固定网格下的特征线法求解溃坝问题

溃坝问题是典型的非线性双曲方程的Riemann问题,其数值求解的难点在于对间断面的捕捉以及避免间断面处在数值计算过程中产生数值色散,因而为求解此问题所产生的各种数值计算方法的优劣也体现在这两个方面。本文针对溃坝问题提出一种新的计算方法。该方法基于对偶变量推导的浅水波方程,根据方程的特点,从方程的特征值和黎曼不变量出发,采用高精度的激波捕捉方法计算黎曼不变量的位置随时间的变化,然后映射至不随时间变化的固定网格。根据黎曼不变量的位置,采用保形分段三次Hermite插值将物理量映射至网格节点。计算结果显示,该方法不仅操作简单,计算量小,而且结果准确。     

基于WENO重构的真正多维黎曼求解器

具有良好守恒性与网格适应性的有限体积格式在流体力学的数值计算中占有重要地位。其中，求解数值流通量是实施有限体积法的关键步骤。一维情形下，通过求解局部黎曼问题来获得数值流通量的相关理论已经比较成熟。但是在计算多维问题时，传统的维度分裂方法仅考虑沿界面法向传播的信息，这不仅影响格式的精度，还可能会造成数值不稳定性从而诱发非物理现象。本文基于对流-压力通量分裂方法来构造真正多维的黎曼求解器，通过求解网格顶点处的多维黎曼问题来实现格式的多维特性。采用五阶WENO重构方法来获得空间的高阶精度，时间离散采用三阶TVD龙格-库塔格式。一系列数值实验的结果表明，真正多维的黎曼求解器不仅具有更高的分辨率还能有效克服多维强激波模拟中的数值不稳定性。     

基于CFD的民用飞机水上迫降动力学仿真研究

针对民用飞机水上迫降动态冲击问题,采用数值仿真方法进行了研究.基于计算流体力学采用雷诺平均N–S方程求解,结合流体体积模型和全流场运动网格捕捉水?气交界面,求解六自由度方程获得飞机的位置和姿态.采用该方法研究了尾吊?高平尾布局飞机的水上迫降过程.结果表明,该方法可以较好地模拟水上迫降的运动和受力,入水早期飞机受到较大水...     

用鲁棒Riemann求解器和运动重叠网格计算旋翼粘性绕流

发展了一种基于鲁棒Riemann求解器和运动重叠网格技术计算直升机悬停旋翼流场的方法。基于惯性坐标系,悬停旋翼流场是非定常流场,控制方程为可压缩Reynolds平均Navier-Stoke方程,其对流项采用Roe近似Reimann求解器离散,使用改进的五阶加权基本无振荡格式进行高阶重构,非定常时间推进采用含牛顿型LUSGS子迭代的全隐式双时间步方法。为实施旋转运动和便于捕捉尾迹,计算采用运动重叠网格技术。计算得到的桨叶表面压力分布及桨尖涡涡核位置都与实验结果吻合较好。数值结果表明:所发展方法对桨尖涡具有较高的分辨率,对激波具有较好的捕捉能力,该方法可进一步推广到前飞旋翼粘性绕流的计算。     

剧变截面圆管内渗流的数值计算方法

对于剧变截面圆管的渗流问题写出不可压缩渗流的基本方程组，对直接求解原始变量(速度和压力)的数值计算方法作出改进。先由非主流方向的运动方程计算压力，后由主流方向的运动方程计算主流方向的速度分量，再由连续性方程计算非主流方向的速度分量。这样可以避免在一般的求解原始变量方法中由连续性方程计算压力时出现的困难和麻烦。根据本方法和剧变截面圆管的特点，采用半交错不等距非正交贴体混合网格系。本文详细写出差分方程和迭代计算公式，对剧变截面圆管内的渗流算例进行数值计算。本方法的优点是简单和实用，在工程上具有较大的应用价值。     

直接边界元法三维自由面兴波时域模拟

应用直接边界元法在时域中求解稳定航速运动的三维自由面兴波问题.基于格林定理,在所有边界面上划分网格,对边界积分方程进行数值离散,采用线性自由面边界条件,随时间步进更新自由面势.由于物体空间位置移动辐射条件不需要单独表述,迭代过程中自由面计算域保持不变.以割划水面NACA0024为例,计算模拟了自由面兴波稳定波形;提出了求解矩阵方程组奇异性的处理方法和解决割划问题的动网格技术.本文计算结果和有限体积法及有关试验结果对比表明,该方法是可靠的.     

Level set方法在自适应Cartesian网格上的应用

采用基于自适应Cartesian网格的level set方法对多介质流动问题进行数值模拟。采用基于四叉树的方法来生成自适应Cartesian网格。采用有限体积法求解Euler方程，控制面通量的计算采用HLLC（Hartern, Lax, van Leer, Contact）近似黎曼解方法。level set方程也采用有限体积法求解，采用Lax-Friedchs方法计算通量，通过窄带方法来减少计算量，界面的处理采用ghost fluid方法。Runge-Kutta显式时间推进，时间、空间都是二阶精度。对两种不同比热比介质激波管问题进行数值模拟，其结果和精确解吻合；对空气/氦气泡相互作用等问题进行模拟，取得令人满意的结果。     

福建海岸带地质环境背景与海水入侵的形成条件探讨

提出一种新的网格自适应方法：在需要加密的网格单元中心加入新结点，并对加密后的相邻 三角形网格单元进行公共边变换, 构成新的网格单元. 与传统的在网格边界中点加入新节点的自 适应方法相比，新方法可以更加灵活地控制网格密度，加密后的网格继承原先的网格质量不 发生畸变，并且算法编程简便，容易实现. 将自适应网格生成方法和基于特征线方程的分离 算法相结合，对空腔内不可压缩黏性流动进行了计算. 在特征线方向上进行时间步离散，动 量方程求解过程中采用非增量型分离算法. 计算中，把求解变量梯度值作为判定准则，在 变化剧烈的区域进行网格局部加密. 计算结果表明该组合算法有很好的计算精度，并有效减 少了计算时间和存储量.     

结合自适应网格的基于特征线方程的分离算法

提出一种新的网格自适应方法:在需要加密的网格单元中心加入新结点,并对加密后的相邻三角形网格单元进行公共边变换,构成新的网格单元.与传统的在网格边界中点加入新节点的自适应方法相比,新方法可以更加灵活地控制网格密度,加密后的网格继承原先的网格质量不发生畸变,并且算法编程简便,容易实现.将自适应网格生成方法和基于特征线方程的分离算法相结合,对空腔内不可压缩黏性流动进行了计算.在特征线方向上进行时间步离散,动量方程求解过程中采用非增量型分离算法.计算中,把求解变量梯度值作为判定准则,在变化剧烈的区域进行网格局部加密.计算结粜表明该组合算法有很好的计算精度,并有效减少了计算时间和存储量.     

求解一维理想磁流体方程的移动网格熵稳定格式

磁流体方程的数值求解在等离子体物理学、天体物理研究以及流动控制等领域具有重要意义，本文构造了用于求解理想磁流体动力学方程的基于移动网格的熵稳定格式，此方法将Roe型熵稳定格式与自适应移动网格算法结合，空间方向采用熵稳定格式对磁流体动力学方程进行离散，利用变分法构造网格演化方程并通过Gauss-Seidel迭代法对其迭代求解实现网格的自适应分布，在此基础上采用守恒型插值公式实现新旧节点上的量值传递，利用三阶强稳定Runge-Kutta方法将数值解推进到下一时间层。数值实验表明，该算法能有效捕捉解的结构(特别是激波和稀疏波),分辨率高，通用性好，具有强鲁棒性。     

An extension of Osher's Riemann solver for chemical and vibrational non-equilibrium gas flows

In this paper we study an extension of Osher's Riemann solver to mixtures of perfect gases whose equation of state is of the form encountered in hypersonic applications. As classically, one needs to compute the Riemann invariants of the system to evaluate Osher's numerical flux. For the case of interest here it is impossible in general to derive simple enough expressions which can lead to an efficient calculation of fluxes. The key point here is the definition of approximate Riemann invariants to alleviate this difficulty. Some of the properties of this new numerical flux are discussed. We give 1D and 2D applications to illustrate the robustness and capability of this new solver. We show by numerical examples that the main properties of Osher's solver are preserved; in particular, no entropy fix is needed even for hypersonic applications.     

A generalized Rusanov method for the Baer‐Nunziato equations with application to DDT processes in condensed porous explosives

The paper addresses a numerical approach for solving the Baer‐Nunziato equations describing compressible 2‐phase flows. We are developing a finite‐volume method where the numerical flux is approximated with the Godunov scheme based on the Riemann problem solution. The analytical solution to this problem is discussed, and approximate solvers are considered. The obtained theoretical results are applied to develop the discrete model that can be treated as an extension of the Rusanov numerical scheme to the Baer‐Nunziato equations. Numerical results are presented that concern the method verification and also application to the deflagration‐to‐detonation transition (DDT) in porous reactive materials.     

Direct Riemann solvers for the time-dependent Euler equations

Approaches for finding direct, approximate solutions to the Riemann problem are presented. These result in three approximate Riemann solvers. Here we discuss the time-dependent Euler equations but the ideas are applicable to other systems. The approximate solvers are (i) assessed on local Riemann problems with exact solutions and (ii) used in conjunction with the Weighted Average Flux (WAF) method to solve the two-dimensional Euler equations numerically. The resulting numerical technique is assessed on a shock reflection problem. Comparison with experimental observation is carried out.     

An approximate‐state Riemann solver for the two‐dimensional shallow water equations with porosity

PorAS, a new approximate‐state Riemann solver, is proposed for hyperbolic systems of conservation laws with source terms and porosity. The use of porosity enables a simple representation of urban floodplains by taking into account the global reduction in the exchange sections and storage. The introduction of the porosity coefficient induces modified expressions for the fluxes and source terms in the continuity and momentum equations. The solution is considered to be made of rarefaction waves and is determined using the Riemann invariants. To allow a direct computation of the flux through the computational cells interfaces, the Riemann invariants are expressed as functions of the flux vector. The application of the PorAS solver to the shallow water equations is presented and several computational examples are given for a comparison with the HLLC solver. Copyright © 2009 John Wiley & Sons, Ltd.     

The discontinuous profile method for simulating two‐phase flow in pipes using the single component approximation

Godunov‐type algorithms are very attractive for the numerical solution of discontinuous flows. The reconstruction of the profile inside the cells is crucial to scheme performance. The non‐linear generalization of the discontinuous profile method (DPM) presented here for the modelling of two‐phase flow in pipes uses a discontinuous reconstruction in order to capture shocks more efficiently than schemes using continuous functions. The reconstructed profile is used to define the Riemann problem at cell interfaces by averaging of the components of the variable in the base of eigenvectors over their domain of dependence. Intercell fluxes are computed by solving the Riemann problem with an approximate‐state solver. The adapted treatment of boundary conditions is essential to ensure the quality of the computational results and a specific procedure using virtual cells at both extremities of the computational domain is required. Internal boundary conditions can be treated in the same way as external ones. Application of the DPM to test cases is shown to improve the quality of computational results significantly. Copyright © 2001 John Wiley & Sons, Ltd.     

空气自由场中强爆炸冲击波传播二维数值模拟

编写了适用于模拟具有高密度比、高压力比的强激波问题的二维柱对称多介质流体计算程序。利用有限体积方法求解流体的Euler方程组，采用level set方法捕捉爆炸产物与空气的运动界面，并通过求解物质界面两侧Riemann问题的精确解来计算爆炸产物与空气之间的数值通量。研制了三角形网格自适应技术来实现网格的自动加密和粗化，在保证捕捉激波峰值的前提下有效地提高了计算效率。利用计算程序对1 kt TNT当量的空气自由场强爆炸问题进行数值模拟，计算得到的峰值超压、冲击波到达时间等物理参数与点爆炸理论结果基本一致。     

Performance of finite volume solutions to the shallow water equations with shock‐capturing schemes

Numerical methods have become well established as tools for solving problems in hydraulic engineering. In recent years the finite volume method (FVM) with shock capturing capabilities has come to the fore because of its suitability for modelling a variety of types of flow; subcritical and supercritical; steady and unsteady; continuous and discontinuous and its ability to handle complex topography easily. This paper is an assessment and comparison of the performance of finite volume solutions to the shallow water equations with the Riemann solvers; the Osher, HLL, HLLC, flux difference splitting (Roe) and flux vector splitting. In this paper implementation of the FVM including the Riemann solvers, slope limiters and methods used for achieving second order accuracy are described explicitly step by step. The performance of the numerical methods has been investigated by applying them to a number of examples from the literature, providing both comparison of the schemes with each other and with published results. The assessment of each method is based on five criteria; ease of implementation, accuracy, applicability, numerical stability and simulation time. Finally, results, discussion, conclusions and recommendations for further work are presented. Copyright © 2002 John Wiley & Sons, Ltd.     

A general approximate‐state Riemann solver for hyperbolic systems of conservation laws with source terms

An approximate‐state Riemann solver for the solution of hyperbolic systems of conservation laws with source terms is proposed. The formulation is developed under the assumption that the solution is made of rarefaction waves. The solution is determined using the Riemann invariants expressed as functions of the components of the flux vector. This allows the flux vector to be computed directly at the interfaces between the computational cells. The contribution of the source term is taken into account in the governing equations for the Riemann invariants. An application to the water hammer equations and the shallow water equations shows that an appropriate expression of the pressure force at the interface allows the balance with the source terms to be preserved, thus ensuring consistency with the equations to be solved as well as a correct computation of steady‐state flow configurations. Owing to the particular structure of the variable and flux vectors, the expressions of the fluxes are shown to coincide partly with those given by the HLL/HLLC solver. Computational examples show that the approximate‐state solver yields more accurate solutions than the HLL solver in the presence of discontinuous solutions and arbitrary geometries. Copyright © 2006 John Wiley & Sons, Ltd.     

A mass‐fraction‐based interface‐capturing method for multi‐component flow

An interface‐capturing method based on mass fraction is developed to solve the Riemann problem in multi‐component compressible flow. Equations of mass fraction with modified form, which is derived from conservative equations of mass, are employed here to capture the interface. By introducing mass fraction into Euler equations system, as well as other conservative coefficients, a quasi‐conservative numerical model is created. Numerical examples show that the mass fraction model performs well not only in multi‐component fluids modeled by simple stiffened gas equation of state (EOS) but also in that modeled by complex Mie–Grüneisen EOS. Moreover, the mass fraction model is applied to Riemann problem with piecewise EOS; the expression of which depends on density. It is found that the mass fraction model can well adapt to the analytic change in piecewise EOS and produce accuracy solutions with fewer unknown quantities, and the model can be easily extended to m‐component fluid mixture by using only m + 4 equations with no additional conditions. Copyright © 2013 John Wiley & Sons, Ltd.