An Hamiltonian interface SPH formulation for multi-fluid and free surface flows

In the present work a new SPH model for simulating interface and free surface flows is presented. This formulation is an extension of the one discussed in Colagrossi and Landrini (2003) and is related to the one proposed by Hu and Adams (2006) to study multi-fluid flows. The new SPH scheme allows an accurate treatment of the discontinuity of quantities at the interface (such as the density), and permits to model flows where both interfaces and a free surface are present. The governing equations are derived following a Lagrangian variational principle leading to an Hamiltonian system of particles. The proposed formulation is validated on test cases for which reference solutions are available in the literature.     

A high-resolution mapped grid algorithm for compressible multiphase flow problems

We describe a simple mapped-grid approach for the efficient numerical simulation of compressible multiphase flow in general multi-dimensional geometries. The algorithm uses a curvilinear coordinate formulation of the equations that is derived for the Euler equations with the stiffened gas equation of state to ensure the correct fluid mixing when approximating the equations numerically with material interfaces. A γ-based and a α-based model have been described that is an easy extension of the Cartesian coordinates counterpart devised previously by the author [30]. A standard high-resolution mapped grid method in wave-propagation form is employed to solve the proposed multiphase models, giving the natural generalization of the previous one from single-phase to multiphase flow problems. We validate our algorithm by performing numerical tests in two and three dimensions that show second order accurate results for smooth flow problems and also free of spurious oscillations in the pressure for problems with interfaces. This includes also some tests where our quadrilateral-grid results in two dimensions are in direct comparisons with those obtained using a wave-propagation based Cartesian grid embedded boundary method.     

A parallel solution – adaptive method for three-dimensional turbulent non-premixed combusting flows

A parallel adaptive mesh refinement (AMR) algorithm is proposed and applied to the prediction of steady turbulent non-premixed compressible combusting flows in three space dimensions. The parallel solution-adaptive algorithm solves the system of partial-differential equations governing turbulent compressible flows of reactive thermally perfect gaseous mixtures using a fully coupled finite-volume formulation on body-fitted multi-block hexahedral meshes. The compressible formulation adopted herein can readily accommodate large density variations and thermo-acoustic phenomena. A flexible block-based hierarchical data structure is used to maintain the connectivity of the solution blocks in the multi-block mesh and to facilitate automatic solution-directed mesh adaptation according to physics-based refinement criteria. For calculations of near-wall turbulence, an automatic near-wall treatment readily accommodates situations during adaptive mesh refinement where the mesh resolution may not be sufficient for directly calculating near-wall turbulence using the low-Reynolds-number formulation. Numerical results for turbulent diffusion flames, including cold- and hot-flow predictions for a bluff-body burner, are described and compared to available experimental data. The numerical results demonstrate the validity and potential of the parallel AMR approach for predicting fine-scale features of complex turbulent non-premixed flames.     

可压缩颗粒圆孔射流并行直接数值模拟算法研究

对空间模式发展的气固两相圆孔射流中颗粒与流体双相耦合作用进行了并行环境下的直接数值模拟算法研究。气相流场采用可压缩的N-S方程直接求解。计算颗粒场时,采用Lagrangian方法跟踪实际的颗粒运动。利用并行求解算法,实现了颗粒穿越边界面的模拟。为了模拟颗粒对流体的作用,考虑了颗粒和流体的双相耦合。在本文的计算条件下,颗粒的直径远小于网格的间距,平均的Kolmogorov尺度和网格的间距在一个量级,保证了DNS的要求。气相和颗粒相的应力与实验的对比研究表明,本文的颗粒并行程序是可信的。     

An RKDG finite element method for the one-dimensional inviscid compressible gas dynamics equations in a Lagrangian coordinate

In this paper,Runge-Kutta Discontinuous Galerkin(RKDG) finite element method is presented to solve the onedimensional inviscid compressible gas dynamic equations in a Lagrangian coordinate.The equations are discretized by the DG method in space and the temporal discretization is accomplished by the total variation diminishing Runge-Kutta method.A limiter based on the characteristic field decomposition is applied to maintain stability and non-oscillatory property of the RKDG method.For multi-medium fluid simulation,the two cells adjacent to the interface are treated differently from other cells.At first,a linear Riemann solver is applied to calculate the numerical ?ux at the interface.Numerical examples show that there is some oscillation in the vicinity of the interface.Then a nonlinear Riemann solver based on the characteristic formulation of the equation and the discontinuity relations is adopted to calculate the numerical ?ux at the interface,which suppresses the oscillation successfully.Several single-medium and multi-medium fluid examples are given to demonstrate the reliability and efficiency of the algorithm.     

A RKDG finite element method for the one-dimensional inviscid compressible gas dynamics equations in Lagrangian coordinate

In this paper, Runge-Kutta Discontinuous Galerkin (RKDG) finite element method is presented to solve the one-dimensional inviscid compressible gas dynamic equations in Lagrangian coordinate. The equations are discretized by the DG method in space and the temporal discretization is accomplished by the total variation diminishing Runge-Kutta method. A limiter based on the characteristic field decomposition is applied to maintain stability and non-oscillatory property of the RKDG method. For multi-medium fluid simulation, the two cells adjacent to the interface are treated differently from other cells. At first, a linear Riemann solver is applied to calculate the numerical flux at the interface. Numerical examples show that there is some oscillation in the vicinity of the interface. Then a nonlinear Riemann solver based on the characteristic formulation of the equation and the discontinuity relations is adopted to calculate the numerical flux at the interface, which suppress the oscillation successfully. Several single-medium and multi-medium fluid examples are given to demonstrate the reliability and efficiency of the algorithm.     

A fluid-mixture type algorithm for barotropic two-fluid flow problems

Our goal is to present a simple interface-capturing approach for barotropic two-fluid flow problems in more than one space dimension. We use the compressible Euler equations in isentropic form as a model system with the thermodynamic property of each fluid component characterized by the Tait equation of state. The algorithm uses a non-isentropic form of the Tait equation of state as a basis to the modeling of the numerically induced mixing between two different barotropic fluid components within a grid cell. Similar to our previous work for multicomponent problems, see [J. Comput. Phys. 171 (2001) 678] and references cited therein, we introduce a mixture type of the model system that consists of the full Euler equations for the basic conserved variables and an additional set of evolution equations for the problem-dependent material quantities and also the approximate location of the interfaces. A standard high-resolution method based on a wave-propagation formulation is employed to solve the proposed model system with the dimensional-splitting technique incorporated in the method for multidimensional problems. Several numerical results are presented in one, two, and three space dimensions that show the feasibility of the method as applied to a reasonable class of practical problems without introducing any spurious oscillations in the pressure near the smeared material interfaces.     

Hilber-Hughes-Taylor-α法在接触约束多体系统动力学中的应用

以柔性梁在重力作用下绕转动铰做大范围定轴转动,并与刚性平面发生碰撞这一动力学过程为例,对Hilber-Hughes-Taylor(HHT-α)法在求解含接触约束的柔性多体系统动力学方程时的数值特性进行了研究.系统运动过程的全局动力学仿真由常微分方程组和微分-代数方程组的数值求解构成.柔性梁在无碰撞阶段系统动力学方程是一组常微分方程组.采用接触约束法模拟接触约束过程,系统的动力学方程为指标3的微分-代数方程组.采用HHT-α法对的该微分-代数方程组进行求解,并与Baumgarte违约修正法进行比较.分析了HHT-α法自由参数和违约修正常数对计算效率、动力学响应和系统机械能的影响,并对数值积分方法对模态截断数的敏感度以及速度约束和加速度约束的违约程度进行了分析.结果表明,违约修正常数对仿真结果影响非常明显,而HHT-α法的自由参数α对动力学响应的影响较小,从而避免了违约修正常数对数值积分结果的影响.HHT-α法的自由参数α可以消除碰撞高频模态的影响.     

Hydrodynamic impulse in a compressible fluid

A suitable expression for hydrodynamic impulse in a compressible fluid is deduced. The development of appropriate impulse formulation for compressible Euler equations confirms the propriety of the hydrodynamic impulse expression for a compressible fluid given here. Implications of the application of this formulation to a compressible vortex ring are pointed out. Extension of Benjamin's variational characterization of a moving axisymmetric vortex system to a compressible fluid is explored.     

颗粒圆孔射流碰撞并行直接数值模拟算法研究

本文对空间模式发展的颗粒圆孔射流碰撞进行了并行直接数值模拟算法研究。气相采用可压缩的N-S方程直接求解。颗粒相采用Lagrangian方法跟踪实际的颗粒运动。利用并行求解算法,实现了颗粒穿越边界面的模拟以及高效颗粒碰撞算法。考虑了颗粒和流体的双相耦合以及颗粒之间的碰撞。在本文的计算条件下,颗粒的直径远小于网格的间距,平均的Kolmogorov尺度和网格的间距在一个量级。气相和颗粒相的应力与实验的对比研究表明,本文的颗粒并行程序是可信的。     

激波和单列水柱、气水固多界面相互作用的数值模拟

研究可压缩多介质流场的激波和多介质界面相互作用问题.在Descartes固定网格采用level-set方法追踪界面,气/气界面边界条件处理采用OGFM方法,采用修正的rGFM方法提高气/水和气/固界面处构造Riemann问题精度,将Riemann近似解得到的界面参数外推到两侧真实和虚拟流体,采用五阶WENO方法求解流场Euler方程和界面level-set方程,给出不同时刻流场数值纹影图像.结果表明：在可压缩流场嵌入固体和水、气体等目标,本文方法可较精确地分辨平面运动激波和单列水柱及包含气/气、气/水和气/固等界面作用后产生的复杂激波结构.和传统的分区与贴体变换方法不同,为Descartes网格包含多介质界面复杂流场计算提供新途径.     

用非结构网格与欧拉方程计算复杂区域的二维流动

提出用Delaunay三角化方法生成非结构网格的一种过程。所生成的网格可用于复杂多连通域内的可压流计算。采用Euler方程和格心有限体积法,研制出程序,给出了算例。     

Aeroelastic flutter of a disk rotating in an unbounded acoustic medium

The linear aeroelastic stability of an unbaffled flexible disk rotating in an unbounded fluid is investigated by modeling the disk-fluid system as a rotating Kirchhoff plate coupled to the irrotational motions of a compressible inviscid fluid. A perturbed eigenvalue formulation is used to compute systematically the coupled system eigenvalues. Both a semi-analytical and a numerical method are employed to solve the fluid boundary value problem. The semi-analytical approach involves a perturbation series solution of the dual integral equations arising from the fluid boundary value problem. The numerical approach is a boundary element method based on the Hadamard finite part. Unlike previous works, it is found that a disk with zero material damping destabilizes immediately beyond its lowest critical speed. Upon the inclusion of small disk material damping, the flutter speeds become supercritical and increase with decreasing fluid density. The competing effects of radiation damping into the surrounding fluid and disk material damping control the onset of flutter at supercritical speed. The results are expected to be relevant for the design of rotating disk systems in data storage, turbomachinery and manufacturing applications.     

基于光滑粒子动力学方法的液滴冲击固壁面问题数值模拟

采用改进的光滑粒子动力学(SPH)方法对液滴冲击固壁面问题进行了数值模拟. 为了提高传统SPH方法的计算精度和数值稳定性, 在传统的SPH方法的基础上对粒子方法中的密度和核梯度进行了修正, 采用了考虑黎曼解法的SPH流体控制方程, 构造了一种新型的粒子间相互作用力(IIF)模型来模拟表面张力的影响. 应用改进的SPH方法对液滴冲击固壁面问题进行了数值模拟. 计算结果表明：新型的IIF 模型能够较好地模拟表面张力的影响, 改进的SPH方法能够精细地描述液滴与固壁面相互作用过程中液滴的内部压力场演变和自由面形态变化, 液滴的铺展因子随初始韦伯数的增大而增大, 数值模拟结果与实验得到的结果基本一致. 关键词： 液滴 固壁面 光滑粒子动力学 表面张力     

Lagrange坐标系下二维气动方程组的RKDG有限元方法

构造Lagrange坐标系下二维可压缩气动方程组的RKDG(Runge-Kutta Discontinuous Galerkin)有限元方法.将流体力学方程组和几何守恒律统-求解,所有计算都在固定的网格上进行,计算过程中不需要网格节点的速度信息.对几个数值算例进行数值模拟,得到较好的数值模拟结果.     

Solid–fluid diffuse interface model in cases of extreme deformations

Diffuse interface methods have been recently proposed and successfully used for accurate compressible multi-fluid computations Abgrall [1]; Kapila et al. [20]; Saurel et al. [30]. These methods deal with extended systems of hyperbolic equations involving a non-conservative volume fraction equation and relaxation terms. Following the same theoretical frame, we derive here an Eulerian diffuse interface model for elastic solid-compressible fluid interactions in situations involving extreme deformations. Elastic effects are included following the Eulerian conservative formulation proposed in Godunov [16], Miller and Colella [23], Godunov and Romenskii [17], Plohr and Plohr [27] and Gavrilyuk et al. [14]. We apply first the Hamilton principle of stationary action to derive the conservative part of the model. The relaxation terms are then added which are compatible with the entropy inequality. In the limit of vanishing volume fractions the Euler equations of compressible fluids and a conservative hyperelastic model are recovered. It is solved by a unique hyperbolic solver valid at each mesh point (pure fluid, pure solid and mixture cell). Capabilities of the model and methods are illustrated on various tests of impacts of solids moving in an ambient compressible fluid.     

非等温非牛顿黏性流体流动问题的修正光滑粒子动力学方法模拟

为准确、有效地模拟非等温非牛顿黏性流体的流动问题,本文基于一种不含核导数计算的核梯度修正格式和不可压缩条件给出了一种改进光滑粒子动力学(SPH)离散格式,它较传统SPH离散格式具有较高精度和较好稳定性.同时,为准确地描述温度场的演化过程,建立了非牛顿黏性的SPH温度离散模型.通过对等温Poiseuille流、喷射流和非等温Couette流、4:1收缩流进行模拟,并与其他数值结果作对比,分别验证了改进SPH方法模拟非牛顿黏性流动问题的可靠性和提出的SPH温度离散模型求解非等温流动问题的有效性和准确性.随后,运用改进SPH方法结合SPH温度离散模型对环形腔和C形腔内非等温非牛顿黏性流体的充模过程进行了试探性模拟研究,分析了数值模拟的收敛性,讨论了不同位置处热流参数对温度和流动的影响.     

光滑粒子流体动力学有限元法接触算法研究

 耦合光滑粒子流体动力学（SPH）方法和有限元法（FEM）,是研究冲击动力学问题的一种有效途径。为解决SPH粒子和有限单元间的接触问题,提出了SPH-FEM接触算法。该算法是在有限元节点处设置背景粒子,采用SPH接触算法的思想,计算施加在SPH粒子和有限元节点上的接触力,并且以外力的形式分别加入到SPH动量方程和有限元动力学方程中。利用SPH-FEM接触算法,对两杆撞击以及圆柱形钢弹正冲击钢板发生的冲塞破坏过程进行了三维数值模拟,靶板采用含损伤的Johnson-Cook模型和Grüneisen状态方程,模拟结果与实验结果吻合较好。     

Asymptotic analysis of ultra-relativistic charge

This article offers a new approach for analysing the dynamic behaviour of distributions of charged particles in an electromagnetic field. After discussing the limitations inherent in the Lorentz-Dirac equation for a single point particle a simple model is proposed for a charged continuum interacting self-consistently with the Maxwell field in vacuo. The model is developed using intrinsic tensor field theory and exploits to the full the symmetry and light-cone structure of Minkowski spacetime. This permits the construction of a regular stress-energy tensor whose vanishing divergence determines a system of non-linear partial differential equations for the velocity and self-fields of accelerated charge. Within this covariant framework a particular perturbation scheme is motivated by an exact class of solutions to this system describing the evolution of a charged fluid under the combined effects of both self and external electromagnetic fields. The scheme yields an asymptotic approximation in terms of inhomogeneous linear equations for the self-consistent Maxwell field, charge current and time-like velocity field of the charged fluid and is defined as an ultra-relativistic configuration. To facilitate comparisons with existing accounts of beam dynamics an appendix translates the tensor formulation of the perturbation scheme into the language involving electric and magnetic fields observed in a laboratory (inertial) frame.     

Stable Galerkin reduced order models for linearized compressible flow

The Galerkin projection procedure for construction of reduced order models of compressible flow is examined as an alternative discretization of the governing differential equations. The numerical stability of Galerkin models is shown to depend on the choice of inner product for the projection. For the linearized Euler equations, a symmetry transformation leads to a stable formulation for the inner product. Boundary conditions for compressible flow that preserve stability of the reduced order model are constructed. Preservation of stability for the discrete implementation of the Galerkin projection is made possible using a piecewise-smooth finite element basis. Stability of the reduced order model using this approach is demonstrated on several model problems, where a suitable approximation basis is generated using proper orthogonal decomposition of a transient computational fluid dynamics simulation.