一种基于半拉格朗日的液体实时仿真方法

近些年,在计算机图形学与虚拟现实技术领域中,自然现象的模拟得到了广泛的关注和研究.如何快速且逼真地模拟自然现象,是此类研究的目的.以液体表面作为研究对象,总结了关于液体模拟近年来的部分研究成果;针对三维液体的复杂流体状态,提出了一种基于半拉格朗日的液体实时仿真方法,并对仿真结果进行了表面构建.该方法首先将Navier-Stokes 方程离散化,并通过求解构造的Poisson 方程得到每一时间步长的数值解,进而精确驱动粒子运动以构建真实液体表面;之后,利用液体表面追踪及Marching Cubes 表面重建,生成了真实的液体表面模型.实验结果表明,该仿真方法不但在运算过程中遵循经典的流体力学方程,从而保证了结果的真实性,并且运算速度快且能取得较好的视觉效果.在计算机游戏、电影制作以及医学等领域的仿真,均有广泛的应用前景.     

Instability in leapfrog and forward–backward schemes: Part II: Numerical simulations of dam break

Following Sun’s approach [17], Shuman smoothing instead of conventional diffusion terms is used in a simple two-time step semi-implicit finite volume scheme to simulate dam break. When the Courant number is less than one, the absolute value of amplification factor of the 1D linearized shallow-water equations is 1 in this new scheme. Compared with the characteristic-based semi-Lagrangian schemes and the Riemann solver, this scheme produces excellent results of free water depth and speed of the shock. Numerical simulations show that the water inside the dam initially moves away radially until water almost depletes near the center; then the water moves back to the center and forms a vertical water column there. This paper proves that Shuman smoothing can be used not only in the linearized shallow-water equations discussed in Sun [17] but also in the nonlinear wave equations to control instability around shocks.     

A Semi-Lagrangian Method for Turbulence Simulations Using Mixed Spectral Discretizations

We present a semi-Lagrangian method for integrating the three-dimensional incompressible Navier–Stokes equations. We develop stable schemes of second-order accuracy in time and spectral accuracy in space. Specifically, we employ a spectral element (Jacobi) expansion in one direction and Fourier collocation in the other two directions. We demonstrate exponential convergence for this method, and investigate the non-monotonic behavior of the temporal error for an exact three-dimensional solution. We also present direct numerical simulations of a turbulent channel-flow, and demonstrate the stability of this approach even for marginal resolution unlike its Eulerian counterpart.     

Convergence analysis of the Hopmoc method

The Hopmoc method combines concepts of the modified method of characteristics (MMOC) and the Hopscotch method. First, Hopmoc resembles Hopscotch because it decomposes the set of grid points into two subsets. Namely, both subsets have their unknowns separately updated within one semi-step. Furthermore, each subset undergoes one explicit and one implicit update of its unknowns in order to lead to a symmetrical procedure. Such decomposition inspired the use of a convergence analysis similar to the one used in alternating direction implicit methods. Secondly, the steps are evaluated along characteristic lines in a semi-Lagrangian approach similar to the MMOC. In this work, both consistency and stability analysis are discussed for Hopmoc applied to a convection–diffusion equation. The analysis produces sufficient conditions for the consistency analysis and proves that the Hopmoc method presents unconditional stability. In addition, numerical results confirm the conducted convergence analysis.     

核设施退役虚拟仿真中烟尘输运过程建模及算法研究

基于三维数值计算可实现核设施退役虚拟仿真中烟尘输运过程仿真，而快速且稳定的数值求解方法是实现动态仿真过程的核心。研究中首先建立相应的数学模型，然后采用半拉格朗日方法对方程进行求解。求解过程中首先对方程采用分裂法，得到各分项方程，然后利用半拉格朗日方法对瞬态项及对流项进行求解，对于不可压缩压力方程采用了基于约束思想的投影算法。研究过程中对立方体空间进行了数值仿真，仿真结果的显示采用OpengGL编程实现，获得了三维流场分布及烟尘浓度分布。该方法能实现模型稳定、快速的求解。     

大规模交互式洪水灾害动态场景预警仿真

洪水是一种严重危害人民生命财产安全的自然灾害.针对我国现有的洪水灾害模拟仿真技术系统化程度不足,难以直观、快速地向决策者预警展示洪水泛滥的现况、发展趋势和灾害损失评估的问题,设计了一个可交互的大规模洪水灾害动态场景预警仿真系统.首先利用半拉格朗日隐式积分的方法在基本保证动量守恒和体积守恒的前提下快速求解浅水方程,达到了洪水演进实时稳定的模拟计算;然后提出了一种建筑物洪灾危机的预警规则,在洪水演进时能够通过变换预警色彩,实时警示有关建筑物的洪水受灾损害危机等级;最后建立起一个可交互大规模洪水模拟仿真系统,其功能包括可增加洪水挡板以展示区域的防洪功能、进排水口添加的泄洪效果和建筑物时变的积水高度显示等.在自行采集的城市高程数据上的仿真实验结果表明,该系统可为建设现代海绵型城市的防洪减灾决策设计提供直观、可靠的依据.     

大时间步长下体积守恒的实时水体模拟

摘 要：基于物理的流体仿真可以真实地捕捉水的运动,一种常用的实时模拟方法是基于 二维浅水方程进行水体仿真。首先介绍了二维浅水方程,并提出一种新的求解方法,通过一种 体积守恒的隐式半拉格朗日方法进行计算,在保持稳定的同时允许较大的时间步长,然后额外 增加修正步以保证计算过程中体积守恒。此外提出了一种基于动量守恒的流固耦合方法,可以 实时地模拟出较为真实的水体,并且保证了水体体积始终守恒,效果良好。     

A fast convergence fourth-order Vlasov model for Hall thruster ionization oscillation analyses

A 1D1V hybrid Vlasov-fluid model was developed for this study to elucidate discharge current oscillations of Hall thrusters (HTs). The Vlasov equation for ions velocity distribution function with ionization source term is solved using a constrained interpolation profile conservative semi-Lagrangian method. The fourth-order weighted essentially non-oscillatory (4th WENO) limiter is applied to the first derivative value to minimize numerical oscillation in the discharge oscillation analyses. The fourth-order accuracy is verified through a 1D scalar test case. Nonoscillatory and high-resolution features of the Vlasov model are confirmed by simulating the test cases of the Vlasov–Poisson system and by comparing the results with a particle-in-cell (PIC) method. A 1D1V HT simulation is performed through the hybrid Vlasov model. The ionization oscillation is analyzed. The oscillation amplitude and plasma density are compared with those obtained from a hybrid PIC method. The comparison indicates that the hybrid Vlasov-fluid model yields noiseless results and that the steady-state waveform is calculable in a short time period.