多分量流计算的高分辨KFVS有限体积方法

论及高分辨分子动力学通向量分裂(KFVS)有限体积方法的推广。在方法中提出了适当修改Maxwell平衡分布用以修复Euler方程。基于熟知的Euler方程与Boltzm方程的关系，提出了一类求解多分量Euler方程的高分辨分子动力学通向量分裂(KFVS)有限体积方法。应用该方法不需要求解任何Riemann问题或求解附加的非守恒压力方程也不需要任何非守恒修正。数值计算表明，数值解在物质界面附近无振荡，激波速度也正确，显示出方法的高精度及其稳健性。     

不规则对接网格的分区求解计算

采用一种保持通量守恒的不规则对接网格分区求解中交界面耦合条件的计算方法, 结合有限体积法求解了Euler 方程, 无粘通量取用Van Leer 分裂格式, 构造了一种限制器以实现格式的二阶精度和TVD 性质, 并给出数值算例。     

二阶STC格式及其对跨音速湍流流动的数值模拟

ＳＴＣ格式是一种求解积分形式物理守恒律的计算方法,具有守恒性好,精度高的特点。目前求解Ｅｕｌｅｒ方程的ＳＴＣ格式已经建立起来,但求解Ｎ－Ｓ方程的ＳＴＣ格式尚在发展之中。为了使ＳＴＣ格式能够有效地求解粘性流动的问题,本文构造出了求解曲线坐标系下的二维Ｎ－Ｓ方程的二阶ＳＴＣ格式。用该格式对跨音速湍流流动问题进行了计算。     

飞机构型Euler绕流结构网格方法计算的可信度

采用三种方法验证飞机构型Ｅｕｌｅｒ绕流结构网格方法计算。第一,同一网格,采用不同的方法或程序进行计算,采用Ｊａｍｅｓｏｎ中心差分有限体积方法和Ｓｔｅｇｅｒ－Ｗａｒｍｉｎｇ流量分裂迎风格式有限体积方法,为计算提供容错手段;第二,网格细化和网格点重新分布,并通过网格收敛指标进行评估;第三,提出新的多块拼接网格拓朴,采用不同的网格拓扑进行计算。     

龙格库塔间断有限元方法在计算爆轰问题中的应用

构造求解带源项守恒律方程组的龙格库塔间断有限元(RKDG)方法,并分别结合源项的Strang分裂法和无分裂法数值求解模型守恒律方程和反应欧拉方程.为了和有限体积型WENO方法进行比较,设计计算源项的WENO重构格式.对一维带源项守恒律的计算表明,对于非刚性问题,RKDG方法比有限体积型WENO方法的误差更小;对于刚性问题,RKDG方法对于间断面位置的捕捉更为精确.对于一二维爆轰波问题的计算结果表明,RKDG方法对爆轰波结构的分辨和爆轰波位置的捕捉能力更强.     

铂Hugoniot曲线的Ab initio计算

对于一个原子平均体积为Ｖ,温度为Ｔ的热力学系统,体系的Ｈｅｌｍｂｏｌｔｚ自由能可以写为Ｆ（Ｖ,Ｔ）＝Ｅｃ（Ｖ）＋Ｆｉｏｎ（Ｖ,Ｔ）＋Ｆｅｌ（Ｖ,Ｔ）＋Ｆｍａｎ（Ｖ,Ｔ）其中Ｅｃ为０－Ｋ冷能。对于其中的电子热激发贡献Ｆｅｌ,目前流行的有三种计算方案,即：Ｍｏｒｕｚｚｉ的Ｄｅｂｙｅ－Ｇｒｕｅｎｅｉｓｅｎ方案、Ｍｏｒｉａｒｔｙ的ＭＧＰＴ方案和Ｗａｓｓｅｒｍａｎ的ＣＥＬＬ模型方案。Ｄｅｂｙｅ－Ｇｒｕｅｎｅ     

不同积叠线形式对涡轮性能的影响

用求解Ｓ２流面平均Ｅｕｌｅｒ方程组程序对一个两级涡轮进行了数值模拟,静叶采用弯叶片,且采用了不同的积叠线生成方式;用高精度三维ＮＳ方程求解软件对第一级静叶进行了不同弯曲方式的数值模拟,分析了不同积叠线生成方式对涡轮性能的影响。     

基于扩散速度方法粘性流场的离散涡数值模拟

基于扩散速度方法粘性流场的离散涡数值模拟吴文权，李春，卜千里（上海机械学院上海２０００９３）关键词：扩散速度模型，粘性流场，离散涡方法。ＮＵＭＥＲＩＣＡＬＳＩＭＵＬＡＴＩＯＮＯＦＶＩＳＣＯＵＳＦＬＯＷＦＩＥＬＤＳＵＳＩＮＧＤＩＦＦＵＳＩＯＮＶＥＬＯＣ...     

用有限元方法求解双曲守恒律

分片线性插值有限元给出了求解双曲守恒律的计算方法。有别于不连续有限元方法求解双曲守恒律在相邻单元边界上求Ｒｉｅｍａｎｎ解,利用双曲守恒律的Ｈａｍｉｌｔｏｎ－Ｊａｃｏｂｉ方程形式,直接应用有限元求解,在ＣＦＬ下,证明了计算格式满足极大值原理,并且是ＴＶＤ格式。数值例子在文后给出。此外,方法推广到流体力学方程组和高维问题,将在另文中邓以讨论。     

基于样条逼近有限体积法的通量分裂算法

研究了任意曲线坐标系中求解双曲型守恒律的高精度、无波动样条逼近有限体积方法,比较了三种不同的通量分裂技术在这种方法中的应用。数值实验表明,在不同的通量分裂技术下,该方法对流场中的激波和接触间断都有很高的分辨率。     

The discontinuous Petrov-Galerkin method for one-dimensional compressible Euler equations in the Lagrangian coordinate

In this paper, a Petrov-Galerkin scheme named the Runge-Kutta control volume (RKCV) discontinuous finite element method is constructed to solve the one-dimensional compressible Euler equations in the Lagrangian coordinate. Its advantages include preservation of the local conservation and a high resolution. Compared with the Runge-Kutta discontinuous Galerkin (RKDG) method, the RKCV method is easier to implement. Moreover, the advantages of the RKCV and the Lagrangian methods are combined in the new method. Several numerical examples are given to illustrate the accuracy and the reliability of the algorithm.     

Positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations with source terms

In [16], [17], we constructed uniformly high order accurate discontinuous Galerkin (DG) schemes which preserve positivity of density and pressure for the Euler equations of compressible gas dynamics with the ideal gas equation of state. The technique also applies to high order accurate finite volume schemes. For the Euler equations with various source terms (e.g., gravity and chemical reactions), it is more difficult to design high order schemes which do not produce negative density or pressure. In this paper, we first show that our framework to construct positivity-preserving high order schemes in [16], [17] can also be applied to Euler equations with a general equation of state. Then we discuss an extension to Euler equations with source terms. Numerical tests of the third order Runge–Kutta DG (RKDG) method for Euler equations with different types of source terms are reported.     

自相似Euler方程的数值方法

Euler方程某些问题的解具有自相似特点，可以使用更准确的方法求解.提出了两种数值方法，分别称为自相似和准自相似方法，新方法可以使用现有守恒律方程的数值格式，无须设计特殊方法.对一维激波管问题、二维Riemann问题、激波反射以及激波折射问题进行了数值计算.对自相似Euler方程，一维计算结果显示数值解基本等同于精确解，二维结果也比现有文献计算的结果有更高的分辨率.对准自相似Euler方程，新方法可以求解不具有自相似性但接近自相似的问题，并在计算时间足够长时可以取得自相似Euler方程的效果.数值求解自相似Euler方程对自相似问题的研究，高分辨率、高精度格式的设计乃至Euler方程的精确解都有重要启示.      

On maximum-principle-satisfying high order schemes for scalar conservation laws

We construct uniformly high order accurate schemes satisfying a strict maximum principle for scalar conservation laws. A general framework (for arbitrary order of accuracy) is established to construct a limiter for finite volume schemes (e.g. essentially non-oscillatory (ENO) or weighted ENO (WENO) schemes) or discontinuous Galerkin (DG) method with first order Euler forward time discretization solving one-dimensional scalar conservation laws. Strong stability preserving (SSP) high order time discretizations will keep the maximum principle. It is straightforward to extend the method to two and higher dimensions on rectangular meshes. We also show that the same limiter can preserve the maximum principle for DG or finite volume schemes solving two-dimensional incompressible Euler equations in the vorticity stream-function formulation, or any passive convection equation with an incompressible velocity field. Numerical tests for both the WENO finite volume scheme and the DG method are reported.     

A Switch Function-Based Gas-Kinetic Scheme for Simulation of Inviscid and Viscous Compressible Flows

In this paper, a switch function-based gas-kinetic scheme (SF-GKS) is presented for the simulation of inviscid and viscous compressible flows. With the finite volume discretization, Euler and Navier-Stokes equations are solved and the SF-GKS is applied to evaluate the inviscid flux at cell interface. The viscous flux is obtained by the conventional smooth function approximation. Unlike the traditional gas-kinetic scheme in the calculation of inviscid flux such as Kinetic Flux Vector Splitting (KFVS), the numerical dissipation is controlled with a switch function in the present scheme. That is, the numerical dissipation is only introduced in the region around strong shock waves. As a consequence, the present SF-GKS can well capture strong shock waves and thin boundary layers simultaneously. The present SF-GKS is firstly validated by its application to the inviscid flow problems, including 1-D Euler shock tube, regular shock reflection and double Mach reflection. Then, SF-GKS is extended to solve viscous transonic and hypersonic flow problems. Good agreement between the present results and those in the literature verifies the accuracy and robustness of SF-GKS.     

可压缩密实介质多流体高精度欧拉算法

 从可压缩密实介质状态方程出发，推导出多介质流体在界面附近满足的动力学方程，与守恒律方程一起，采用高精度有限体积方法进行求解，物质界面用LevelSet函数捕捉。并给出了一维和二维数值算例。     

用改进的耦合型Level Set方法计算一维双介质可压缩流动

用带有虚拟流体(Ghost Fluid)修正的Level Set方法计算了一维可压缩双介质流动,把描述流动的Euler方程和描述流体界面运动的Level Set方程耦合起来,得到一个整体的守恒律系统,应用高分辨率差分格式求解;为了解决流体界面附近的数值跳动问题,在界面附近引入了虚拟流体方法的Isobaric修正,并给出了算例.     

Extension of the spectral volume method to high-order boundary representation

In this paper, the spectral volume method is extended to the two-dimensional Euler equations with curved boundaries. It is well-known that high-order methods can achieve higher accuracy on coarser meshes than low-order methods. In order to realize the advantage of the high-order spectral volume method over the low order finite volume method, it is critical that solid wall boundaries be represented with high-order polynomials compatible with the order of the interpolation for the state variables. Otherwise, numerical errors generated by the low-order boundary representation may overwhelm any potential accuracy gains offered by high-order methods. Therefore, more general types of spectral volumes (or elements) with curved edges are used near solid walls to approximate the boundaries with high fidelity. The importance of this high-order boundary representation is demonstrated with several well-know inviscid flow test cases, and through comparisons with a second-order finite volume method.     

A high order kinetic flux-vector splitting method for the reduced five-equation model of compressible two-fluid flows

We present a high order kinetic flux-vector splitting (KFVS) scheme for the numerical solution of a conservative interface-capturing five-equation model of compressible two-fluid flows. This model was initially introduced by Wackers and Koren (2004) [21]. The flow equations are the bulk equations, combined with mass and energy equations for one of the two fluids. The latter equation contains a source term in order to account for the energy exchange. We numerically investigate both one- and two-dimensional flow models. The proposed numerical scheme is based on the direct splitting of macroscopic flux functions of the system of equations. In two space dimensions the scheme is derived in a usual dimensionally split manner. The second order accuracy of the scheme is achieved by using MUSCL-type initial reconstruction and Runge–Kutta time stepping method. For validation, the results of our scheme are compared with those from the high resolution central scheme of Nessyahu and Tadmor [14]. The accuracy, efficiency and simplicity of the KFVS scheme demonstrate its potential for modeling two-phase flows.     

间断有限元方法在弹尾超音速喷流计算中的应用

采用间断有限元方法对超音速无粘喷流流动进行数值模拟.将二维双曲守恒方程的间断有限元方法发展到轴对称Euler方程,并就某导弹尾部超音速伴随射流进行数值计算.计算结果与实验照片反映的流动特征吻合较好,与高精度、高分辨率TVD格式的计算结果相比,间断有限元方法的计算结果在轴线反射点附近具有较高的分辨率,表明该方法对激波具有较强的捕捉能力,在激波阵面上不会产生振荡或抹平间断现象.