二维多介质可压缩流的RKDG有限元方法

应用RKDG(Runge-Kutta Discontinuous Galerkin)有限元方法、Level Set方法和Ghost Fluid方法数值模拟二维多介质可压缩流,其中Euler方程组、Level Set方程和重新初始化方程的空间离散采用DG(Discontinuous Galerkin)有限元方法,时间离散采用Runge-Kutta方法.对二维的气-气和气-液两相流进行了数值计算,得到了分辨率较高的计算结果.     

气液两相流的间断有限元模拟

基于非结构网格,给出模拟两相流的统一间断有限元框架.其中,不可压Navier-Stokes方程采用IPDG(Interior penalty discontinuous Galerkin)方法求解;Level Set方程采用RKDG(Runge-Kutta discontinuous Galerkin)方法求解.方腔驱动流在不同Re数时的数值结果验证了该方法在单相流动中的有效性.气泡上升过程的模拟结果表明:该方法避免了重新初始化,且计算量小、实施简单,可有效求解具有运动界面的不可压两相流问题.     

非结构网格上Level Set方程的间断有限元解法

针对间断有限元弱形式难于求解可压缩流场中Level Set方程的问题提出间断有限元强形式,从而在统-框架下解决Level Set方程在可压缩与不可压缩流场中的求解问题.通过非结构网格上采用Legendre-Gauss-Lobatto节点构造基函数,在复杂区域上可以达到任意高阶的精度.将若干-、二、三维算例与已有文献或解析解比较,验证方法追踪自由界面的有效性.结果表明,该方法适合各种情形下Level Set方程求解,易于在复杂区域的非结构网格上实施,精度高、分辨率高且具有高质量守恒性,既能避免重新初始化过程又方便向高维扩展.     

一维多介质可压缩Euler方程的高精度RKDG有限元方法

采用RKDG有限元目的、Level Set目的和改进的带"Isentropic"修正的Ghost Fluid目的模拟了一维多介质可压缩Euler方程,其中Euler方程、Level Set方程和重新初始化方程都采用了三阶精度的RKDG有限元目的进行离散,并对一维两种介质可压缩流体进行了数值实验,得到了较高分辨率的计算结果.     

移动网格与Level Set耦合方法在气-液两相流数值模拟中的应用

本文采用自适应移动网格与Level Set函数相耦合的方法来实现气-液两相流的数值模拟与计算.作为自适应网格方法的一种,移动网格方法主要是为了解决发展方程的计算问题而设计的方法.文中给出了移动网格的生成方程,并针对方程的非线性,给出了一种半隐式的离散方法用于进行求解.本文将移动网格方法与Level Set方法相耦合,将控制流体运动的Navier-Stokes方程以及追踪相界面的Level Set方程转换到曲线坐标下,应用一套曲线坐标方程组来同时描述气、液两相流的运动规律,成功实现了对气-液两相流问题的数值模拟.通过对顶盖驱动流的计算以及对液滴沉降现象的模拟计算,验证了本文方法的可靠性.本文对常重力与微重力下两气泡融合的发展规律进行了数值模拟,通过分析对比,得到了重力对两气泡融合变形的影响规律.     

重新初始化的LS方法跟踪二维可压缩多介质流界面运动

 用非耦合求解方法计算Level Set函数方程与流体力学方程组，应用重新初始化的Level Set函数确保距离函数性质，流体力学方程组采用二阶精度多介质流波传播差分格式计算，重新初始化方程采用五阶WENO格式计算。并给出了二维可压缩多介质流界面运动的计算结果。     

隐-显积分因子间断Galerkin方法求解二维辐射扩散方程

提出一种求解二维非平衡辐射扩散方程的数值方法.空间离散上采用加权间断Galerkin有限元方法,其中数值流量的构造采用一种新的加权平均;时间离散上采用隐-显积分因子方法,将扩散系数线性化,然后用积分因子方法求解间断Galerkin方法离散后的非线性常微分方程组.数值试验中在非结构网格上求解了多介质的辐射扩散方程.结果表明:对于强非线性和强耦合的非线性扩散方程组,该方法是一种非常有效的数值算法.     

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.     

二维GEL耦合方法的研究及对爆炸容器的数值模拟

 将以Euler方法为基础的MF PPM（Piecewise-Parabolic Method）程序和以Lagrange方法为基础的DEFEL（2-D Finite Elements Code,二维流体弹塑性动力有限元）程序,根据压力和法向速度连续准则进行耦合,发展了基于Level Set的GEL（Ghost-Fluid Euler-Lagrange）方法。该方法在处理大变形流场与小变形结构以及复杂流动与多物体相互作用等问题具有优越性。通过二维算例的计算结果与文献比较,检验了GEL方法和耦合程序的正确性,并对球形和椭球封头的爆炸容器进行了数值模拟,通过与实验结果的比较分析,表明本研究程序可以比较好地处理内爆引起的壳体流固耦合问题。     

模拟研究推流式曝气池内横向水流对气泡生成的影响

应用限制项改进Level Set方法的容积守恒性.以改进的Level Set方法,结合ALE数值算法,三维模拟研究了推流式曝气池内横向水流对气泡生成的影响.模拟结果与文献中实验结果定性符合.数值结果显示,曝气池内横向水流对气泡的生成过程有重要的影响:气泡生成的尺寸和时间随着水流速度的增加而减小,随着曝气速度的增加而增加.该研究从流体动力学角度为提高活性污泥法处理效率提供了理论依据.     

Local discontinuous Galerkin method for solving Burgers and coupled Burgers equations

In the current work, we extend the local discontinuous Galerkin method to a more general application system. The Burgers and coupled Burgers equations are solved by the local discontinuous Galerkin method. Numerical experiments are given to verify the efficiency and accuracy of our method. Moreover the numerical results show that the method can approximate sharp fronts accurately with minimal oscillation.     

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.     

统一坐标系下二维气动方程组的Runge-Kutta间断Galerkin有限元方法

构造了统一坐标系下二维可压缩气动方程组的Runge-Kutta 间断Galerkin(RKDG)有限元格式. 文中将流体力学方程组和几何守恒律统一求解, 所有计算都在固定的网格上进行, 在计算过程中不需要网格节点的速度信息. 文中对几个数值算例进行了数值模拟, 得到了较好的数值模拟结果.     

曲率相关的爆轰波在非结构四边形网格上的数值方法

假设爆轰波阵面的法向速度是曲率的线性函数,在非结构四边形网格上采用水平集方法模拟爆轰波阵面的运动过程.水平集方程的曲率无关项采用正格式离散,曲率项采用伽辽金等参有限元方法空间离散,时间离散采用半隐格式.在笛卡儿网格和随机网格上,含曲率的水平集方程的离散格式为强一阶精度,重新初始化方程的离散格式精度为近似一阶精度.曲率收缩的不光滑界面和多个爆轰波阵面相互作用的算例说明格式可有效地模拟爆轰波与曲率相关的运动.     

Solving coupled nonlinear Schrodinger equations via a direct discontinuous Galerkin method

In this work,we present the direct discontinuous Galerkin(DDG) method for the one-dimensional coupled nonlinear Schrdinger(CNLS) equation.We prove that the new discontinuous Galerkin method preserves the discrete mass conservations corresponding to the properties of the CNLS system.The ordinary differential equations obtained by the DDG space discretization is solved via a third-order stabilized Runge-Kutta method.Numerical experiments show that the new DDG scheme gives stable and less diffusive results and has excellent long-time numerical behaviors for the CNLS equations.     

Solving coupled nonlinear Schrödinger equations via a direct discontinuous Galerkin method

In this work, we present the direct discontinuous Galerkin (DDG) method for the one-dimensional coupled nonlinear Schrödinger (CNLS) equation. We prove that the new discontinuous Galerkin method preserves the discrete mass conservations corresponding to the properties of the CNLS system. The ordinary differential equations obtained by the DDG space discretization is solved via a third-order stabilized Runge-Kutta method. Numerical experiments show that the new DDG scheme gives stable and less diffusive results and has excellent long-time numerical behaviors for the CNLS equations.     

A domain decomposition method for solving the three-dimensional time-harmonic Maxwell equations discretized by discontinuous Galerkin methods

We present here a domain decomposition method for solving the three-dimensional time-harmonic Maxwell equations discretized by a discontinuous Galerkin method. In order to allow the treatment of irregularly shaped geometries, the discontinuous Galerkin method is formulated on unstructured tetrahedral meshes. The domain decomposition strategy takes the form of a Schwarz-type algorithm where a continuity condition on the incoming characteristic variables is imposed at the interfaces between neighboring subdomains. A multifrontal sparse direct solver is used at the subdomain level. The resulting domain decomposition strategy can be viewed as a hybrid iterative/direct solution method for the large, sparse and complex coefficients algebraic system resulting from the discretization of the time-harmonic Maxwell equations by a discontinuous Galerkin method.     

Space–time discontinuous Galerkin finite element method for two-fluid flows

A novel numerical method for two-fluid flow computations is presented, which combines the space–time discontinuous Galerkin finite element discretization with the level set method and cut-cell based interface tracking. The space–time discontinuous Galerkin (STDG) finite element method offers high accuracy, an inherent ability to handle discontinuities and a very local stencil, making it relatively easy to combine with local hp-refinement. The front tracking is incorporated via cut-cell mesh refinement to ensure a sharp interface between the fluids. To compute the interface dynamics the level set method (LSM) is used because of its ability to deal with merging and breakup. Also, the LSM is easy to extend to higher dimensions. Small cells arising from the cut-cell refinement are merged to improve the stability and performance. The interface conditions are incorporated in the numerical flux at the interface and the STDG discretization ensures that the scheme is conservative as long as the numerical fluxes are conservative. The numerical method is applied to one and two dimensional two-fluid test problems using the Euler equations.     

A Discontinuous Galerkin Method Based on a BGK Scheme for the Navier-Stokes Equations on Arbitrary Grids

A discontinuous Galerkin Method based on a Bhatnagar-Gross-Krook (BGK) formulation is presented for the solution of the compressible Navier-Stokes equations on arbitrary grids. The idea behind this approach is to combine the robustness of the BGK scheme with the accuracy of the DG methods in an effort to develop a more accurate, efficient, and robust method for numerical simulations of viscous flows in a wide range of flow regimes. Unlike the traditional discontinuous Galerkin methods, where a Local Discontinuous Galerkin (LDG) formulation is usually used to discretize the viscous fluxes in the Navier-Stokes equations, this DG method uses a BGK scheme to compute the fluxes which not only couples the convective and dissipative terms together, but also includes both discontinuous and continuous representation in the flux evaluation at a cell interface through a simple hybrid gas distribution function. The developed method is used to compute a variety of viscous flow problems on arbitrary grids. The numerical results obtained by this BGKDG method are extremely promising and encouraging in terms of both accuracy and robustness, indicating its ability and potential to become not just a competitive but simply a superior approach than the current available numerical methods.