刘铁钢

Beihang University

Adjoint-based airfoil optimization with adaptive isogeometric discontinuous Galerkin method

In this work, an adjoint-based airfoil shape optimization algorithm is developed based on the adaptive isogeometric discontinuous Galerkin method for compressible Euler equations to investigate the significance of each design variable of airfoil B-spline parameterization. We first parameterize the airfoil by B-spline curve approximation with some control points viewed as design variables, and build the B-spline representation of the flow field with the curve to apply the goaloriented h-adaptive isogeometric DG method for flow solution. Then we compute and employ the discrete adjoint solutions for both multi-target error estimation in adaptive mesh refinement and gradients evaluation involved in SQP optimization algorithm. With the isogeometric nature, not only all the geometrical cells but also the numerical basis functions can be analytically expressed by the design variables, indicating that the numerical solutions and objective could be differentiable with respect to those variables. Consequentl, the gradient is totally estimated in an accurate approach, and the sensitivity analysis is thus improved, by reducing the spatial discretization error and introducing the expression of derivative, to reveal the key parameters for optimization in an intuitive and efficient manner. The proposed algorithm is demonstrated on RAE2822 airfoil with inviscid transonic flow, where the shape is optimized to minimize the drag coefficient at a constrained lift and airfoil area. The numerical results show that the drag is much more sensitive to the design variables near the tailing edge at the beginning but closed when optimal.

2018年5月19日，8:30-9:10

蔡 力

Northwestern Polytechnical University

A Double-Distribution-Function Lattice Boltzmann Method for Bed-Load Sediment Transport

The governing equations of bed-load sediment transport are the shallow water equations and the Exner equation. To embody the advantages of the lattice Boltzmann method, the three-velocity(D1Q3) and five-velocity(D1Q5) double-distribution-function lattice Boltzmann models (DDF-LBMs), which can present the numerical solution for one-dimensional bed-load sediment transport, are proposed here based on the quasi-steady approach. The so-called DDF-LBM means we use two distribution functions to describe the movement of the two components, respectively. By using the Chapman-Enskog expansion, the governing equations can be recovered correctly from the DDF-LBMs. To illustrate the efficiency of these, two benchmark tests are used, and excellent agreements between the numerical and analytical solutions are demonstrated. In addition, we show that the D1Q5 DDF-LBM has better accuracy compared to the Hudson's method.

2018年5月19日，9:10-9:50

李杰权

Institute of Applied Physics and Computational Mathematics

High Order Temporal-Spatially Coupled and Thermodynamically Consistent GRP Schemesfor Compressible Multi-fluid Flows

The most distinct feature of compressible multi-fluid flows is the presence of singularities (shocks, material interfaces, vortices and other discontinuities etc) in flows, which arises notorious difficulties in all aspects of theoretical justification, numerical analysis, scientific computation as well as engineering applications. Just from the viewpoint of the design of numerical methods, high resolution schemes have become the mainstream for several decades, however, there are still many bottleneck problems unsolved. This lecture will address some fundamentals in this aspect, based the celebrated Lax-Wendroff method, which can be traced back traced back to Cauchy-Kowalevski’s theory in 1700's in terms of power series solution for hyperbolic problems. The irreplaceable values the Lax-Wendroff approach can be summarized as follows. (i) It is a unique three-point second order accurate scheme. Any high order scheme should be consistent with the Lax-Wendroff method when it reduces to its second order version. Hence the Lax-Wendroff method is the reference of all high order accurate methods for compressible fluid flows. (ii) It uses the least stencils (just three points for each time step) and is therefore most compact in the family of schemes of second order both in space and time. The compactness determines the numerical dissipation of a scheme near singularities. (iii) It is a temporal-spatial coupled method and all useful information of the governing equations are fully incorporated into the scheme. There is no need to exert extra effort even when any other physical or geometrical effects are included. The spatial-temporal coupling is a key element that is consistent with relevant physical features such as the temporal-spatial coherence in the turbulent flows. Nevertheless, the Lax-Wendroff approach just works for smooth flows, and it should be modified to suit for capturing discontinuities. The currently-used generalized Riemann problem (GRP) method is regarded as the discontinuous version of Lax-Wendrof method, and it uses both the Cauchy-Kowalevski methodology and the singularity tracking technique. The resulting scheme is consistent directly with the corresponding physical balance laws in integral form rather than in PDE form. Hence the GRP method works well even when the flows contain very strong singularities (shocks, interfaces etc). The lecture has four parts: (1) We will rigorously define high order/resolution schemes as singularities are present in fluid flows; (2) As singularities are present, non-equilibrium effect becomes important and thus thermodynamics should be seriously taken into account. We will clarify how build the thermodynamic effect into the design of schemes; (3) We will formulate a new framework to design temporal-spatial coupled high order numerical methods, in sharp contrast with the line method with Runge-Kutta type methods as representatives; (4) We will display the performance of the schemes through a serious application for real engineering problems.

2018年5月19日，10:10-10:50

夏银华

University of Science and Technology of China

Maximum principle of arbitrary Lagrangian-Eulerian discontinuous Galerkin methods for conservation laws

In this talk, we present the arbitrary Lagrangian-Eulerian discontinuousGalerkin (ALE-DG) methods for conservation laws. The method will be designed for simplex meshes. This will ensure that the method satisfies the geometric conservation law for any time integration method with the accuracy order at least the same as spatial dimension. For the semi-discrete method the -stability and the suboptimal (k+1/2) convergence with respect to the -norm will be proven, when an arbitrary monotone flux is used and for each cell the approximating functions are given by polynomials of degree k. The two dimensional fully-discrete explicit method will be combined with the bound preserving limiter. This limiter does not affect the high order accuracy of the numerical method. Then, for the ALE-DG method revised by the limiter the validity of a discrete maximum-principle will be proven. This approach can also be developed for the positivity preserving of ALE-DG methods for Euler equations. The numerical stability, robustness and accuracy of the method will be shown by a variety of computational experimens on moving meshes.

2018年5月19日，10:50-11:30

成 娟

Institute of Applied Physics and Computational Mathematics

High order and robust Lagrangian schemes for compressible fluid flows

There are two typical frameworks to describe the motion of fluid flow, that is, the Eulerian framework and the Lagrangian framework. In the Eulerian formulation the mesh is fixed in space, which makes these methods very suitable for flows with large deformations. On the other hand, Lagrangian methods, e.g., in which the computational mesh moves with the fluid, are more suitable for problems involving interfaces between materials or free surfaces. Thus they are widely used in many fields for multi-material flows simulations. In applications such as astrophysics and inertial confinement fusion, there are many three-dimensional cylindrical-symmetric multi-material problems which are usually simulated by Lagrangian schemes in the two-dimensional cylindrical coordinates. For this type of simulation, the critical issues for the schemes are high order accuracy and robustness which include keeping positivity of physically positive variables such as density and internal energy and keeping spherical symmetry in the cylindrical coordinate system if the original physical problem has this symmetry. In this talk, we will introduce our recent work on high order positivity-preserving and symmetry-preserving Lagrangian schemes solving compressible Euler equations. The properties of positivity- preserving and symmetry-preserving are proven rigorously. One- and two-dimensional numerical results are provided to verify the designed characteristics of these schemes.

2018年5月19日，14:00-14:40

李 鹏

Shijiazhuang Tiedao University

Hybrid Schemes for the Detonation Structure Simulations

In the first part of this talk, the Hybrid FC-WENO-Z scheme (Hybrid) conjugating the Fourier-Continuation (FC) method with the improved fifth order WENO-Z finite difference scheme is employed in the long time simulations of multi-dimensional detonation structures which contain both discontinuous and complex smooth structures. The fine scale structures behind the detonation front and the quasi-steady state cellular structures of the peak pressure in the half reaction zone are well captured. A classical stable two-dimensional detonation waves shows that an improved resolution of the more fine scale structures of detonation waves as computed by the Hybrid scheme with less CPU times when compares with the pure WENO-Z scheme. The influence of initial and boundary conditions on the formation and evolution of the detonation structures are also illustrated with examples. The in-phase rectangular, out-of-phase rectangular and in-phase diagonal cellular structures in the three- dimensional detonation simulations are shown to demonstrate the ability of the Hybrid scheme in capturing the intrinsic evolution of the detonation fronts. In the second part, to handle the problems with extreme conditions, such as high pressure and density ratios and near vacuum states, and detonation diffraction problems, we design a positivity- and bound-preserving limiter for the improved hybrid scheme which employing the nonlinear 5th-order characteristic-wise WENO-Z5 finite difference scheme and the linear 5th-order conservative compact upwind (CUW5) scheme, the detonation diffraction problems and detonation passing multiple obstacles problems are well solved by the positivity-preserving hybrid schemes.

2018年5月19日，14:40-15:20

徐 岩

University of Science and Technology of China

Local discontinuous Galerkin methods for the µ-Camassa-Holm and µ-Degasperis-Procesi equations

In this paper, we develop and analyze a series of conservative and dissipative local discontinuous Galerkin (LDG) methods for the µ-Camassa-Holm(µCH) and µ-Degasperis-Procesi (µDP) equations. The conservative schemes for both two equations can preserve discrete versions of their own first two Hamiltonian invariants, while the dissipative ones guarantee the corresponding stability. An error estimate of the conservative scheme for the µ-CH equation is given via following the ideas of the distributions on the LDG method to the Camassa-Holm equation, in addition to some important tools to handle the unexpected terms caused by its particular Hamiltonian invariants. Moreover, a priori error estimates of two LDG schemes for the µ-DP equation are proven in detail. Numerical experiments for both two equations in different circumstances are provided to illustrate the accuracy and capability of these schemes and give some comparisons about their performance on simulations.

2018年5月19日，15:40-16:20

张林林

中国科学院海洋研究所

西太平洋环流三维结构与变异及相关数学问题

西太平洋毗邻我国，对我国的海洋环境安全保障和气候变化研究至关重要。西太平洋具有复杂的三维海洋环流结构，除了上层的风生环流之外，在温跃层之下还存在着反向的多支潜流。 经过近年来在西太平洋开展的一系列大规模强化观测，我们在该区域三维环流的结构方面取得了许多新的认识，尤其是揭示出潜流强劲的季节内变化规律，指出了其空间不均匀特征以及与不同类型涡旋活动之间的关系。这些新现象的发现也给经典的二维环流理论带来了巨大的挑战，传统的风生环流模型较好地解释了上层环流的基本结构，但对于环流的三维结构以及活跃的、不同类型的中尺度涡旋现象，则需要建立多层的非线性模型以及合理的数值计算方法来予以解决。

2018年5月19日，16:20-18:00

王瑞利

北京应用物理与计算数学研究所

自主研发流体力学软件与不确定度量化面临挑战

在航空、航天、大气、海洋、兵器与国防等国家重大工程，基于常微分方程（ODEs）与偏微分方程（PDEs）描述物理现象或多物理过程的物理建模，基于偏微分方程数值解构造离散格式与求解方法的数值建模，基于软件工程和高级语言自主开发软件的计算建模，自主研发高可信度数值模拟软件已成为CFD/CAE科技工作者和工程师不断追求的目标。但由于物理过程的复杂性和人们认知的缺陷，在物理建模、数值建模、计算建模过程中含有抽象、简化和近似， 严重影响数值模拟结果的可信度，使得决策者、理论研究者、工程设计家对基于数值模拟技术为复杂系统可靠性认证、性能评估和事故分析提供依据的这条途径产生疑问，严重阻碍着数值模拟技术在实际中的应用和“自造血能力”，制约着自主创新。自主研发具有预测能力的CFD/CAE数值仿真软件，其最大瓶颈是物理模型参数、同效异构模型形式、逼近方法等众多因素融合在一起引起的不确定度量化（UQ）问题。报告针对流体动力学与化学反应动力学耦合的复杂过程，从工程界遇到的多工况、多工序、多因素等物理模型可信度评估方面，从试验界遇到的点数据、时序数据、空间数据、时空数据等数学建模方面，剖析了自主研发预测性CFD/CAE数值仿真应用软件的现状及面临瓶颈，如几十甚至几百个不确定性参数带来的“维数灾难”、不确定性沿非线性传播、基于试验数据模型确认的时逆反问题、产生样本的超大计算量等挑战性问题。针对不确定度量化、参数标定、模型确认等挑战问题，提出了基于代理模型的贝叶斯参数标定方法。该方法分为正问题（DP）数值模拟建立数值试验样本的代理模型和反问题（IP）的贝叶斯推断方法确定可信参数值两部分。首先，利用先验知识对参数粗估一个概率密度函数，据此进行抽样，代入流体力学软件，通过正问题（DP）数值模拟，建立响应量与输入参数相关的参考样本；第二，基于数值试验样本，构造了基于参数非线性标定指标函数的代理模型；第三，利用反问题（IP）的贝叶斯推断方法来获得参数可信值或全局最优值，以达到提高基于试验数据反推参数可信值的求解速度和避免参数标定陷入随机解的目的。最后，建议基于人工智能思想建立“复杂工程建模与模拟仿真软件可信度评估智能平台”，以有效支撑模型不确定性量化及软件可信度评估，自主研发预测性的CFD/CAE数值仿真应用软件。

2018年5月20日，8:30-9:10

田 浩

Ocean University of China

A nonlocal convection-diffusion model and its numerical approximations

In this talk, we first propose a nonlocal convection-diffusion model, in which the convection term is constructed in a special upwind manner so that mass conservation and maximum principle are maintained. The well-posedness of the resulting nonlocal model and its convergence to the classical, local convection-diffusion model are established. A quadrature-based finite difference discretization is then developed to numerically solve the nonlocal problem and it is shown to be consistent and unconditionally stable. We also prove that this numerical scheme is asymptotically compatible, that is, the approximate solutions converge to the exact solution of the corresponding local problem. Consistent error orders are carefully derived to illustrate the effect of the nonlocal convection term. Numerical experiments are also performed to validate the theoretical results.

2018年5月20日，9:10-9:50

吕咸青

Ocean University of China

伴随同化方法在物理海洋学研究中的应用

2018年5月20日，10:10-10:50

马洪余

国家海洋局第一海洋研究所

波-湍相互作用实验室实验研究

基于风-浪-流多功能实验水槽，开展波-湍相互作用的实验研究，由格栅振动产生可控强度、均匀且各向同性的湍流，此湍流可以重复产生；在水槽的一端由造波机产生波高5cm，周期1s的表面波，在水槽的另一端安装有消波板，尽可能减小波浪的反射。开展了三类实验，单纯造波实验、单纯格栅振动产生湍流实验、格栅振动产生湍流加造波实验，利用ADV高频测量流体的速度，每一个实验采集10分钟的数据，选取水平速度分量u，利用全息谱方法对数据进行分析，在AM为1 Hz上下的位置上，有显著的能量分布，在FM上占据约10 Hz至25 Hz的频率带宽，可见低频1 Hz的波动对湍流有显著的调制作用。即波浪对湍流有显著的调制作用，使得湍流增强。且由湍流强度锁相分析，可以看出波对湍流的调制主要发生在波谷位相处。

2018年5月20日，10:50-11:30