Mie-Grneisen状态方程可压缩多流体流动的PPM方法

采用流体体积分数的混合型多流体数值模型，将piecewise parabolic method (PPM)方法应用于可压缩多流体流动的数值模拟，拓展了以前提出的模型和数值方法，使它能够处理一般的Mie-Grneisen状态方程。采用双波近似和两层迭代算法求解一般状态方程的Riemann问题；并根据多流体接触界面无振荡原则设计高精度计算格式，对典型的纯界面平移问题可以从理论上证明本算法在接触间断附近压力和速度没有振荡，而且数值模拟结果表明界面数值耗散也被控制在2~3个网格之内。模拟了多种复杂的可压缩多流体流动，算例结果表明本文方法可以有效地处理接触间断、激波等物理问题，且具有耗散小精度高的特点。     

基于WENO-THINC/WLIC模型的水气二相流数值模拟

水气二相流与诸多领域的实际工程问题密切相关. 对二相流运动进行高精度的数值模拟是计算流体力学研究的难点和热点. 针对开敞水域的自由表面流运动问题, 将水和空气均视为不可压缩流体, 采用五阶加权基本无震荡(weighted essentially non-oscillatory, WENO)格式求解描述流体运动的纳维斯托克斯(Navier-Stokes, NS)方程, 利用以加权线性界面算法改进的多维双曲正切函数界面捕捉法(tangent of hyperbola for interface capturing with weighed line interface calculation, THINC/WLIC)追踪水气界面, 建立WENO-THINC/WLIC水气二相流运动数值模型. 模型采用分步计算法离散求解控制方程, 通过压力投影法求解压强场, 并利用三阶总变差递减(total variation diminishing, TVD)龙格库塔(Runge-Kutta, RK)法对时间项进行离散求解. 通过对环境速度场下Zalesak's disk和shearing vortex界面运动问题, 线性液舱晃荡问题以及溃坝问题的模拟结果与理论分析或试验结果的比较, 对所建立的水气二相流数值模型的适用性及模拟精度进行了验证. 结果表明, 本模型的模拟结果与物理模型或理论分析结果吻合良好, 能较为准确地再现不可压缩水气二相流运动现象. 鉴于WENO格式和THINC法本身在算法及应用等方面仍在不断改进, 本研究提出的WENO-THINC耦合模型为后续更高精度的二相流计算模型开发提供了一种研究思路.      

真实虚拟流方法在多介质可压缩流动模拟中的应用

为了克服原始虚拟流方法(ghost fluid method,GFM)在处理激波与大密度比流体-流体（气-水）界面相互作用时遇到的困难,采用真实虚拟流法(real ghost fluid method,RGFM)处理流体界面附近的虚拟点,结合HLLC(Harten-Lax-Van Leer with contact discontinuities)格式求解Euler方程,采用五阶WENO(weighted essentially nonoscillatory)格式求解level set输运方程。通过一维和二维算例的物质界面捕捉研究,证明RGFM在处理小密度比界面问题时优于GFM,同时RGFM还可用于求解激波与大密度比物质界面相互作用问题。计算表明,将RGFM引入到本文算法中,可精确捕捉到激波与界面（气-气、气-水界面）相互作用的变化细节,包括大密度比界面的剧烈变形和破碎,并具有较高的计算分辨率。     

多介质流体非守恒律欧拉方程组的数值计算方法

对多介质流体在界面处满足的Euler方程进行了探讨,方程组中增加了描述材料参数间断性质的对流形式非守恒律方程组 .以波传播算法为基础,通过Roe方程近似求解Riemann问题,同时采用相同的数值差分格式求解流体动力学Euler方程组和界面方程组.该方法可以有效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.给出了部分典型一维和二维数值计算结果.     

多介质流体非守恒律欧拉方程组的数值计算方法

对多介质流体在界面处满足的Euler方程进行了探讨 ,方程组中增加了描述材料参数间断性质的对流形式非守恒律方程组。以波传播算法为基础 ,通过Roe方程近似求解Riemann问题 ,同时采用相同的数值差分格式求解流体动力学Euler方程组和界面方程组。该方法可以有效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。给出了部分典型一维和二维数值计算结果。     

流固耦合分析的一种改进CBS有限元算法

针对流固耦合问题, 发展了一种基于任意拉格朗日-欧拉(ALE)描述有限元法的弱耦合分区算法. 运用半隐式特征线分裂算法求解Navier-Stokes方程, 在压力Poisson 方程中引入质量源项以满足几何守恒律; 运用子块移动技术更新动态网格, 并配以光滑处理防止网格质量下降; 采用Newmark-β 法求解结构运动方程. 为保持流体-结构界面处速度和动量守恒, 利用修正结合界面边界条件方法求解界面处速度通量和动量通量. 运用本方法分别模拟了不同雷诺数下单圆柱横向和两向流致振动、串列双圆柱两向流致振动. 计算表明, 本文方法计算效率高, 计算结果与已有实验和数值计算数据吻合.     

时刻追踪多介质界面运动的动网格方法

在对可压缩多介质流动的数值模拟中,定义介质界面为一种内部边界,由网格的边组成,界面边两侧对应两种不同介质中的网格。通过求解Riemann问题追踪介质界面上网格节点的运动,同时采用局部重构的动网格技术处理介质界面的大变形问题,并将介质界面定义为网格变形边界,以防止该边界上网格体积为负。运用HLLC格式求解ALE方程组得到整个多介质流场的数值解。最后从几个多介质流模型的计算结果可以看出,本文的动网格方法是可行的,而且可以时刻追踪介质界面的运动状态。     

基于四阶半离散中心迎风格式的虚拟流方法的应用

给出了求解多维无粘可压Euler方程组的四阶半离散中心迎风格式,该格式根据非线性波在网格单元边界上传播的局部速度来更准确地估计局部Riemann的宽度,避免了计算网格的交错,降低了格式的数值粘性。同时,考虑到Level Set函数能隐式地追踪到界面的位置,而虚拟流的构造能隐式地捕捉到界面的边界条件,因此再将新的四阶半离散中心迎风格式与Level Set方法以及虚拟流方法相结合,成功地处理了非反应激波和多介质流中爆轰间断的追踪问题。     

用改进的ghost fluid方法模拟强激波与界面的相互作用

为了解决原来的ghost fluid方法在计算强激波和界面相互作用时界面附近出现的速度和压力振荡问题,对原来的ghost fluid方法进行了改进,通过在界面处构造Riemann问题并求出界面的压力和速度,ghost fluid流体的压力和速度分别用界面的压力和速度代替,ghost流体的密度通过熵常数外推得到。改进的ghost fluid保持了原来的ghost fluid的简单性,对一维强激波与气-气、气-液界面的相互作用问题以及射流问题进行了数值计算,得到了分辨率较高的计算结果。     

可压缩流体流动多尺度混合有限元数值方法研究

可压缩流体是天然油藏中广泛存在的一种流体,研究其在多孔介质中的渗流规律对于油藏开发具有重要意义。本文采用多尺度混合有限元方法,对可压缩流体渗流问题进行了研究。考虑流体的可压缩性以及介质形变,推导得到了可压缩流体渗流问题的多尺度计算格式。数值计算结果表明,多尺度混合有限元适于求解非均质性和可压缩流问题,具有节省计算量、计算精度高等优势,对于实际大规模油藏模拟具有重要意义。     

High-resolution algorithms of sharp interface treatment for compressible two-phase flows

In this paper, a kind of arbitrary high order derivatives (ADER) scheme based on the generalised Riemann problem is proposed to simulate multi-material flows by a coupling ghost fluid method. The states at cell interfaces are reconstructed by interpolating polynomials which are piece-wise smooth functions. The states are treated as the equivalent of the left and right states of the Riemann problem. The contact solvers are extrapolated in the vicinity of contact points to facilitate ghost fluids. The numerical method is applied to compressible flows with sharp discontinuities, such as the collision of two fluids of different physical states and gas–liquid two-phase flows. The numerical results demonstrate that unexpected physical oscillations through the contact discontinuities can be prevented effectively and the sharp interface can be captured efficiently.     

A CWENO ghost fluid method for compressible multimaterial flow

In this work a new ghost fluid method (GFM) is introduced for multimaterial compressible flow with arbitrary equation of states. In previous researches, it has been shown that accurate wave decomposition at the interface by solving a Riemann problem alleviates the shortcomings of the standard GFM in dealing with the impingement of strong waves onto the interface but these Riemann‐based GFM are not consistent with the framework of the central WENO scheme in which the emphasis is to avoid solving Riemann problems at control volume faces and enjoy the black box property (being independent of equation of state). The aim of this work is to develop a new GFM that is completely consistent with the methodology behind central schemes; that is, it enjoys a black box property. The capabilities of the proposed GFM method is shown by solving various types of multimaterial compressible flows including gas–gas, gas–water and fluid–solid interfaces interacting with strong shock waves in one and two space dimensions. Copyright © 2013 John Wiley & Sons, Ltd.     

On the Riemann problem for liquid or gas-liquid media

Self-similar solutions to the Riemann problem for water with the modified Tait equation of state are presented. The methods of Smoller for gas dynamics are employed to reduce the problem to the solution of a single non-linear equation. The same methods are used for solving the Riemann problem at a gas-water interface. In both cases the method of interval bisections affords a solution technique free of problems with convergence.     

NUMERICAL SCHEME OF MULTI-MATERIAL COMPRESSIBLE FLOW WITH SHARP INTERFACE ON EULERIAN GRIDS

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.     

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.      

A discontinuous Galerkin‐based sharp‐interface method to simulate three‐dimensional compressible two‐phase flow

A numerical method for the simulation of compressible two‐phase flows is presented in this paper. The sharp‐interface approach consists of several components: a discontinuous Galerkin solver for compressible fluid flow, a level‐set tracking algorithm to follow the movement of the interface and a coupling of both by a ghost‐fluid approach with use of a local Riemann solver at the interface. There are several novel techniques used: the discontinuous Galerkin scheme allows locally a subcell resolution to enhance the interface resolution and an interior finite volume Total Variation Diminishing (TVD) approximation at the interface. The level‐set equation is solved by the same discontinuous Galerkin scheme. To obtain a very good approximation of the interface curvature, the accuracy of the level‐set field is improved and smoothed by an additional P_NP_M‐reconstruction. The capabilities of the method for the simulation of compressible two‐phase flow are demonstrated for a droplet at equilibrium, an oscillating ellipsoidal droplet, and a shock‐droplet interaction problem at Mach 3. Copyright © 2015 John Wiley & Sons, Ltd.     

Numerical simulation of compressible multifluid flows using an adaptive positivity-preserving RKDG-GFM approach

The Runge-Kutta discontinuous Galerkin method together with a refined real-ghost fluid method is incorporated into an adaptive mesh refinement environment for solving compressible multifluid flows, where the level set method is used to capture the moving material interface. To ensure that the Riemann problem is exactly along the normal direction of the material interface, a simple and efficient modification is introduced into the original real-ghost fluid method for constructing the interfacial Riemann problem, and the initial conditions of the Riemann problem are obtained directly from the solution polynomials of the discontinuous Galerkin finite element space. In addition, a positivity-preserving limiter is introduced into the Runge-Kutta discontinuous Galerkin method to suppress the failure of preserving positivity of density or pressure for the problems involving strong shock wave or shock interaction with material interface. For interfacial cells in adaptive mesh refinement, the data transfer between different grid levels is achieved by using a L² projection approach along with the least squares fitting. Various numerical cases, including multifluid shock tubes, underwater explosions, and shock-induced collapse of a underwater air bubble, are computed to assess the capability of the present adaptive positivity-preserving RKDG-GFM approach, and the simulated results show that the present approach is quite robust and can provide relatively reasonable results across a wide variety of flow regimes, even for problems involving strong shock wave or shock wave impacting high acoustic impedance mismatch material interface.     

A robust algorithm for moving interface of multi-material fluids based on Riemann solutions

In the paper, the numerical simulation of interface problems for multiple material fluids is studied. The level set function is designed to capture the location of the material interface. For multi-dimensional and multi-material fluids, the modified ghost fluid method needs a Riemann solution to renew the variable states near the interface. Here we present a new convenient and effective algorithm for solving the Riemann problem in the normal direction. The extrapolated variables are populated by Taylor series expansions in the direction. The anti-diffusive high order WENO difference scheme with the limiter is adopted for the numerical simulation. Finally we implement a series of numerical experiments of multi-material flows. The obtained results are satisfying, compared to those by other methods.The English text was polished by Boyi Wang.     

Modified ghost fluid method for three-dimensional compressible multimaterial flows with interfaces exhibiting large curvature and topological change

In order to capture the material interface dynamics, especially under the impact of strong shocks, the key feature of the modified ghost fluid method (MGFM) is to construct a multimaterial Riemann problem normal to the interface and use its solution to define interface conditions. However, such process sometimes may not be easily or accurately implemented when the multidimensional interfaces come into contact or undergo significant deformations. In this article, a three-dimensional interface treating procedure is developed for a wide range of compressible multimaterial flows. It utilizes the MGFM with an explicit approximate Riemann problem solver to define interface conditions. More importantly, a weighted average technique is designed to optimize the treatment for interfaces exhibiting large curvature and topological change. This remedies two defects of the traditional approach in these extreme cases. One is that the normal directions of interfacial ghost nodes may not be easily calculated. The other is that the interface conditions may not be accurately defined. The numerical methodology is validated through several typical problems, including gas-liquid Riemann problem and shock-bubble/droplet interaction. These results indicate that the developed method is capable of dealing with interfacial evolutions in three dimensions, especially when interfaces undergo merger, fragmentation, and other complex changes.