A large eddy simulation of flows around an underwater vehicle model using an immersed boundary method

A large eddy simulation （LES） of the flows around an underwater vehicle model at intermediate Reynolds numbers is performed. The underwater vehicle model is taken as the DARPA SUBOFF with full appendages, where the Reynolds number based on the hull length is 1.0x 105, An immersed boundary method based on the moving-least-squares reconstruction is used to handle the complex geometric boundaries. The adaptive mesh refinement is utilized to resolve the flows near the hull, The parallel scalabilities of the flow solver are tested on meshes with the number of cells varying from 50 million to 3.2 billion, The parallel solver reaches nearly linear scalability for the flows around the underwater vehicle model, The present simulation captures the essential features of the vortex structures near the hull and in the wake, Both of the time-averaged pressure coefficients and srreamwise velocity profiles obtained from the LES are consistent with the characteristics of the flows pass an appended axisymmetric body. The code efficiency and its correct predictions on flow features allow us to perform the full-scale simulations on tens of thousands of cores with billions of grid points for higher-Reynolds-number flows around the underwater vehicles.

Numerical Simulation of Fluid and Heat Transfer in a Biological Tissue Using an Immersed Boundary Method Mimicking the Exact Structure of the Microvascular Network

The aim of this study is to develop a model of fluid and heat transfer in a biological tissue taking into account the exact structure of the related microvascular network,and to analyze the influence of structural changes of such a network induced by diabetes.A cubic region representing local skin tissue is selected as the computational domain,which in turn includes two intravascular and extravascular sub-domains.To save computational resources,the capillary network is reduced to a 1D pipeline model and embedded into the extravascular region.On the basis of the immersed boundary method(IBM)strategy,fluid and heat fluxes across a capillary wall are distributed to the surrounding tissue nodes by a delta function.We consider both steady and periodic blood pressure conditions at the entrances of the capillary network.Under steady blood pressure conditions,both the interstitial fluid pressure and tissue temperature around the capillary network are larger than those in other places.When the periodic blood pressure condition is considered,tissue temperature tends to fluctuate with the same frequency of the forcing,but the related waveform displays a smaller amplitude and a certain time(phase)delay.When the connectivity of capillary network is diminished,the capacity of blood redistribution through the capillary network becomes weaker and a subset of the vessel branches lose blood flow,which further aggravates the amplitude attenuation and time delay of the skin temperature fluctuation.

Numerical Investigation on Vortex-Induced Rotations of A Triangular Cylinder Using An Immersed Boundary Method

A numerical study of vortex-induced rotations(VIRs) of an equivalent triangular cylinder, which is free to rotate in the azimuthal direction in a uniform flow, is presented. Based on an immersed boundary method, the numerical model is established, and is verified through the benchmark problem of flow past a freely rotating rectangular body.The computation is performed for a fixed reduced mass of m~*=2.0 and the structural stiffness and damping ratio are set to zero. The effects of Reynolds number(Re=25-180) on the characteristics of VIR are studied. It is found that the dynamic response of the triangular cylinder exhibits four distinct modes with increasing Re: a rest position,periodic rotational oscillation, random rotation and autorotation. For the rotational oscillation mode, the cylinder undergoes a periodic vibration around an equilibrium position with one side facing the incoming flow. Since the rotation effect, the outset of vortex shedding from cylinder shifts to a much lower Reynolds number. Further increase in Re leads to 2 P and P+S vortex shedding modes besides the typical 2 S pattern. Our simulation results also elucidate that the free rotation significantly changes the drag and lift forces. Inspired by these facts, the effect of free rotation on flow-induced vibration of a triangular cylinder in the in-line and transverse directions is investigated. The results show that when the translational vibration is coupled with rotation, the triangular cylinder presents a galloping response instead of vortex-induced vibration(VIV).

Accuracy analysis of immersed boundary method using method of manufactured solutions

The immersed boundary method is an effective technique for modeling and simulating fluid-structure interactions especially in the area of biomechanics.This paper analyzes the accuracy of the immersed boundary method.The procedure contains two parts,i.e.,the code verification and the accuracy analysis.The code verification provides the confidence that the code used is free of mistakes,and the accuracy analysis gives the order of accuracy of the immersed boundary method.The method of manufactured solutions is taken as a means for both parts.In the first part,the numerical code employs a second-order discretization scheme,i.e.,it has second-order accuracy in theory.It matches the calculated order of accuracy obtained in the numerical calculation for all variables.This means that the code contains no mistake,which is a premise of the subsequent work.The second part introduces a jump in the manufactured solution for the pressure and adds the corresponding singular forcing terms in the momentum equations.By analyzing the discretization errors,the accuracy of the immersed boundary method is proven to be first order even though the discretization scheme is second order.It has been found that the coarser mesh may not be sensitive enough to capture the influence of the immersed boundary,and the refinement on the Lagrangian markers barely has any effect on the numerical calculation.

New Immersed Boundary Method on the Adaptive Cartesian Grid Applied to the Local Discontinuous Galerkin Method

Currently, many studies on the local discontinuous Galerkin method focus on the Cartesian grid with low computational e ciency and poor adaptability to complex shapes. A new immersed boundary method is presented, and this method employs the adaptive Cartesian grid to improve the adaptability to complex shapes and the immersed boundary to increase computational e ciency. The new immersed boundary method employs different boundary cells(the physical cell and ghost cell) to impose the boundary condition and the reconstruction algorithm of the ghost cell is the key for this method. The classical model elliptic equation is used to test the method. This method is tested and analyzed from the viewpoints of boundary cell type, error distribution and accuracy. The numerical result shows that the presented method has low error and a good rate of the convergence and works well in complex geometries. The method has good prospect for practical application research of the numerical calculation research.

Combined immersed boundary method and multiple-relaxation-time lattice Boltzmann flux solver for numerical simulations of incompressible flows

A method combining the immersed boundary technique and a multi- relaxation-time （MRT） lattice Boltzmann flux solver （LBFS） is presented for numerical simulation of incompressible flows over circular and elliptic cylinders and NACA 0012 Airfoil. The method uses a simple Cartesian mesh to simulate flows past immersed complicated bodies. With the Chapman-Enskog expansion analysis, a transform is performed between the Navier-Stokes and lattice Boltzmann equations （LBEs）. The LBFS is used to discretize the macroscopic differential equations with a finite volume method and evaluate the interface fluxes through local reconstruction of the lattice Boltzmann solution. The immersed boundary technique is used to correct the intermediate velocity around the solid boundary to satisfy the no-slip boundary condition. Agreement of simulation results with the data found in the literature shows reliability of the proposed method in simulating laminar flows on a Cartesian mesh.

On the capability of the curvilinear immersed boundary method in predicting near-wall turbulence of turbulent channel flows

The immersed boundary method has been widely used for simulating flows over complex geometries.However,its accuracy in predicting the statistics of near-wall turbulence has not been fully tested.In this work,we evaluate the capability of the curvilinear immersed boundary(CURVIB)method in predicting near-wall velocity and pressure fluctuations in turbulent channel flows.Simulation results show that quantities including the time-averaged streamwise velocity,the rms(root-mean-square)of velocity fluctuations,the rms of vorticity fluctuations,the shear stresses,and the correlation coefficients of u'and v"computed from the CURVIB simulations are in good agreement with those from the body-fitted simulations.More importantly,it is found that the time-averaged pressure,the rms and wavenumber-frequency spectra of pressure fluctuations computed using the CURVIB method agree well with the body-fitted results.

A three dimensional implicit immersed boundary method with application

Most algorithms of the immersed boundary method originated by Peskin are explicit when it comes to the computation of the elastic forces exerted by the immersed boundary to the fluid. A drawback of such an explicit approach is a severe restriction on the time step size for maintaining numerical stability. An implicit immersed boundary method in two dimensions using the lattice Boltzmann approach has been proposed. This paper reports an extension of the method to three dimensions and its application to simulation of a massive flexible sheet interacting with an incompressible viscous flow.

Effect of regularized delta function on accuracy of immersed boundary method

The immersed boundary method is an effective technique for modeling and simulating fluid-structure interactions especially in the area of biomechanics. The effect of the regularized delta function on the accuracy is an important subject in the property study. A method of manufactured solutions is used in the research. The computational code is first verified to be mistake-free by using smooth manufactured solutions. Then, a jump in the manufactured solution for pressure is introduced to study the accuracy of the immersed boundary method. Four kinds of regularized delta functions are used to test the effect on the accuracy analysis. By analyzing the discretization errors, the accuracy of the immersed boundary method is proved to be first-order. The results show that the regularized delta function cannot improve the accuracy, but it can change the discretization errors in the entire computational domain.

A three-dimensional immersed boundary method for non-Newtonian fluids

Fluid-structure-interaction （FSI） phenomenon is common in science and engineering. The fluidinvolved in an FSI problem may be non-Newtonian such as blood. A popular framework for FSIproblems is Peskin’s immersed boundary （IB） method. However, most of the IB formulations arebased on Newtonian fluids. In this letter, we report an extension of the IB framework to FSIinvolving Oldroyd-B and FENE-P fluids in three dimensions using the lattice Boltzmann approach.The new method is tested on two FSI model problems. Numerical experiments show that themethod is conditionally stable and convergent with the first order of accuracy.

Application of immersed boundary method in turbomachines

Simulating unsteady turbulent flow in turbomachines is still challenging due to the complexity of blade geometry and relative motion between rotor and stator.This study presents an Immersed Boundary Method(IBM)for high-Reynolds turbomachinery internal flows,and shows the advantage of the automatic grid generation techniques and flexible moving boundary treatments.The wall functions are used in the present method to alleviate the wall resolution restriction of turbulence simulation.The Two-Dimensional(2-D)IBM solver,which was previously developed and tested for a low-speed compressor,is further validated for a well-documented Low-Pressure Turbine(LPT)cascade.Both the blade loading and the total pressure losses in the wake are well captured by the present 2-D solver.The complex Three-Dimensional(3-D)effects in turbomachines motivate the further development of an extended 3-D IBM solver by using a curvilinear-coordinate system that facilitates the hub and casing boundary treatment.The good performance of the 3-D solver is demonstrated through comparison with CFX solver solutions for the rotor configuration of Advanced Noise Control Fan(ANCF).Further effects of the grid resolution on capturing the blade wake are discussed.The results indicate that the present 3-D solver is capable of reproducing the evolution of the blade wake with suitable computational grid.

Lattice Boltzmann Simulations of Two Linear Microswimmers Using the Immersed Boundary Method

The performance of a single or the collection of microswimmers strongly depends on the hydrodynamic coupling among their constituents and themselves.We present a numerical study for a single and a pair of microswimmers based on lattice Boltzmann method(LBM)simulations.Our numerical algorithm consists of two separable parts.Lagrange polynomials provide a discretization of the microswimmers and the lattice Boltzmann method captures the dynamics of the surrounding fluid.The two components couple via an immersed boundary method.We present data for a single swimmer system and our data also show the onset of collective effects and,in particular,an overall velocity increment of clusters of swimmers.

Effective Force Stabilising Technique for the Immersed Boundary Method

The immersed boundary method has emerged as an efficient approach for the simulation of finite-sized solid particles in complex fluid flows.However,one of the well known shortcomings of the method is the limited support for the simulation of light particles,i.e.particles with a density lower than that of the surrounding fluid,both in terms of accuracy and numerical stability.Although a broad literature exists,with several authors reporting different approaches for improving the stability of the method,most of these attempts introduce extra complexities and are very costly from a computational point of view.In this work,we introduce an effective force stabilizing technique,allowing to extend the stability range of the method by filtering spurious oscillations arising when dealing with light-particles,pushing down the particle-to-fluid density ratio as low as 0.04.We thoroughly validate the method comparing with both experimental and numerical data available in literature.

Sharp interface direct forcing immersed boundary methods： A summary of some algorithms and applications

Body-fitted mesh generation has long been the bottleneck of simulating fluid flows involving complex geometries. Immersed boundary methods are non-boundary-conforming methods that have gained great popularity in the last two decades for their simplicity and flexibility, as well as their non-compromised accuracy. This paper presents a summary of some numerical algori- thms along the line of sharp interface direct forcing approaches and their applications in some practical problems. The algorithms include basic Navier-Stokes solvers, immersed boundary setup procedures, treatments of stationary and moving immersed bounda- ries, and fluid-structure coupling schemes. Applications of these algorithms in particulate flows, flow-induced vibrations, biofluid dynamics, and free-surface hydrodynamics are demonstrated. Some concluding remarks are made, including several future research directions that can further expand the application regime of immersed boundary methods.

Simulation of dynamic fluid-solid interactions with an improved direct-forcing immersed boundary method

Dynamic fluid-solid interactions are widely found in chemical engineering, such as in particle-laden flows, which usually contain complex moving boundaries. The immersed boundary method （IBM） is a convenient approach to handle fluid-solid interactions with complex geometries. In this work, Uhlmann＇s direct-forcing IBM is improved and implemented on a supercomputer with CPU-GPU hybrid architec- ture. The direct-forcing IBM is modified as follows： the Poisson＇s equation for pressure is solved before evaluation of the body force, and the force is only distributed to the Cartesian grids inside the immersed boundary. A multidirect forcing scheme is used to evaluate the body force. These modifications result in a divergence-free flow field in the fluid domain and the no-slip boundary condition at the immersed boundary simultaneously. This method is implemented in an explicit finite-difference fractional-step scheme, and validated by 2D simulations of lid-driven cavity flow, Couette flow between two concentric cylinders and flow over a circular cylinder. Finally, the method is used to simulate the sedimentation of two circular particles in a channel. The results agree very well with previous experimental and numerical data, and are more accurate than the conventional direct-forcing method, especially in the vicinity of a moving boundary.

Numerical Simulation of Low Reynolds Number Fluid-Structure Interaction with Immersed Boundary Method

This article introduces a numerical scheme on the basis of semi-implicit method for pressure-linked equations （SIMPLE） algorithm to simulate incompressible unsteady flows with fluid-structure interaction. The Navier-Stokes equation is discretized spatially with collocated finite volume method and Eulerian implicit method in time domain. The hybrid method that combines immersed boundary method （IBM） and volume of fluid （VOF） method is used to deal with rigid body motion in fluid domain. The details of movement of immersed boundary （IB） and calculation of VOF are also described. This method can be easily applied to any existing finite-volume-based computational fluid dynamics （CFD） solver without complex operation, with which fluid flow interaction of arbitrarily complex geometry can be realized on a fixed mesh. The method is verified by low Reynolds number flows passing both stationary and oscillating cylinders. The drag and lift coefficients acquired by the study well accord with other published results, which indicate the reasonability of the proposed method.

A Level Set Immersed Boundary Method for Water Entry and Exit

The interaction between free surface flow and structure is investigated using a new level set immersed boundary method.The incorporation of an improved immersed boundary method with a free surface capture scheme implemented in a Navier-Stokes solver allows the interaction between fluid flow with free surface and moving body/bodies of almost arbitrary shape to be modelled.A new algorithm is proposed to locate exact forcing points near solid boundaries,which provides an accurate numerical solution.The discretized linear system of the Poisson pressure equation is solved using the Generalized Minimum Residual(GMRES)method with incomplete LU preconditioning.Uniform flow past a cylinder at Reynolds number Re=100 is modelled using the present model and results agree well with the experiment and numerical data in the literature.Water exit and entry of a cylinder at the prescribed velocity is also investigated.The predicted slamming coefficient is in good agreement with experimental data and previous numerical simulations using a ComFlow model.The vertical slamming force and pressure distribution for the free falling wedge is also studied by the present model and comparisons with available theoretical solutions and experimental data are made.

2008 Stability Analysis of the Immersed Boundary Method for a Two-Dimensional Membrane with Bending Rigidity

In this paper,we analyze the stability of the Immersed Boundary Methodapplied to a membrane-fluid system with a plasma membrane immersed in an incompressibleviscous fluid.We show that for small deformations,the planar rest state isstable for a membrane with bending rigidity.The smoothed version,using a standardregularization technique for the singular force,is also shown to be stable.Furthermore,we show that the coupled fluid-membrane system is stiff and smoothing helpsto reduce the stiffness.Compared to the system of elastic fibers immersed in an incompressiblefluid,membrane with bending rigidity consist of a wider range of decayrates.Therefore numerical instability could occur more easily for an explicit methodwhen the time step size is not sufficiently small,even though the continuous problemis stable.

Adaptive mesh refinement immersed boundary method for simulations of laminar flows past a moving thin elastic structure

One of the critical issues in numerical simulation of fluid-structure interaction problems is inaccuracy of the solutions,especially for flows past a stationary thin elastic structure where large deformations occur.High resolution is required to capture the flow characteristics near the fluid-structure interface to enhance accuracy of the solutions within proximity of the thin deformable body.Hence,in this work,an algorithm is developed to simulate fluid-structure interactions of moving deformable structures with very thin thicknesses.In this algorithm,adaptive mesh refinement(AMR)is integrated with immersed boundary finite element method(IBFEM)with two-stage pressure-velocity corrections.Despite successive interpolation of the flow field by IBM,the governing equations were solved using a fixed structured mesh,which significantly reduces the computational time associated with mesh reconstruction.The cut-cell IBM is used to predict the body forces while FEM is used to predict deformation of the thin elastic structure in order to integrate the motions of the fluid and solid at the interface.AMR is used to discretize the governing equations and obtain solutions that efficiently capture the thin boundary layer at the fluid-solid interface.The AMR-IBFEM algorithm is first verified by comparing the drag coefficient,lift coefficient,and Strouhal number for a benchmark case(laminar flow past a circular cylinder at Re=100)and the results showed good agreement with those of other researchers.The algorithm is then used to simulate 2-D laminar flows past stationary and moving thin structures positioned perpendicular to the freestream direction.The results also showed good agreement with those obtained from the arbitrary Lagrangian-Eulerian(ALE)algorithm for elastic thin boundaries.It is concluded that the AMR-IBFEM algorithm is capable of predicting the characteristics of laminar flow past an elastic structure with acceptable accuracy(error of-0.02%)with only-1%of the computational time for simulations with full mesh refinement.

NUMERICAL METHOD FOR MULTI-BODY FLUID INTERACTION BASED ON IMMERSED BOUNDARY METHOD

A Cartesian grid based on Immersed Boundary Method （IBM）, proposed by the present authors, is extended to unstructured grids. The advantages of IBM and Body Fitted Grid （BFG） are taken to enhance the computation efficiency of the fluid structure interaction in a complex domain. There are many methods to generate the BFG, among which the unstructured grid method is the most popular. The concept of Volume Of Solid （VOS） is used to deal with the multi rigid body and fluid interaction. Each body surface is represented by a set of points which can be traced in an anti-clockwise order with the solid area on the left side of surface. An efficient Lagrange point tracking algorithm on the fixed grid is applied to search the moving boundary grid points. This method is verified by low Reynolds number flows in the range from Re = 100 to 1000 in the cavity with a moving lid. The results are in a good agreement with experimental data in literature. Finally, the flow past two moving cylinders is simulated to test the capability of the method.