界面不稳定性的自适应欧拉数值计算

采用欧拉网格自适应算法数值模拟Richtmyer Meshkov和Rayleigh Taylor不稳定多介质流界面,获得了高精度界面特征。对不同流体引入不同位标函数跟踪界面运动,将位标函数方程与流体动力学方程耦合求解,在笛卡儿坐标系中运用二阶精度有限体积算法,保持流场守恒条件下,通过采用多层网格级对笛卡儿网格嵌套细化,从而实现多介质流体界面的高精度自适应跟踪。给出的方法逻辑简单,可以大大节省CPU时间。     

聚能装药的欧拉数值模拟

用二维有限差分欧拉程序MEPH2Y模拟了聚能装药的作用过程,包括爆轰波的形成、传播及与其他介质的相互作用,高温高压下射流（或射弹）的形成、延展、减压、断裂,射流（或射弹）对靶的侵彻及靶的成坑和动态响应等过程。介绍了程序所用的数学模型、数值方法,以及模拟的部分问题与实验结果的比较。结果表明,数值模拟结果与实验结果符合较好。     

高精度欧拉流体弹塑性问题的数值方法研究

将描述固体材料的应力应变关系与欧拉流体动力学方程组耦合求解,通过引入界面捕捉方法描述多物质界面,将带弹塑性的多材料相互作用问题从形式上转化为计算单一材料问题,采用Roe方法近似求解Riemann问题,给出以Godunov方法为基础的二阶精度欧拉弹塑性流动的数值计算方法,适用于计算大变形流动等问题,并通过数值实验进行验证.     

混凝土动态冲击问题的一种欧拉数值方法

针对混凝土的动态冲击问题给出了混凝土的Holmquist Johnson Cook本构关系 ,本构关系中的等效强度作为压力、应变率和损伤的函数 ;压力表示为体积应变的函数 ,并考虑了永久破碎的效应 ;积累损伤作为等效塑性应变、塑性体积应变和压力的函数。结合三维弹塑性流体力学欧拉数值方法 ,提出了混凝土的Holmquist Johnson Cook本构关系与欧拉程序相结合的计算方法。介绍了带混凝土Holmquist Johnson Cook本构关系的三维弹塑性流体力学欧拉程序。     

高速碰撞的三维欧拉数值模拟方法

介绍一种可用于高速碰撞问题数值模拟的三维弹塑性流体动力学数值计算方法,以及应用该方法研制的应用软件ＭＥＰＨ３Ｄ,并给出了一些高速碰撞问题的数值计算结果,计算结果表明该程序具有计算三维高速碰撞问题的能力。     

基于欧拉-欧拉方法的气液两相流数值模型发展综述

深海油气多相混输系统内部油气混输本质上是一种高压高含气率的气液两相流问题。现如今多采用欧拉–欧拉方法对该问题进行数值研究,然而该方法的准确性依赖于相间力模型与群体平衡子模型的构建与选择。因此,本文对现有的相间力模型进行了总结,主要包括曳力、升力、壁面润滑力、湍流扩散力、虚拟质量力,并对相关模型的理论与发展进行了阐述,总结了压力以及高含气率下泡群对相间力模型的修正方法。此外,考虑到高含气率工况下气泡与气泡之间的相互作用,针对气泡群体平衡模型进行介绍,对气泡的破碎与聚并模型进行了梳理,总结了高压情况下群体平衡模型的修正思路。以期对深海高压高含气率环境下的气液混输模拟计算提供借鉴。     

磁流体力学数值计算处理方法

介绍电磁内爆实验中求解磁流体力学方程组的处理方法。方程组采用分裂法以克服非线性耦合可能引起的数值不稳定性；采用隐式差分格式避免过小时间步长限制。隐式格式采用Ｎｅｗｔｏｎ－Ｒａｐｈｓｏｎ法叠代求解，使用比较简单的叠代初值的给定方法。对一些特殊边界处理作了说明。     

欧拉坐标系下具有锐利相界面的可压缩多介质流动数值方法研究

可压缩多介质流动问题的数值模拟在国防和工业领域内均具有重要的研究价值,诸如武器设计、爆炸安全防护等,通常具有大变形、高度非线性等特点,是一项极具挑战性的研究课题. 本文提出了一种基于 Euler 坐标系的非结构网格、具有锐利相界面的二维和三维守恒型多介质流动数值方法,可用于模拟可压缩流体和弹塑性固体在极端物理条件下的大变形动力学行为. 利用分片线性的水平集函数重构出单纯形网格内分段线性的相界面,并在混合网格内构建出具有多种介质的相界面几何结构,理论上可以处理全局任意种介质、局部 3 种介质的多介质流动问题. 利用传统的有限体积格式来计算单元边界上同种介质间的数值通量,并通过在相界面法向上求解局部一维多介质 Riemann 问题的精确解来计算不同介质间的数值通量,保证了相界面上的通量守恒. 提出了一种非结构网格上的单元聚合算法,消除了由于网格被相界面分割成较小碎片、违反 CFL 条件,进而可能带来数值不稳定的问题. 针对一维多介质 Riemann 问题、激波与气泡相互作用问题、浅埋爆炸问题、空中强爆炸冲击波和典型坑道内冲击波传播问题开展了数值模拟研究,将计算结果与相关的理论、实验结果进行比对,验证了数值方法的正确性和可靠性.      

二维磁流体力学ALE数值模拟

介绍采用ALE方法进行的电磁内爆二维磁流体（MHD）力学模拟。二维MHD力学模拟的ALE方法分成拉格朗日、网格重分、对流输运三步。拉格朗日步采用文献[4]的时间分裂法,分成辐射冷却、热扩散、磁扩散、Lagrangian流动四步求解,并对Lagrangian流动步的方法进行了改进,消除了其拉氏计算的质量损失等。编制了二维计算程序并通过验证,获得的二维电磁内爆不稳定性发展与文献[2,5,11]吻合。     

自适应网格技术在流体力学界面处理中的应用

自适应网格技术是流体力学数值计算中的重要内容之一．不仅能够处理大变形问题，而且能够大大提高物质界面的计算精度。针对结构网格给出了网格细化结构、误差估计、数据管理、网格产生算法等。通过对强激波双马赫反射及Rayleigh-Taylor界面不稳定性现象进行数值模拟．获得符合精度要求的对激波阵面及物质界面自适应跟踪结果。     

A hybrid Lagrangian–Eulerian particle‐level set method for numerical simulations of two‐fluid turbulent flows

A coupled Lagrangian interface‐tracking and Eulerian level set (LS) method is developed and implemented for numerical simulations of two‐fluid flows. In this method, the interface is identified based on the locations of notional particles and the geometrical information concerning the interface and fluid properties, such as density and viscosity, are obtained from the LS function. The LS function maintains a signed distance function without an auxiliary equation via the particle‐based Lagrangian re‐initialization technique. To assess the new hybrid method, numerical simulations of several ‘standard interface‐moving’ problems and two‐fluid laminar and turbulent flows are conducted. The numerical results are evaluated by monitoring the mass conservation, the turbulence energy spectral density function and the consistency between Eulerian and Lagrangian components. The results of our analysis indicate that the hybrid particle‐level set method can handle interfaces with complex shape change, and can accurately predict the interface values without any significant (unphysical) mass loss or gain, even in a turbulent flow. The results obtained for isotropic turbulence by the new particle‐level set method are validated by comparison with those obtained by the ‘zero Mach number’, variable‐density method. For the cases with small thermal/mass diffusivity, both methods are found to generate similar results. Analysis of the vorticity and energy equations indicates that the destabilization effect of turbulence and the stability effect of surface tension on the interface motion are strongly dependent on the density and viscosity ratios of the fluids. Copyright © 2007 John Wiley & Sons, Ltd.     

多介质可压缩流体动力学界面捕捉方法

研究多介质流界面捕捉方法的主要目的是消除多介质流体在界面处压力、速度可能出现的非物理振荡现象 ,并通过流体动力学方程和界面捕捉方程的耦合 ,将多介质流体动力学计算形式上转化为单介质流体计算 ,从而可以采用对计算单介质有效的高精度计算方法来处理多介质流动问题。推广了Shyue界面捕捉和其等效方程的推导方法 ,给出的结果可以适用于具有状态方程 p =( ,e,a1 , ,an) +( ,e,b1 , ,bn)e的介质 ,并通过了数值试验验证。     

An efficient implicit mesh‐less method for compressible flow calculations

A dual‐time implicit mesh‐less scheme is presented for calculation of compressible inviscid flow equations. The Taylor series least‐square method is used for approximation of spatial derivatives at each node which leads to a central difference discretization. Several convergence acceleration techniques such as local time stepping, enthalpy damping and residual smoothing are adopted in this approach. The capabilities of the method are demonstrated by flow computations around single and multi‐element airfoils at subsonic, transonic and supersonic flow conditions. Results are presented which indicate good agreements with other reliable finite‐volume results. The computational time is considerably reduced when using the proposed mesh‐less method compared with the explicit mesh‐less and finite‐volume schemes using the same point distributions. Copyright © 2010 John Wiley & Sons, Ltd.     

Three-dimensional arbitrary Lagrangian–Eulerian numerical prediction method for non-linear free surface oscillation

A numerical prediction method has been proposed to predict non-linear free surface oscillation in an arbitrarily-shaped three-dimensional container. The liquid motions are described with Navier–Stokes equations rather than Laplace equations which are derived by assuming the velocity potential. The profile of a liquid surface is precisely represented with the three-dimensional curvilinear co-ordinates which are regenerated in each computational step on the basis of the arbitrary Lagrangian–Eulerian (ALE) formulation. In the transformed space, the governing equations are discretized on a Lagrangian scheme with sufficient numerical accuracy and the boundary conditions near the liquid surface are implemented in a complete manner. In order to confirm the applicability of the present computational technique, numerical simulations are conducted for the free oscillations of viscid and inviscid liquids and for highly non-linear oscillation. In addition, non-linear sloshing motions caused by horizontal and vertical excitations and a transition from non-linear sloshing to swirling are numerically predicted in three-dimensional cylindrical containers. Conclusively, it is shown that these sloshing motions associated with high non-linearity are reasonably predicted with the present numerical technique. © 1998 John Wiley & Sons, Ltd.     

Eulerian weakly compressible smoothed particle hydrodynamics (SPH) with the immersed boundary method for thin slender bodies

Fluid–structure interaction (FSI) problems involving thin slender bodies are a difficult modelling problem particularly for highly flexible bodies. An accurate, numerically stable approach is presented for fixed bodies as a first stage where weakly compressible smoothed particle hydrodynamics in Eulerian form (EWCSPH) is coupled with the immersed boundary method (IBM) and applied to the problems of an accelerating square box, as a non-slender case, and an impulsively started flat plate as a slender body case. The results for the box case show that vortical flow structures are virtually identical to those predicted by industry standard finite-volume solvers for lower Reynolds numbers (up to 150). For a higher Reynolds number of 450 there is some evidence that EWCSPH provides more accurate vortical structures for equivalent mesh/particle resolutions. Computational resource requirements are similar. The results for the plate case demonstrate that to simulate strong dynamic shear layers and vortex shedding the Eulerian form of SPH offers significantly greater stability and accuracy in comparison to the conventional Lagrangian form.     

Cut cell strategy for 3-D blast waves numerical simulations

   Abstract. This paper presents the results obtained by a generalized cut cells strategy on 3-D blast waves problems. The mesh is cartesian except when it is intersected by the surface of the solids inserted in the computational domain. The improvement, relatively to a classical cut-cells method, is the treatment of the cut which preserves the real geometry of the surface instead of approximating it by a plane. This approach avoids a loss of precision of the numerical scheme at the boundaries and allows future extension to higher order schemes (). Moreover it is useful for any kind of geometry with a high efficiency in computation time. The drawback is the complexity of the geometrical problems which can rise because of the diversity of situations in the treatment of the cuts. The performance of the approach is tested on a few examples allowing comparisons with experiments or other techniques and physical discussions. Received 15 November 1999 / Accepted 11 July 2000