A high order boundary scheme to simulate complex moving rigid body under impingement of shock wave

In the paper, we study a high order numerical boundary scheme for solving the complex moving boundary problem on a fixed Cartesian mesh, and numerically investigate the moving rigid body with the complex boundary under the impingement of an inviscid shock wave. Based on the high order inverse Lax-Wendroff(ILW) procedure developed in the previous work(TAN, S. and SHU, C. W. A high order moving boundary treatment for compressible inviscid flows. Journal of Computational Physics, 230(15),6023–6036(2011)), in which the authors only considered the translation of the rigid body,we consider both translation and rotation of the body in this paper. In particular, we reformulate the material derivative on the moving boundary with no-penetration condition, and the newly obtained formula plays a key role in the proposed algorithm. Several numerical examples, including cylinder, elliptic cylinder, and NACA0012 airfoil, are given to indicate the effectiveness and robustness of the present method.

Numerical Simulation of the Protective Effect of Complex Boundaries Toward Shock Waves in a 3D Explosive Field

A numerical method is presented that simulates 3D explosive field problems. A code MMIC3D using this method can be used to simulate the propagation and reflected effects of all kinds of rigid boundaries to shock waves produced by an explosive source. These numerical results indicate that the code MMIC3D has the ability in computing cases such as 3D shock waves produced by air explosion, vortex region of the shock wave, the Mach wave, and reflected waves behind rigid boundaries.

Electrical properties of m×n cylindrical network

We consider the problem of electrical properties of an m×n cylindrical network with two arbitrary boundaries,which contains multiple topological network models such as the regular cylindrical network,cobweb network,globe network,and so on.We deduce three new and concise analytical formulae of potential and equivalent resistance for the complex network of cylinders by using the RT-V method(a recursion-transform method based on node potentials).To illustrate the multiplicity of the results we give a series of special cases.Interestingly,the results obtained from the resistance formulas of cobweb network and globe network obtained are different from the results of previous studies,which indicates that our research work creates new research ideas and techniques.As a byproduct of the study,a new mathematical identity is discovered in the comparative study.

Computational Study on Interaction Between Swimming Fish and Drifting Vortices Behind the Cylinder

To predict the flow evolution of fish swimming problems,a flow solver based on the immersed boundary lattice Boltzmann method is developed.A flexible iterative algorithm based on the framework of implicit boundary force correction is used to save the computational cost and memory,and the momentum forcing is described by a simple direct force formula without complicated integral calculation when the velocity correction at the boundary node is determined.With the presented flow solver,the hydrodynamic interaction between the fish-induced dynamic stall vortices and the incoming vortices in unsteady flow is analyzed.Numerical simulation results unveil the mechanism of fish exploiting vortices to enhance their own hydrodynamic performances.The superior swimming performances originate from the relative movement between the“merged vortex”and the locomotion of the fishtail,which is controlled by the phase difference.Formation conditions of the“merged vortex”become the key factor for fish to exploit vortices to improve their swimming performance.We further discuss the effect of the principal components of locomotion.From the results,we conclude that lateral translation plays a crucial role in propulsion while body undulation in tandem with rotation and head motion reduce the locomotor cost.

SOLUTION OF DIFFERENT HOLES SHAPE BORDERS OF FIBRE REINFORCED COMPOSITE PLATES BY INTEGRAL EQUATIONS

Accurate boundary conditions of composite material plates with different holes are founded to settle boundary condition problems of complex holes by conformal mapping method upon the nonhomogeneous anisotropic elastic and complex function theory. And then the two stress functions required were founded on Cauchy integral by boundary conditions. The final stress distributions of opening structure and the analytical solution on composite material plate with rectangle hole and wing manholes were achieved. The influences on hole-edge stress concentration factors are discussed under different loads and fiber direction cases, and then contrast calculates are carried through FEM.

Lattice Boltzmann simulation of fluid flows in two-dimensional channel with complex geometries

Boundary conditions （BCs） play an essential role in lattice Boltzmann （LB） simulations. This paper investigates several most commonly applied BCs by evaluating the relative L2-norm errors of the LB simulations for two-dimensional （2-D） Poiseuille flow. It is found that the relative L2-norm error resulting from FHML＇s BC is smaller than that from other BCs as a whole. Then, based on the FHML＇s BC, it formulates an LB model for simulating fluid flows in 2-D channel with complex geometries. Afterwards, the flows between two inclined plates, in a pulmonary blood vessel and in a blood vessel with local expansion region, are simulated. The numerical results are in good agreement with the analytical predictions and clearly show that the model is effective. It is expected that the model can be extended to simulate some real biologic flows, such as blood flows in arteries, vessels with stenosises, aneurysms and bifurcations,

Amended influence matrix method for removal of rigid motion in the interior BVP for plane elasticity

A conventional complex variable boundary integral equation （CVBIE） in plane elasticity is provided. After using the Somigliana identity between a particular fundamental stress field and a physical stress field, an additional integral equality is obtained. By adding both sides of this integral equality to both sides of the conventional CVBIE, the amended boundary integral equation （BIE） is obtained. The method based on the discretization of the amended BIE is called the amended influence matrix method. With this method, for the Neumann boundary value problem （BVP） of an interior region, a unique solution for the displacement can be obtained. Several numerical examples are provided to prove the efficiency of the suggested method.

CVBEM and FVM Computational Model Comparison for Solving Ideal Fluid Flow in a 90-Degree Bend

While finite volume methodologies (FVM) have predominated in fluid flow computations, many flow problems, including groundwater models, would benefit from the use of boundary methods, such as the Complex Variable Boundary Element Method (CVBEM). However, to date, there has been no reporting of a comparison of computational results between the FVM and the CVBEM in the assessment of flow field characteristics. In this work, the CVBEM is used to develop a flow field vector outcome of ideal fluid flow in a 90-degree bend which is then compared to the computational results from a finite volume model of the same situation. The focus of the modelling comparison in the current work is flow field trajectory vectors of the fluid flow, with respect to vector magnitude and direction. Such a comparison is necessary to validate the development of flow field vectors from the CVBEM and is of interest to many engineering flow problems, specifically groundwater modelling. Comparison of the CVBEM and FVM flow field trajectory vectors for the target problem of ideal flow in a 90-degree bend shows good agreement between the considered methodologies.

NUMERICAL SIMULATION OF LEVEE BREACH FLOWS UNDER COMPLEX BOUNDARY CONDITIONS

Levee or dam failure can cause a significant disaster in most cases. A good prediction of the flood process especially in a real complex terrain is necessary for working out emergency plans for levee or dam breaches. Numerical simulations of levee or dam breach flow were carried out often with constant flow parameters and in relatively simple channels rather than in natural rivers with complex boundaries. This article presents our dedicated studies on the 2-D numerical model of levee or dam breach hydraulics with finite difference schemes. The good performance of the model is demonstrated by comparisons with the theoretical solution of an idealized dam-break flow over a frictionless flat rectangular channel. The model is also validated through its stability and conservation properties. The model is applied to simulate the flood propagation under complex boundary conditions, and the unsteady flood process in a river and in the dry floodplain with a complex bed terrain simultaneously. Furthermore, with respect to engineering practice, the numerical solutions can give special guidance to the effects of parameters such as the flood depth at different sites and the inundated area at different time periods after the levee breach and the travel time of the flood waves, which may be very important for practicing engineers in an efficient flood management.

Numerical Study of Stability and Accuracy of the Immersed Boundary Method Coupled to the Lattice Boltzmann BGK Model

This paper aims to study the numerical features of a coupling scheme between the immersed boundary(IB)method and the lattice Boltzmann BGK(LBGK)model by four typical test problems:the relaxation of a circular membrane,the shearing flow induced by a moving fiber in the middle of a channel,the shearing flow near a non-slip rigid wall,and the circular Couette flow between two inversely rotating cylinders.The accuracy and robustness of the IB-LBGK coupling scheme,the performances of different discrete Dirac delta functions,the effect of iteration on the coupling scheme,the importance of the external forcing term treatment,the sensitivity of the coupling scheme to flow and boundary parameters,the velocity slip near non-slip rigid wall,and the origination of numerical instabilities are investigated in detail via the four test cases.It is found that the iteration in the coupling cycle can effectively improve stability,the introduction of a second-order forcing term in LBGK model is crucial,the discrete fiber segment length and the orientation of the fiber boundary obviously affect accuracy and stability,and the emergence of both temporal and spatial fluctuations of boundary parameters seems to be the indication of numerical instability.These elaborate results shed light on the nature of the coupling scheme and may benefit those who wish to use or improve the method.

Immersed Boundary-Lattice Boltzmann Coupling Scheme for Fluid-Structure Interaction with Flexible Boundary

Coupling the immersed boundary(IB)method and the lattice Boltzmann(LB)method might be a promising approach to simulate fluid-structure interaction(FSI)problems with flexible structures and complex boundaries,because the former is a general simulation method for FSIs in biological systems,the latter is an efficient scheme for fluid flow simulations,and both of them work on regular Cartesian grids.In this paper an IB-LB coupling scheme is proposed and its feasibility is verified.The scheme is suitable for FSI problems concerning rapid flexible boundary motion and a large pressure gradient across the boundary.We first analyze the respective concepts,formulae and advantages of the IB and LB methods,and then explain the coupling strategy and detailed implementation procedures.To verify the effectiveness and accuracy,FSI problems arising from the relaxation of a distorted balloon immersed in a viscous fluid,an unsteady wake flow caused by an impulsively started circular cylinder at Reynolds number 9500,and an unsteady vortex shedding flow past a suddenly started rotating circular cylinder at Reynolds number 1000 are simulated.The first example is a benchmark case for flexible boundary FSI with a large pressure gradient across the boundary,the second is a fixed complex boundary problem,and the third is a typical moving boundary example.The results are in good agreement with the analytical and existing numerical data.It is shown that the proposed scheme is capable of modeling flexible boundary and complex boundary problems at a second-order spatial convergence;the volume leakage defect of the conventional IB method has been remedied by using a new method of introducing the unsteady and non-uniform external force;and the LB method makes the IB method simulation simpler and more efficient.

Recent progress on the jetting of single deformed cavitation bubbles near boundaries

Cavitation occurs widely in nature and engineering and is a complex problem with multiscale features in both time and space due to its associating violent oscillations. To understand the important but complicated phenomena and fluid mechanics behind cavitation, a great deal of effort has been invested in investigating the collapse of a single bubble near different boundaries. This review aims to cover recent developments in the collapse of single bubbles in the vicinity of complex boundaries, including single boundaries and two parallel boundaries, and open questions for future research are discussed. Microjets are the most prominent features of the non-spherical collapse of cavitation bubbles near boundaries and are directed toward rigid walls and away from free surfaces. Such a bubble generally splits, resulting in the formation of two axial jets directed opposite to each other under the constraints of an elastic boundary or two parallel boundaries. The liquid jet penetrates the bubble, impacts the boundary, and exerts a great deal of stress on any nearby boundary. This phenomenon can cause damage, such as the erosion of blades in hydraulic machinery, the rupture of human blood vessels, and underwater explosions, but can also be exploited for applications, such as needle-free injection, drug and gene delivery, surface cleaning, and printing. Many fascinating developments related to these topics are presented and summarized in this review. Finally, three directions are proposed that seem particularly fruitful for future research on the interaction of cavitation bubbles and boundaries.

Hydrodynamic Performance of Euplectella aspergillum:Simulating Real Life Conditions in the Abyss

We detail some of the understudied aspects of the flow inside and around the Hexactinellid Sponge Euplectella aspergillum.By leveraging the flexibility of the Lattice Boltzmann Method,High Performance Computing simulations are performed to dissect the complex conditions corresponding to the actual environment at the bottom of the ocean,at depths between 100 and 1,000 m.These large-scale simulations unveil potential clues on the evolutionary adaptations of these deep-sea sponges in response to the surrounding fluid flow,and they open the path to future investigations at the interface between physics,engineering and biology.

Numerical simulation of a complex moving rigid body under the impingement of a shock wave in 3D

In this paper,we take a numerical simulation of a complex moving rigid body under the impingement of a shock wave in three-dimensional space.Both compressible inviscid fluid and viscous fluid are considered with suitable boundary conditions.We develop a high order numerical boundary treatment for the complex moving geometries based on finite difference methods on fixed Cartesian meshes.The method is an extension of the inverse Lax-Wendroff(ILW)procedure in our works(Cheng et al.,Appl Math Mech(Engl Ed)42:841-854,2021;Liu et al.)for 2D problems.Different from the 2D case,the local coordinate rotation in 3D required in the ILW procedure is not unique.We give a theoretical analysis to show that the boundary treatment is independent of the choice of the rotation,ensuring the method is feasible and valid.Both translation and rotation of the body are taken into account in this paper.In particular,we reformulate the material derivative for inviscid fluid on the moving boundary with no-penetration condition,which plays a key role in the proposed algorithm.Numerical simulations on the cylinder and sphere are given,demonstrating the good performance of our numerical boundary treatments.

ANALYSIS OF A NUMERICAL METHOD FOR RADIATIVE TRANSFER EQUATION BASED BIOLUMINESCENCE TOMOGRAPHY

In the bioluminescence tomography （BLT） problem, one constructs quantitatively the bioluminescence source distribution inside a small animal from optical signals detected on the animal＇s body surface. The BLT problem is ill-posed and often the Tikhonov regularization is used to obtain stable approximate solutions. In conventional Tikhonov regularization, it is crucial to choose a proper regularization parameter to balance the accuracy and stability of approximate solutions. In this paper, a parameter-dependent coupled complex boundary method （CCBM） based Tikhonov regularization is applied to the BLT problem governed by the radiative transfer equation （RTE）. By properly adjusting the parameter in the Robin boundary condition, we achieve one important property： the regularized solutions are uniformly stable with respect to the regularization parameter so that the regularization parameter can be chosen based solely on the consideration of the solution accuracy. The discrete-ordinate finite-element method is used to compute numerical solutions. Numerical results are provided to illustrate the performance of the proposed method.