Chimera technique for transporting disturbances

The Chimera technique for moving grids is used to take into account nonhomogeneous unsteady inflow conditions in the simulation of aerodynamic flows. The method is applied to simulate the transport of a large‐scale vortex by a mean velocity field over a large distance, where it finally interacts with an airfoil. The Chimera approach allows one to resolve the vortex on a fine grid, whereas the unstructured background grid covering most of the computational domain can be much coarser. This method shows the same low numerical dissipation as a simulation on a globally fine grid. Several precursor tests are performed with a finite modified analytical Lamb–Oseen type vortex to study the influence of spatial and temporal resolution and the employed numerical scheme. Then, the interaction of an analytical vortex with a NACA0012 airfoil and with an ONERA‐A airfoil near stall is studied. Finally, a realistic vortex is generated by a ramping airfoil and is transported on a moving Chimera block and then interacts with a two‐element airfoil, which allows one to simulate a typical setup for a gust generator in aerodynamic facilities. Copyright © 2012 John Wiley & Sons, Ltd.     

Large eddy simulation of free surface shallow‐water flow

Shallow‐water flow with free surface frequently occurs in ambient water bodies, in which the horizontal scale of motion is generally two orders of magnitude greater than the water depth. To accurately predict this flow phenomenon in more detail, a three‐dimensional numerical model incorporating the method of large eddy simulation (LES) has been developed and assessed. The governing equations are split into three parts in the finite difference solution: advection, dispersion and propagation. The advection part is solved by the QUICKEST scheme. The dispersion part is solved by the central difference method and the propagation part is solved implicitly using the Gauss–Seidel iteration method. The model has been applied to free surface channel flow for which ample experimental data are available for verification. The inflow boundary condition for turbulence is generated by a spectral line processor. The computed results compare favourably with the experimental data and those results obtained by using a periodic boundary condition. The performance of the model is also assessed for the case in which anisotropic grids and filters with horizontal grid size of the order of the water depth are used for computational efficiency. The coarse horizontal grid was found to cause a significant reduction in the large‐scale turbulent motion generated by the bottom turbulence, and the turbulent motion is predominately described by the sub‐grid scale (SGS) terms. The use of the Smagorinsky model for SGS turbulence in this situation is found inappropriate. A parabolic mixing length model, which accounts for the filtered turbulence, is then proposed. The new model can reproduce more accurately the flow quantities. Copyright © 2000 John Wiley & Sons, Ltd.     

A collocated grid,projection method for time‐accurate calculation of low‐Mach number variable density flows in general curvilinear coordinates

A time‐accurate algorithm is proposed for low‐Mach number, variable density flows on curvilinear grids. Spatial discretization is performed on collocated grid that offers computational simplicity in curvilinear coordinates. The flux interpolation technique is used to avoid the pressure odd–even decoupling of the collocated grid arrangement. To increase the stability of the method, a two‐step predictor–corrector time integration scheme is employed. At each step, the projection method is used to calculate the hydrodynamic pressure and to satisfy the continuity equation. The robustness and accuracy of the method is illustrated with a series of numerical experiments including thermally driven cavity, polar cavity, three‐dimensional cavity, and direct numerical simulation of non‐isothermal turbulent channel flow. Copyright © 2012 John Wiley & Sons, Ltd.     

Numerical simulation of lateral migration of red blood cells in Poiseuille flows

A spring model is applied to simulate the skeleton structure of the red blood cell (RBC) membrane and to study the RBC rheology in two‐dimensional Poiseuille flows using an immersed boundary method. The lateral migration properties of the cells in Poiseuille flows have been investigated. The simulation results show that the rate of migration toward the center of the channel depends on the swelling ratio and the deformability of the cells. We have also combined the above methodology with a fictitious domain method to study the motion of RBCs in a two‐dimensional micro‐channel with a constriction with an application to blood plasma separation. Copyright © 2010 John Wiley & Sons, Ltd.     

SPH for 3D floating bodies using variable mass particle distribution

A floating body with substantial heave motion is a challenging fluid–structure interaction problem for numerical simulation. In this paper we develop SPH in three dimensions to include variable particle mass distribution using an arbitrary Lagrange–Eulerian formulation with an embedded Riemann solver. A wedge or cone in initially still water is forced to move with a displacement equal to the surface elevation of a focused wave group. A two‐dimensional wedge case is used to evaluate two forms of repulsive‐force boundary condition on the body; the force depending on the normal distance from the object surface produced closer agreement with the experiment. For a three‐dimensional heaving cone the comparison between SPH and experiment shows excellent agreement for the force and free surface for motion with low peak spectral frequencies while for a higher peak frequency the agreement is reasonable in terms of phase and magnitude, but a small discrepancy appears at the troughs in the motion. Capturing the entire three‐dimensional flow field using an initially uniform particle distribution with sufficiently fine resolution requires an extremely large number of particles and consequently large computing resource. To mitigate this issue, we employ a variable mass distribution with fine resolution around the body. Using a refined mass distribution in a preselected area avoids the need for a dynamic particle refinement scheme and leads to a computational speedup of more than 600% or much improved results for a given number of particles. SPH with variable mass distribution is then applied to a single heaving‐float wave energy converter, the ‘Manchester Bobber’, in extreme waves and compared with experiments in a wave tank. The SPH simulations are presented for two cases: a single degree‐of‐freedom system with motion restricted to the vertical direction and with general motion allowing six degrees‐of‐freedom. The motion predicted for the float with general motion is in much closer agreement with experimental data than the vertically constrained system. Using variable particle mass distribution is shown to produce close agreement with a computation time 20% of that required with a uniformly fine resolution. Copyright © 2012 John Wiley & Sons, Ltd.     

Application of hybrid Cartesian grid and gridless approach to moving boundary flow problems

The paper presents a hybrid Cartesian grid and gridless approach to solve unsteady moving boundary flow problems. Unlike the Chimera clouds of points approach, the hybrid approach uses a Cartesian grid to cover most of the computational domain and a gridless method to calculate a relatively small region adjacent to the body surface, making use of the flexibility of the gridless method in handling surface grid with complicated geometry and the computational efficiency of the Cartesian grid. Four cases were conducted to examine the applicability, accuracy and robustness of the hybrid approach. Steady flows over a single NACA0012 airfoil and dual NACA0012 airfoils at different Mach numbers and angles of attack were simulated. Moreover, by implementing a dynamic hole cutting, node identification and information communication between the Cartesian grid and the gridless regions, unsteady flows over a pitching NACA0012 airfoil (small displacement) and two‐dimensional airfoil/store separation (large displacement) were performed. The computational results were found to agree well with earlier experimental data as well as computational results. Shock waves were accurately captured. The computational results show that the hybrid approach is of potential to solve the moving boundary flow problems. Copyright © 2013 John Wiley & Sons, Ltd.     

Optimized sixth‐order monotonicity‐preserving scheme by nonlinear spectral analysis

In this paper, sixth‐order monotonicity‐preserving optimized scheme (OMP6) for the numerical solution of conservation laws is developed on the basis of the dispersion and dissipation optimization and monotonicity‐preserving technique. The nonlinear spectral analysis method is developed and is used for the purpose of minimizing the dispersion errors and controlling the dissipation errors. The new scheme (OMP6) is simple in expression and is easy for use in CFD codes. The suitability and accuracy of this new scheme have been tested through a set of one‐dimensional, two‐dimensional, and three‐dimensional tests, including the one‐dimensional Shu–Osher problem, the two‐dimensional double Mach reflection, and the Rayleigh–Taylor instability problem, and the three‐dimensional direct numerical simulation of decaying compressible isotropic turbulence. All numerical tests show that the new scheme has robust shock capturing capability and high resolution for the small‐scale waves due to fewer numerical dispersion and dissipation errors. Moreover, the new scheme has higher computational efficiency than the well‐used WENO schemes. Copyright © 2013 John Wiley & Sons, Ltd.     

A numerical continuous model for the hydrodynamics of fluid particle systems

In order to understand the hydrodynamic interactions that can appear in a fluid particle motion, an original method based on the equations governing the motion of two immiscible fluids has been developed. These momentum equations are solved for both the fluid and solid phases. The solid phase is assumed to be a fluid phase with physical properties, such as its behaviour can be assimilated to that of pseudo‐rigid particles. The only unknowns are the velocity and the pressure defined in both phases. The unsteady two‐dimensional momentum equations are solved by using a staggered finite volume formulation and a projection method. The transport of each particle is solved by using a second‐order explicit scheme. The physical model and the numerical method are presented, and the method is validated through experimental measurements and numerical results concerning the flow around a circular cylinder. Good agreement is observed in most cases. The method is then applied to study the trajectory of one settling particle initially off‐centred between two parallel walls and the corresponding wake effects. Different particle trajectories related to particulate Reynolds numbers are presented and commented. A two‐body interaction problem is investigated too. This method allows the simulation of the transport of particles in a dilute suspension in reasonable time. One of the important features of this method is the computational cost that scales linearly with the number of particles. Copyright © 1999 John Wiley & Sons, Ltd.     

Computations of flow over a flexible plate using the hybrid Cartesian/immersed boundary method

A hybrid Cartesian/immersed boundary code is developed and applied to interactions between a flexible plate and a surrounding fluid. The velocities at the immersed boundary (IB) nodes are reconstructed by interpolations along local normal lines to an interface. A new criterion is suggested to distribute the IB nodes near an interface. The suggested criterion guarantees a closed fluid domain by a set of the IB nodes and it is applicable to a zero‐thickness body. To eliminate the pressure interpolation at the IB nodes, the hybrid staggered/non‐staggered grid method is adapted. The developed code is validated by comparisons with other experimental and computational results of flow around an in‐line oscillating cylinder. Good agreements are achieved for velocity profiles and vorticity and pressure contours. As applications to the fluid–structure interaction, oscillations of flexible plate in a resting fluid and flow over a flexible plate are simulated. The elastic deformations of the flexible plate are modelled based on the equations of motion for plates considering the fluid pressure as the external load on the plate. Two non‐dimensional parameters are identified and their effects on the damping of the plate motion are examined. Grid convergence tests are carried out for both cases. Copyright © 2007 John Wiley & Sons, Ltd.     

Three‐dimensional immersed boundary conditions for moving solids in the lattice‐Boltzmann method

This paper establishes the range of validity for a previously published three‐dimensional moving solid boundary condition for the lattice‐Boltzmann method. This method was reasonably formulated from a mass and momentum balance perspective, but was only verified for a small range of (primarily two‐dimensional) problems. One of the advantages of this boundary condition is that it offers resolution at the sub‐grid scale, allowing for accurate and stable calculation of the force and torque for solids which are moving through a lattice, even for small solid sizes relative to the computational grid size. We verify the boundary condition for creeping flows by comparison to analytical solutions that include both the force and the torque on fixed and moving spheres, and then follow this with comparisons to experimental and empirical results for both fixed as well moving spheres in inertial flows. Finally, we compare simulation results to numerical results of other investigators for the settling of an offset sphere and the drafting–kissing–tumbling of two sedimenting spheres. We found that an accurate calculation of the collision‐operator weighting used to obtain sub‐grid‐scale resolution was necessary in order to prevent spikes in the velocities, forces, and moments when solid objects cross‐computational cells. The wide range of comparisons collected and presented in this paper can be used to establish the validity of other numerical models, in addition to the one examined here. Published in 2007 by John Wiley & Sons, Ltd.     

Control functions and grid qualities measurements in the elliptic grid generation around arbitrary surfaces

This paper describes the three‐dimensional elliptic grid generation. The two‐dimensional approach for the control functions obtained by modifying the Thomas–Middlecoff method is applied on the planes perpendicular to the main flow direction co‐ordinate, which is assumed to be the function of only one corresponding co‐ordinate in the computational domain. The grid orthogonality is improved by about 40 per cent compared with that of the algebraic initial grid. Copyright © 2000 John Wiley & Sons, Ltd.     

Vortex‐in‐cell method combined with a boundary element method for incompressible viscous flow analysis

In this study, an immersed boundary vortex‐in‐cell (VIC) method for simulating the incompressible flow external to two‐dimensional and three‐dimensional bodies is presented. The vorticity transport equation, which is the governing equation of the VIC method, is represented in a Lagrangian form and solved by the vortex blob representation of the flow field. In the present scheme, the treatment of convection and diffusion is based on the classical fractional step algorithm. The rotational component of the velocity is obtained by solving Poisson's equation using an FFT method on a regular Cartesian grid, and the solenoidal component is determined from solving an integral equation using the panel method for the convection term, and the diffusion term is implemented by a particle strength exchange scheme. Both the no‐slip and no‐through flow conditions associated with the surface boundary condition are satisfied by diffusing vortex sheet and distributing singularities on the body, respectively. The present method is distinguished from other methods by the use of the panel method for the enforcement of the no‐through flow condition. The panel method completes making use of the immersed boundary nature inherent in the VIC method and can be also adopted for the calculation of the pressure field. The overall process is parallelized using message passing interface to manage the extensive computational load in the three‐dimensional flow simulations. Copyright © 2011 John Wiley & Sons, Ltd.     

An immersed‐boundary finite‐volume method for direct simulation of flows with suspended paramagnetic particles

In the present study, we have proposed an immersed‐boundary finite‐volume method for the direct numerical simulation of flows with inertialess paramagnetic particles suspended in a nonmagnetic fluid under an external magnetic field without the need for any model such as the dipole–dipole interaction. In the proposed method, the magnetic field (or force) is described by the numerical solution of the Maxwell equation without current, where the smoothed representation technique is employed to tackle the discontinuity of magnetic permeability across the particle–fluid interface. The flow field, on the other hand, is described by the solution of the continuity and momentum equations, where the discrete‐forcing‐based immersed‐boundary method is employed to satisfy the no‐slip condition at the interface. To validate the method, we performed numerical simulations on the two‐dimensional motion of two and three paramagnetic particles in a nonmagnetic fluid subjected to an external uniform magnetic field and then compared the results with the existing finite‐element and semi‐analytical solutions. Comparison shows that the proposed method is robust in the direct simulation of such magnetic particulate flows. This method can be extended to more general flows without difficulty: three‐dimensional particulate flows, flows with a great number of particles, or flows under an arbitrary external magnetic field. Copyright © 2010 John Wiley & Sons, Ltd.     

Incompressible multiphase flow and encapsulation simulations using the moment‐of‐fluid method

A moment‐of‐fluid method is presented for computing solutions to incompressible multiphase flows in which the number of materials can be greater than two. In this work, the multimaterial moment‐of‐fluid interface representation technique is applied to simulating surface tension effects at points where three materials meet. The advection terms are solved using a directionally split cell integrated semi‐Lagrangian algorithm, and the projection method is used to evaluate the pressure gradient force term. The underlying computational grid is a dynamic block‐structured adaptive grid. The new method is applied to multiphase problems illustrating contact‐line dynamics, triple junctions, and encapsulation in order to demonstrate its capabilities. Examples are given in two‐dimensional, three‐dimensional axisymmetric (R–Z), and three‐dimensional (X–Y–Z) coordinate systems. Copyright © 2015 John Wiley & Sons, Ltd.     

Theoretical analysis for achieving high‐order spatial accuracy in Lagrangian/Eulerian source terms

In a fully coupled Lagrangian/Eulerian two‐phase calculation, the source terms from computational particles must be agglomerated to nearby gas‐phase nodes. Existing methods are capable of accomplishing this particle‐to‐gas coupling with second‐order accuracy. However, higher‐order methods would be useful for applications such as two‐phase direct numerical simulation and large eddy simulation. A theoretical basis is provided for producing high spatial accuracy in particle‐to‐gas source terms with low computational cost. The present work derives fourth‐ and sixth‐order accurate methods, and the procedure for even higher accuracy is discussed. The theory is also expanded to include two‐ and three‐dimensional calculations. One‐ and two‐dimensional tests are used to demonstrate the convergence of this method and to highlight problems with statistical noise. Finally, the potential for application in computational fluid dynamics codes is discussed. It is concluded that high‐order kernels have practical benefits only under limited ranges of statistical and spatial resolution. Additionally, convergence demonstrations with full CFD codes will be extremely difficult due to the worsening of statistical errors with increasing mesh resolution. Copyright © 2006 John Wiley & Sons, Ltd.     

膛口反应流并行数值模拟

采用轴对称多组分N-S方程对含有高速运动弹丸的膛口反应流进行了数值模拟.控制方程采用时间分裂方法并在大型计算机上采用MPI方法进行多核并行求解,其中对流项采用二阶AUSM+格式和MUSCL插值方法进行处理,燃气采用氢气-空气混合气,反应机理为9组分19步基元反应.对于弹丸引起的网格运动,采用嵌套网格法处理.并行验证算例与串行计算结果一致,采用20个CPU计算时效率为64％.根据数值结果详细讨论了发射过程中的气体动力学和化学动力学过程,并且通过对两种条件下的计算结果比较分析了化学反应对膛口流场发展的影响.结果表明,上述算法能够较为正确地模拟弹丸和化学反应对膛口流场的影响,并大大提高了计算速度.     

Three‐dimensional finite element analysis of transient fluid flow with free‐surface using marker surface method and adaptive grid refinement

For three‐dimensional finite element analysis of transient fluid flow with free‐surface, a new marker surface method is proposed, in which the fluid flow is represented by the marker surface composed of marker elements instead of marker particles used in the marker particle method. This also involves an adaptive grid that is created under a new criterion of element categorization of filling states and the locations in the total region at each time step. The marker surface is used in order to represent the free‐surface accurately, as well as to decrease the memory and computation time, and to effectively display the predicted three‐dimensional free‐surface. By using the adaptive grid in which the elements, finer than those in internal and external regions, are distributed in the surface region through refinement and coarsening procedures, the analysis of three‐dimensional transient fluid flow with free‐surface is achieved more efficiently. Through three‐dimensional analysis of two kinds of problems using several grids, the efficiency of the proposed marker surface method and the adaptive grid are verified. Copyright © 1999 John Wiley & Sons, Ltd.     

A parallel cell‐based DSMC method on unstructured adaptive meshes

A parallel DSMC method based on a cell‐based data structure is developed for the efficient simulation of rarefied gas flows on PC‐clusters. Parallel computation is made by decomposing the computational domain into several subdomains. Dynamic load balancing between processors is achieved based on the number of simulation particles and the number of cells allocated in each subdomain. Adjustment of cell size is also made through mesh adaptation for the improvement of solution accuracy and the efficient usage of meshes. Applications were made for a two‐dimensional supersonic leading‐edge flow, the axi‐symmetric Rothe's nozzle, and the open hollow cylinder flare flow for validation. It was found that the present method is an efficient tool for the simulation of rarefied gas flows on PC‐based parallel machines. Copyright © 2004 John Wiley & Sons, Ltd.     

Unified one‐fluid formulation for incompressible flexible solids and multiphase flows: Application to hydrodynamics using the immersed structural potential method (ISPM)

In this paper, we present a two‐dimensional computational framework for the simulation of fluid‐structure interaction problems involving incompressible flexible solids and multiphase flows, further extending the application range of classical immersed computational approaches to the context of hydrodynamics. The proposed method aims to overcome shortcomings such as the restriction of having to deal with similar density ratios among different phases or the restriction to solve single‐phase flows. First, a variation of classical immersed techniques, pioneered with the immersed boundary method (IBM), is presented by rearranging the governing equations, which define the behaviour of the multiple physics involved. The formulation is compatible with the “one‐fluid” formulation for two‐phase flows and can deal with large density ratios with the help of an anisotropic Poisson solver. Second, immersed deformable structures and fluid phases are modelled in an identical manner except for the computation of the deviatoric stresses. The numerical technique followed in this paper builds upon the immersed structural potential method developed by the authors, by adding a level set–based method for the capturing of the fluid‐fluid interfaces and an interface Lagrangian‐based meshless technique for the tracking of the fluid‐structure interface. The spatial discretisation is based on the standard marker‐and‐cell method used in conjunction with a fractional step approach for the pressure/velocity decoupling, a second‐order time integrator, and a fixed‐point iterative scheme. The paper presents a wide d range of two‐dimensional applications involving multiphase flows interacting with immersed deformable solids, including benchmarking against both experimental and alternative numerical schemes.     

Numerical simulation of liquid crystalline polymer flow into two‐dimensional thin cavity moulds

In this paper, flows of liquid crystalline polymers into two‐dimensional thin cavity moulds are simulated. The flows are modelled by Ericksen–Leslie equations of motion in the high viscosity limit. An elliptic pressure equation is derived under Hele–Shaw approximations, and the non‐isothermal natures of the flow are modelled. The equations are solved using the finite‐difference technique. A new boundary‐mapping technique is developed in this study to solve the difficulty in the finite‐difference treatment of arbitrarily shaped boundaries, which possess no natural coordinate system. This new method avoids the difficult mesh control in the body‐fitted mapping process and makes the mapping process easy to implement. It can also solve the problems caused by the uneven distribution of grid nodes in the traditional body‐fitted mapping technique. Copyright © 2008 John Wiley & Sons, Ltd.