a DLD device with shaped pillars. A new formula is thus proposed to estimate the critical size for spherical particle separation in this kind of new DLD microfluidic arrays. The simulation results show that both rectangular and I-shaped arrays have considerably smaller critical sizes. The ratio of sub-channel widths is also found to play an important role in reducing the critical sizes. This paves a valuable way toward designing high-performance DLD microfluidic arrays. [ABSTRACT FROM PUBLISHER]

A higher-order immersed boundary method for solving the compressible Navier–Stokes equations is presented. The distinguishing feature of this new immersed boundary method is that the coefficients of the irregular finite-difference stencils in the vicinity of the immersed boundary are optimized to obtain improved numerical stability. This basic idea was introduced in a previous publication by the authors for the advection step in the projection method used to solve the incompressible Navier–Stokes equations. This paper extends the original approach to the compressible Navier–Stokes equations considering flux vector splitting schemes and viscous wall boundary conditions at the immersed geometry. In addition to the stencil optimization procedure for the convective terms, this paper discusses other key aspects of the method, such as imposing flux boundary conditions at the immersed boundary and the discretization of the viscous flux in the vicinity of the boundary. Extensive linear stability investigations of the immersed scheme confirm that a linearly stable method is obtained. The method of manufactured solutions is used to validate the expected higher-order accuracy and to study the error convergence properties of this new method. Steady and unsteady, 2D and 3D canonical test cases are used for validation of the immersed boundary approach. Finally, the method is employed to simulate the laminar to turbulent transition process of a hypersonic Mach 6 boundary layer flow over a porous wall and subsonic boundary layer flow over a three-dimensional spherical roughness element. [ABSTRACT FROM AUTHOR]

The behavior of a tandem of symmetric flapping wings immersed in a quiescent viscous fluid is numerically dissected. The attention focuses on the effect on the flight performance of a solid surface which idealizes the presence of the ground. A wide numerical campaign is carried out. The author demonstrates that the presence of a solid surface can drastically modify the lift force, thus giving a remarkable advantage for the vertical take-off. Therefore, a proper governing parameter is proposed, which accounts for the ratio between the initial gap from the solid surface and the length of the wing. [ABSTRACT FROM AUTHOR]

In this work, a ghost-cell immersed boundary method is proposed for the hydrodynamic response of earthquake excited dam-reservoirs. The numerical method employs a second order accurate two-step projection algorithm including compressibility effects in pressure field due to earthquake. The effects of reservoir bottom absorption are treated by introducing damping terms into the momentum equations. Hydrodynamic response of earthquake excited dam with a sloping face is simulated to demonstrate the accuracy of the present numerical method. Numerical results compared with previous numerical and analytical solutions show that the present immersed boundary method can accurately compute the hydrodynamic forces on inclined and curved dam faces including the effects of water compressibility and reservoir bottom absorption for the possibility of resonance. The proposed numerical method was shown to have significant advantages in computational time and memory usage for the hydrodynamic simulation of large dam-reservoirs with arbitrary geometries. Hydrodynamic forces on a double curvature arch dam subjected to real earthquake induced ground motion are also simulated to demonstrate the capability of the method. [ABSTRACT FROM AUTHOR]

An improved near-wall modeling for large-eddy simulation using the immersed boundary method is proposed. It is shown in this study that the existing near-wall modeling for the immersed boundary (IB) methods that imposes the velocity boundary condition at the IB node is not sufficient to enforce a correct wall shear stress at the IB node. A new method that imposes a shear stress condition through the modification of the subgrid scale-eddy viscosity at the IB node is proposed. In this method, the subgrid eddy viscosity at the IB node is modified such that the viscous flux at the face adjacent to the IB node correctly approximates the total shear stress. The method is applied to simulate the fully developed turbulent flows in a plane channel and a circular pipe. It is demonstrated that the new method improves the prediction of the mean velocity and turbulence stresses in comparison with the existing wall modeling based solely on the velocity boundary condition. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents a computational fluid–structure interaction analysis for free movements with a flapping wing in a quiescent fluid. We demonstrated the moving velocity of a flapping wing according to the phase difference between the angle of attack and the positional angle in the case of a fruit fly with a Reynolds number of 136. If we considered the moving velocity of the flapping wing, the physics were different from that of hovering flight of previous studies, which did not consider the propulsive velocity and presented the advanced rotation of the angle of attack as the best mechanism for propulsion force, as compared to symmetric rotation and delayed rotation. We found that symmetric rotation produced a better propulsion velocity with less fluctuation in other direction than the advanced rotation. The hairpin vortex generated at the end of a stroke did not clearly contribute to the enhancement of propulsion; the wake capture is considered to be one of the main enhancements of the advanced rotation in a previous studies. We studied the effects of the angle of attack to determine why the fruit fly uses a large angle of attack during a constant angle of attack period. Larger angles of attack produced greater propulsion velocities. Further, larger angles of attack did not generate greater peak force during the rotation of the angle of attack at the reversal of stroke, but they produced less fluctuation at the reversal of the stroke and greater force during the constant angle of attack period. [ABSTRACT FROM AUTHOR]

The coupled dynamics of multiple flexible filaments (also called monodimensional flags) flapping in a uniform fluid flow is studied numerically for the cases of a side-by-side arrangement, and an in-line configuration. The modal behaviour and hydrodynamical properties of the sets of filaments are studied using a Lattice Boltzmann–Immersed Boundary method. The fluid momentum equations are solved on a Cartesian uniform lattice while the beating filaments are tracked through a series of markers, whose dynamics are functions of the forces exerted by the fluid, the filaments flexural rigidity and the tension. The instantaneous wall conditions on the filaments are imposed via a system of singular body forces, consistently discretised on the lattice of the Boltzmann equation. The results exhibit several flapping modes for two and three filaments placed side-by-side and are compared with experimental and theoretical studies. The hydrodynamical drafting, observed so far only experimentally on configurations of in-line flexible bodies, is also revisited numerically in this work, and the associated physical mechanism is identified. In certain geometrical and structural configuration, it is found that the upstream body experiences a reduced drag compared to the downstream body, which is the contrary of what is encountered on rigid bodies (cars, bicycles). [ABSTRACT FROM AUTHOR]

Hydrodynamic focusing of particles instraight channel flows is studied by a hybrid immersed boundary (IB)-lattice Boltzmann (LB) method. In this method, the multi relaxation time (MRT)-LB equation with a force term is utilized to model the incompressible fluid flow over a regular Eulerian grid, and the IB method is employed to couple the finite element method based membrane model which represents the particle dynamics in fluid flow. The present method was validated by studying the three-dimensional top-lid-driven flow and the transient deformation of an initially spherical capsule under shear flow, and there were good agreements with previous theoretical and numerical results. Simulations of hydrodynamic dynamics in straight channels were performed to demonstrate the versatility of the hybrid method. The results show that Reynolds number and particle size are the important factors influencing focusing dynamics. The particles are focused onto their equilibrium positions at suitable Reynolds numbers of the channel flow. The higher the Reynolds number is, the more outward the equilibrium positions will be. The capability of the present method in studying the hydrodynamic separation of particles with different sizes and the transition of multi equilibrium positions were also discussed. This work also demonstrates the potential usefulness of IB-LBM in studying particle focusing, separation and sorting in confined flows. [ABSTRACT FROM AUTHOR]