Efficient Finite Difference WENO Scheme for Hyperbolic Systems withNon-conservativeProducts

Higher order finite difference weighted essentially non-oscillatory(WENO)schemes have been constructed for conservation laws.For multidimensional problems,they offer a high order accuracy at a fraction of the cost of a finite volume WENO or DG scheme of the comparable accuracy.This makes them quite attractive for several science and engineering applications.But,to the best of our knowledge,such schemes have not been extended to non-linear hyperbolic systems with non-conservative products.In this paper,we perform such an extension which improves the domain of the applicability of such schemes.The extension is carried out by writing the scheme in fluctuation form.We use the HLLI Riemann solver of Dumbser and Balsara(J.Comput.Phys.304:275-319,2016)as a building block for carrying out this extension.Because of the use of an HLL building block,the resulting scheme has a proper supersonic limit.The use of anti-diffusive fluxes ensures that stationary discontinuities can be preserved by the scheme,thus expanding its domain of the applicability.Our new finite difference WENO formulation uses the same WENO reconstruction that was used in classical versions,making it very easy for users to transition over to the present formulation.For conservation laws,the new finite difference WENO is shown to perform as well as the classical version of finite difference WENO,with two major advantages:(i)It can capture jumps in stationary linearly degenerate wave families exactly.(i)It only requires the reconstruction to be applied once.Several examples from hyperbolic PDE systems with non-conservative products are shown which indicate that the scheme works and achieves its design order of the accuracy for smooth multidimensional flows.Stringent Riemann problems and several novel multidimensional problems that are drawn from compressible Baer-Nunziato multiphase flow,multiphase debris flow and twolayer shallow water equations are also shown to document the robustness of the method.For some test problems that require well-balancing we have even been able to apply the scheme without any modification and obtain good results.Many useful PDEs may have stiff relaxation source terms for which the finite difference formulation of WENO is shown to provide some genuine advantages.

Lagrangian coherent structure analysis on transport of Acetes chinensis along coast of Lianyungang,China

Spatial heterogeneity or“patchiness”of plankton distributions in the ocean has always been an attractive and challenging scientific issue to oceanographers.We focused on the accumulation and dynamic mechanism of the Acetes chinensis in the Lianyungang nearshore licensed fishing area.The Lagrangian frame approaches including the Lagrangian coherent structures theory,Lagrangian residual current,and Lagrangian particle-tracking model were applied to find the transport pathways and aggregation characteristics of Acetes chinensis.There exist some material transport pathways for Acetes chinensis passing through the licensed fishing area,and Acetes chinensis is easy to accumulate in the licensed fishing area.The main mechanism forming this distribution pattern is the local circulation induced by the nonlinear interaction of topography and tidal flow.Both the Lagrangian coherent structure analysis and the particle trajectory tracking indicate that Acetes chinensis in the licensed fishing area come from the nearshore estuary.This work contributed to the adjustment of licensed fishing area and the efficient utilization of fishery resources.

对抗条件下基于SAC-Lagrangian的UAV智能规划

无人机因其低成本、可消耗、分布部署、敏捷灵活的优势,在多个民用领域大放异彩。但受其智能化程度限制,如何在复杂对抗条件下自主安全完成任务仍存在巨大挑战。针对目前无人机任务规划存在的智能性和安全性问题,提出一种基于安全强化学习算法的无人机智能规划方法(SAC-Lagrangian)。考虑了雷达威胁、禁飞区安全约束和地导对抗条件,将任务规划问题建模为约束马尔可夫决策过程(CMDP),通过拉格朗日乘子法变为对偶问题,采用最大熵柔性行动者-评论家(SAC)算法近似求解最优策略,保证了智能体在遵守安全约束条件下最大化期望回报。仿真结果表明,与其他基线算法相比,所提方法能在保证任务性能的同时确保安全性,适应动态变化的场景,任务完成率达到96%,因此,具有高效、鲁棒和安全的优势。

An Updated Lagrangian Particle Hydrodynamics (ULPH)-NOSBPD Coupling Approach forModeling Fluid-Structure Interaction Problem

A fluid-structure interaction approach is proposed in this paper based onNon-Ordinary State-Based Peridynamics(NOSB-PD)and Updated Lagrangian Particle Hydrodynamics(ULPH)to simulate the fluid-structure interaction problem with large geometric deformation and material failure and solve the fluid-structure interaction problem of Newtonian fluid.In the coupled framework,the NOSB-PD theory describes the deformation and fracture of the solid material structure.ULPH is applied to describe the flow of Newtonian fluids due to its advantages in computational accuracy.The framework utilizes the advantages of NOSB-PD theory for solving discontinuous problems and ULPH theory for solving fluid problems,with good computational stability and robustness.A fluidstructure coupling algorithm using pressure as the transmission medium is established to deal with the fluidstructure interface.The dynamic model of solid structure and the PD-ULPH fluid-structure interaction model involving large deformation are verified by numerical simulations.The results agree with the analytical solution,the available experimental data,and other numerical results.Thus,the accuracy and effectiveness of the proposed method in solving the fluid-structure interaction problem are demonstrated.The fluid-structure interactionmodel based on ULPH and NOSB-PD established in this paper provides a new idea for the numerical solution of fluidstructure interaction and a promising approach for engineering design and experimental prediction.

Updated Lagrangian Particle Hydrodynamics (ULPH)Modeling of Natural Convection Problems

Natural convection is a heat transfer mechanism driven by temperature or density differences,leading to fluid motion without external influence.It occurs in various natural and engineering phenomena,influencing heat transfer,climate,and fluid mixing in industrial processes.This work aims to use the Updated Lagrangian Particle Hydrodynamics(ULPH)theory to address natural convection problems.The Navier-Stokes equation is discretized using second-order nonlocal differential operators,allowing a direct solution of the Laplace operator for temperature in the energy equation.Various numerical simulations,including cases such as natural convection in square cavities and two concentric cylinders,were conducted to validate the reliability of the model.The results demonstrate that the proposed model exhibits excellent accuracy and performance,providing a promising and effective numerical approach for natural convection problems.

An Unconventional Divergence Preserving Finite-Volume Discretization of Lagrangian Ideal MHD

We construct an unconventional divergence preserving discretization of updated Lagrangian ideal magnetohydrodynamics(MHD)over simplicial grids.The cell-centered finite-volume(FV)method employed to discretize the conservation laws of volume,momentum,and total energy is rigorously the same as the one developed to simulate hyperelasticity equations.By construction this moving mesh method ensures the compatibility between the mesh displacement and the approximation of the volume flux by means of the nodal velocity and the attached unit corner normal vector which is nothing but the partial derivative of the cell volume with respect to the node coordinate under consideration.This is precisely the definition of the compatibility with the Geometrical Conservation Law which is the cornerstone of any proper multi-dimensional moving mesh FV discretization.The momentum and the total energy fluxes are approximated utilizing the partition of cell faces into sub-faces and the concept of sub-face force which is the traction force attached to each sub-face impinging at a node.We observe that the time evolution of the magnetic field might be simply expressed in terms of the deformation gradient which characterizes the Lagrange-to-Euler mapping.In this framework,the divergence of the magnetic field is conserved with respect to time thanks to the Piola formula.Therefore,we solve the fully compatible updated Lagrangian discretization of the deformation gradient tensor for updating in a simple manner the cell-centered value of the magnetic field.Finally,the sub-face traction force is expressed in terms of the nodal velocity to ensure a semi-discrete entropy inequality within each cell.The conservation of momentum and total energy is recovered prescribing the balance of all the sub-face forces attached to the sub-faces impinging at a given node.This balance corresponds to a vectorial system satisfied by the nodal velocity.It always admits a unique solution which provides the nodal velocity.The robustness and the accuracy of this unconventional FV scheme have been demonstrated by employing various representative test cases.Finally,it is worth emphasizing that once you have an updated Lagrangian code for solving hyperelasticity you also get an almost free updated Lagrangian code for solving ideal MHD ensuring exactly the compatibility with the involution constraint for the magnetic field at the discrete level.

Conformal invariance and conserved quantities of non-conservative Lagrange systems by point transformations

This paper studies the conformal invariance by infinitesimal point transformations of non-conservative Lagrange systems. It gives the necessary and sufficient conditions of conformal invariance by the action of infinitesimal point transformations being Lie symmetric simultaneously. Then the Noether conserved quantities of conformal invariance are obtained. Finally an illustrative example is given to verify the results.

Lie Symmetry and Conserved Quantity of Three-Order Lagrangian Equations for Non-conserved Mechanical System

Based on the infinitesimal and one parameter transformation, the problem of Lie symmetry of three-order Lagrangian equations has been studied. Under Lie transformation, the sufficient and necessary condition which keeps three-order Lagrangian equations to be unchanged and the invariant are obtained in this paper.

Noether's theorem for non-conservative Hamilton system based on El-Nabulsi dynamical model extended by periodic laws

This paper focuses on the Noether symmetries and the conserved quantities for both holonomic and nonholonomic systems based on a new non-conservative dynamical model introduced by E1-Nabulsi. First, the E1-Nabulsi dynamical model which is based on a fractional integral extended by periodic laws is introduced, and E1-Nabulsi-Hamilton＇s canoni- cal equations for non-conservative Hamilton system with holonomic or nonholonomic constraints are established. Second, the definitions and criteria of E1-Nabulsi-Noether symmetrical transformations and quasi-symmetrical transformations are presented in terms of the invariance of E1-Nabulsi-Hamilton action under the infinitesimal transformations of the group. Fi- nally, Noether＇s theorems for the non-conservative Hamilton system under the E1-Nabulsi dynamical system are established, which reveal the relationship between the Noether symmetry and the conserved quantity of the system.

复辛空间■^(2),■^(4)中的完全Lagrangian子空间的分类

讨论复辛空间■^(2),■^(4)中的完全Lagrangian子空间的标准型。通过参数化的方法研究复辛空间■^(2),■^(4)中的完全Lagrangian子空间的表示与分类。

A new type of adiabatic invariants for disturbed non-conservative nonholonomic system

According to the Herglotz variational principle and differential variational principle of Herglotz type, we study the adiabatic invariants for a non-conservative nonholonomic system. Firstly, the differential equations of motion of the non-conservative nonholonomic system based upon the generalized variational principle of Herglotz type are given, and the exact invariant for the non-conservative nonholonomic system is introduced. Secondly, a new type of adiabatic invariant for the system under the action of a small perturbation is obtained. Thirdly, the inverse theorem of the adiabatic invariant is given. Finally, an example is given.

A drift-kinetic perturbed Lagrangian for low-frequency nonideal MHD applications

We find that the perturbed Lagrangian derived from the drift-kinetic equation in[Porcelli F et al 1994 Phys.Plasmas 1470]is inconsistent with the ordering for the low-frequency large-scale magnetohydrodynamic(MHD).Here,we rederive the expression for the perturbed Lagrangian within the framework of nonideal MHD using the ordering system for the low-frequency largescale MHD in a low-beta plasma.The obtained perturbed Lagrangian is consistent with Chen's gyrokinetic theory[Chen L and Zonca F 2016 Rev.Mod.Phys.88015008],where the terms related to the field curvature and gradient are small quantities of higher order and thus negligible.As the perturbed Lagrangian has been widely used in the literature to calculate the plasma nonadiabatic response in low-frequency MHD applications,this finding may have a significant impact on the understanding of the kinetic driving and dissipative mechanisms of MHD instabilities and the plasma response to electromagnetic perturbations in fusion plasmas.

Path Integral Quantization of Non-Natural Lagrangian

Path integral technique is discussed using Hamilton Jacobi method. The Hamilton Jacobi function of non-natural Lagrangian is obtained using separation of variables method. This function makes an important role in path integral quantization. The path integral is obtained as integration over the canonical phase space coordinates, which contains the generalized coordinate q and the generalized momentum p. One illustrative example is considered to explain the application of our formalism.

草地贪夜蛾迁飞气象预报方法探索及应用

为了准确预报害虫的迁飞轨迹,将天气预报技术应用于迁飞性害虫的预测预报,基于天气预报平台,利用欧洲中心中短期气象数值预报产品以及大气环流形势及低层风动力对草地贪夜蛾(Spodoptera frugiperda)的迁飞路径、迁入时间(包括首见日及高峰日)、落区等进行预报,并基于2021年草地贪夜蛾迁飞的2次典型预报案,分析2021年草地贪夜蛾春季北迁至湖北(首见日)以及秋季南迁回湖北(高峰日)的典型天气过程以及迁飞层气象要素场,运用HYSPLIT轨迹模型模拟迁飞后向轨迹,再利用草地贪夜蛾田间监测数据、测报灯监测数据以及迁飞轨迹对预报结论进行验证。结果显示,2次典型预报案例的预报结论与草地贪夜蛾田间监测数据及测报灯监测数据以及轨迹模拟的情景吻合度较好,草地贪夜蛾迁入时间、落区及路径预报基本正确。研究表明,将天气预报技术应用于迁飞性害虫的预报具有实际可行性。

基于多目标优化的跨介质航行体水面滑跳初始运动参数设计

基于耦合欧拉-拉格朗日方法,开展了初始运动参数对带滑板跨介质航行体近水面滑跳过程的影响规律研究。采用参数回归方法分别建立最大浸深、最大过载和俯仰角变化3个变量随航行体初始速度、入水角、滑板倾角变化的关系式,得到了跨介质航行体稳定滑跳的参数包络,在入水角2°~5°、滑板倾角10°~25°、速度60~80 m/s范围之间,且在范围内各参数之间会相互制约。在此基础上,基于多目标优化算法获得了最适宜航行体稳定滑跳的初始参数为入水速度60.1 m/s、滑板倾角18.8°、入水角2°,在此参数范围内,跨介质航行体的水面滑跳过程可以在不超过航行体过载要求的条件下获得相对最小的入水浸深和俯仰角变化。

6061铝合金超声辅助搅拌摩擦焊温度场分析

为了分析超声振动对6061铝合金超声辅助搅拌摩擦焊接过程温度场的影响,采用解析建模和数值模拟的方法,建立了超声辅助搅拌摩擦焊过程中接触界面摩擦系数模型和热力耦合有限元分析模型,开展了6061铝合金超声辅助搅拌摩擦焊温度测量试验,结合有限元与试验结果进行对比分析.结果表明,仿真得到的工件表面温度分布曲线及取样点温度都与试验结果基本吻合,验证了建立模型的准确性;超声振动可以改变摩擦状态,降低焊接摩擦产热,减少峰值温度及高温区域的面积,振幅对焊接峰值温度影响的显著性高于频率.

基于拉格朗日对偶的小样本学习隐私保护和公平性约束方法

小样本学习旨在利用少量数据训练并大幅提升模型效用,为解决敏感数据在神经网络模型中的隐私与公平问题提供了重要方法。在小样本学习中,由于小样本数据集中往往包含某些敏感数据,并且这些敏感数据可能有歧视性,导致数据在神经网络模型的训练中存在隐私泄露的风险和公平性问题。此外,在许多领域中,由于隐私或安全等,数据很难或无法获取。同时在差分隐私模型中,噪声的引入不仅会导致模型效用的降低,也会引起模型公平性的失衡。针对这些挑战,提出了一种基于Rényi差分隐私过滤器的样本级自适应隐私过滤算法,利用Rényi差分隐私以实现对隐私损失的更精确计算。进一步,提出了一种基于拉格朗日对偶的隐私性和公平性约束算法,该算法通过引入拉格朗日方法,将差分隐私约束和公平性约束加到目标函数中,并引入拉格朗日乘子来平衡这些约束。利用拉格朗日乘子法将目标函数转化为对偶问题,从而实现同时优化隐私性和公平性,通过拉格朗日函数实现隐私性和公平性的平衡。实验结果证明,该方法既提升了模型性能,又保证了模型的隐私性和公平性。

水-空气耦合介质中冰载荷对闸墩的撞击影响研究

西北干寒地区长距离输水工程中河道修建的闸墩受到冰载荷撞击破坏,为确保冬季安全稳定供水,需进行冰载荷对闸墩撞击破坏力学特性研究。该文采用任意拉格朗日-欧拉(arbitrary Lagrangian-Eulerian, ALE)流固耦合(fluid structure interaction, FSI)方法模拟不同碰撞工况下冰体楔入闸墩碰撞过程,并通过对比实验,验证了冰材料模型参数和ALE算法的适用性,分析了网格尺寸对撞击力的影响。研究结果表明:计算得到冰载荷对闸墩撞击力极值与实验值具有良好的吻合性,表明该模拟所采用的冰材料模型参数、ALE算法和网格尺寸能够较准确模拟冰载荷对闸墩的作用力;闸墩损伤变形与冰排破损主要集中在碰撞接触区,接触区撞击力大小受到“水垫效应”的影响,空气介质对撞击力影响较小;不同冰厚和冰速工况下撞击力时程曲线呈现“Sawtooth”(上下波动)现象,撞击力加载-卸载时间较短;冰排楔入闸墩的过程中,撞击力极值出现在0°正碰接触区,在冰速1.2 m/s~3.0 m/s范围内,撞击力逐渐减小,在不改变冰速工况下,随着冰厚的增加,墩体结构响应越大,冰速和冰厚两种影响工况下闸墩顶端位移均为周期性振动。其仿真结果拟为西北干寒地区冰期河道中墩体结构安全提供指导。

基于CEL方法的带结构物溃坝流数值模拟

随着全球气温的不断升高,极端天气现象增多,溃坝现象成为水工结构方向需要重点防范的自然灾害。溃坝流的发展会对下游结构物产生巨大的破坏作用,因此深入探究溃坝流现象的水动力学特性以及溃坝流下游结构物所受到的冲击力影响势在必行。本文针对带有结构物的溃坝流动问题现象,采用CEL方法(Coupled Eulerian-Lagrangian analysis,耦合欧拉-拉格朗日方法),对于溃坝流的发展、演化进行了数值模拟。研究结果表明,模拟结果中溃坝流自由表面及流体尖端时程变化与文献试验结果拟合较好,CEL方法可应用在溃坝流现象的模拟,并且具有较好的准确性和精度。结构物材料性能、高度及与结构物与溃坝流间的位置,均会影响溃坝流的运动状态以及结构物的受力变形状态,在不考虑结构物破坏的情况下,提高结构物弹性模量,增加结构物高度,以及减小结构物与溃坝流间的距离均可提高结构物对于溃坝流的阻挡作用。

基于CEL法熔滴冲击基板的TPF/FSI数值模拟

航空发动机和燃气轮机的高温工作环境会对其热端金属部件造成不可逆损伤,热障涂层(thermal barrier coatings,TBCs)能够承受高温和高压的侵蚀性环境,从而保证金属部件使用的安全性及可靠性。以空心Y_(2)O_(3)-ZrO_(2)(yttrium-stabilized zirconia,YSZ)粒子在等离子焰流中的2种形态,即全熔熔滴和空心熔滴为研究对象对其冲击铺展过程进行了模拟。基于ABAQUS/EXPLICIT耦合欧拉-拉格朗日(coupled Eulerian-Lagrangian,CEL)有限元方法,首先针对ABAQUS缺少相变模型,导致使用CEL方法计算熔滴铺展形貌失真的问题,给出了适用的动力黏度随温度变化的经验公式。此外,考虑周围空气对熔滴铺展过程的影响,提出了“两相流(two phase flow,TPF)/流-固耦合(fluid-structure-interaction,FSI)”2.5D模型,对熔滴冲击基板凝固成型及空气卷入的过程进行了模拟,并揭示了2种熔滴铺展形貌存在较大差异的机理,对制备隔热性能更优的热障涂层具有指导意义。