MacCormack方法优化烟雾模拟中Navier-Stokes方程对流项的求解

烟雾作为大规模虚拟战场和复杂环境仿真中的重要组成部分,对其进行模拟具有重要的意义.针对基于物理方法烟雾模拟中Navier-Stokes方程求解复杂、影响实时性的问题,提出用MacCormack求解Navier-Stokes方程对流项的方法.首先利用前向对流算子求解前向烟雾速度,然后利用后向对流算子求解后向烟雾速度,最后通过误差评估来修正已经计算的前向对流速度,得到下一时刻的烟雾速度.该方法简化了进退误差补偿修正方法对直接影响烟雾模拟实时性和真实性的对流项的求解步骤,从而减少计算时间.实验结果表明,采用文中方法模拟出的效果比较真实,且使基于物理方法的烟雾模拟达到了实时性的要求.     

基于物理的烟雾动画

基于物理的烟雾模拟中,需要求解Navier-Stokes偏微分方程组．通过量纲分析,简化了该方程．在求解对流项时采用半拉格朗日方法,为弥补该方法带来的数值耗散,引入了高阶精度紧致格式,在较粗的网格上亦可得到较高精度的导数值．实验结果表明：该算法效果比较真实,速度较快．     

实时稳定的二维烟雾模拟

烟雾模拟是计算机动画模拟的重要组成部分.在模拟过程中保证实时性和稳定性是烟雾动画模拟的一个重要方面.该文的目的是在计算机上模拟出真实感的烟雾.文中采用无粘不可压欧拉方程作为烟雾的基本物理模型,对这种简化的流体方程求解可以加快计算的速度,使模拟的速度加快.数值上,引入了CIP方法的一种改进形式USCIP方法来求解N-S方程的对流项,该方法是无条件稳定的.求解方法的稳定实现了大时间步长模拟,保证了模拟实时性和稳定性,最后模拟得到二维的烟雾效果.实验证明本方法能实时稳定地模拟出具有真实感的二维烟雾效果.     

基于物理模型的烟雾实时模拟

本文提出了一种基于物理模型的烟雾的实时数值模拟方法.真实感和实时性是计算机图形学追求的两个目标.传统的动画技术生成的物体运动是虚拟的,并不能完全反映物体的真实运动.与传统的动画技术相比,基于物理的动画更能表现运动的真实性.在用非粘性不可压欧拉方程表示烟雾的物理模型的基础上,利用破开算子法将其分解成外力项、对流项和投影项分别进行求解,每一步都稳定,因而整个求解也就稳定.求解过程的稳定性保证了模拟可以用大时间步长,也就保证了模拟的实时性.与传统的方法相比,能同时满足计算机图形学的真实感和实时性要求.     

基于物理模型的实时烟雾模拟

针对使用直接绘制法渲染烟雾时,在高网格分辨率下实时性差的问题,文中提出了一种新的基于纹理的烟雾渲染算法。该算法采用不可压缩的Navier-Stokes方程作为烟雾模拟的基本物理计算模型,从而保证烟雾物理运动的真实性,同时利用OpenGL中的纹理映射技术渲染烟雾,保证了烟雾渲染效果真实,烟雾模拟细节更能体现出来;另外文中还给出了在烟雾中添加障碍物时边界条件的计算方式。模拟实验结果表明,该算法既能满足烟雾模拟的实时性,又能真实有效地模拟烟雾流动情况。     

基于物理的流体运动模拟方法研究

提出了一种基于物理的流体运动模拟方法,同传统的模拟技术相比,基于物理的模拟更能表现真实感运动。选用的物理模型是完整的Navier-Stokes方程组,针对完整的Navier-Stokes方程组,利用破开算子法将模型分解成外力、对流、扩散和投影项分别进行计算。因为每一步都稳定,所以整个求解过程也稳定。因此可以用大时间步长来模拟流体运动。Navier-Stokes方程组保证了真实感,而此求解方法保证了效率。     

风环境下烟雾的实时模拟

在复杂环境仿真中,烟雾的模拟具有重要的意义.提出一种基于流体力学方程的烟雾模拟方法,并实现了脉动风与烟雾的交互,使烟雾的形态和运动更加逼真自然.采用简化的Von Karman模型建立风场,并引入特征正交分解技术(POD)和快速傅立叶变换技术(FFT)简化其建立过程.利用非粘性不可压缩的N-S(Navier-Stokes)方程描述烟雾运动,并将风场的作用加入到N-S方程中,利用破开算子法和MacCormack法简化N-S方程的求解过程,减少计算量,并保证求解过程在大的时间步长上的稳定性.同时,引入了"漩涡限制",将数值求解过程中的插值耗散补充回流场,增强烟雾的真实性.实验证明,利用本文的方法能够实时高效的模拟出自然逼真三维烟雾效果.     

求解Navier-Stokes方程的一类有限元有限体积迎风方法及其实现

Navier-Stokes方程是一类非线性的鞍点问题,在高Reynolds数流的情形下,标准Galerkin有限元方法会导致数值伪震荡.迎风有限元方法在算法结构上表征了流体＂上游＂决定＂下游＂的流动性态,它能够有效地消除高Reynolds数流的对流占优扩散所产生的非物理震荡.基于此,将Navier-Stokes方程的对流项采用有限体积框架下的迎风离散,对其它项仍使用Galerkin有限元离散,研究了二维定常Navier-Stokes方程的数值求解,编程藉助于有限元程序自动生成软件FEPG.通过对方腔流动和圆柱绕流问题与基准测试已有数值结果的比较,验证了所构造方法的可行性和有效性.     

三维烟雾的实时模拟

提出了一种基于流体力学方程并采取欧拉法实时模拟三维真实感烟雾的算法。通过Navier-Stokes方程建立烟雾流场的物理模型,以保证视觉的真实感。为了保证运算的实时性,烟雾流场划分为三维网格空间,并将烟雾速度场的分布定义于每个立方网格单元的中心点;通过线性插值获取整幅图像中每个像素的烟雾浓度。将烟雾模拟技术用于图像的显示特技中,以产生图像消散成烟雾的视觉效果,得到了比较满意的模拟效果。     

一种改进的自适应漩涡限制实时烟雾模拟

针对模拟烟雾过程中,漩涡效果不真实,小尺度漩涡细节丢失的问题,对漩涡限制(Vorticity Confinement)方法进行改进.首先,用可变的空间螺旋性强度取代作用在整个网格上的漩涡系数常量,在低分辨率网格下将自适应漩涡限制作为外力项求解N-S(Navier-Stokes)方程;然后,用B样条插值前采样速度场,减少高分辨率时求解计算量;最后,在高分辨率时将自适应漩涡限制与前采样得到的速度场混合,平滑去除过程中的噪音,产生高分辨率漩涡细节.实验结果表明,采用本文方法改进漩涡限制,烟雾漩涡细节表现更为真实,且达到了烟雾模拟实时性的要求.     

A conjugate gradient iterative method

A strongly implicit pre-conditioned form of the conjugate gradient method is considered. The resulting iterative technique is applicable for sparse systems of difference equations arising from boundary value problems. The method is used to solve two- and three-dimensional potential flows. In addition, it is extended to a 2 x 2 coupled system to solve the Navier-Stokes equations in stream function-vorticity form.     

A B-spline collocation method for solving the incompressible Navier-Stokes equations using an ad hoc method: the Boundary Residual method

Collocation methods using piece-wise polynomials, including B-splines, have been developed to find approximate solutions to both ordinary and partial differential equations. Such methods are elegant in their simplicity and efficient in their application. The spline collocation method is typically more efficient than traditional Galerkin finite element methods, which are used to solve the equations of fluid dynamics. The collocation method avoids integration. Exact formulae are available to find derivatives on spline curves and surfaces. The primary objective of the present work is to determine the requirements for the successful application of B-spline collocation to solve the coupled, steady, 2D, incompressible Navier-Stokes and continuity equations for laminar flow. The successful application of B-spline collocation included the development of ad hoc method dubbed the Boundary Residual method to deal with the presence of the pressure terms in the Navier-Stokes equations. Historically, other ad hoc methods have been developed to solve the incompressible Navier-Stokes equations, including the artificial compressibility, pressure correction and penalty methods. Convergence studies show that the ad hoc Boundary Residual method is convergent toward an exact (manufactured) solution for the 2D, steady, incompressible Navier-Stokes and continuity equations. C¹ cubic and quartic B-spline schemes employing orthogonal collocation and C² cubic and C³ quartic B-spline schemes with collocation at the Greville points are investigated. The C³ quartic Greville scheme is shown to be the most efficient scheme for a given accuracy, even though the C¹ quartic orthogonal scheme is the most accurate for a given partition. Two solution approaches are employed, including a globally-convergent zero-finding Newton's method using an LU decomposition direct solver and the variable-metric minimization method using BFGS update.     

基于流体动力学的火焰实时绘制技术

为了实时有效地渲染真实的火焰,引入了基于流体动力学的气体建模方法和分形插值技术,在粗网格下采用半拉格朗日方法和隐式差分格式,直接求取火焰的纳威-斯托克斯方程,这种数值解法在粗糙网格、大的时间步下也能无条件稳定,能达到实时渲染的目的。在细网格下,为了渲染湍流火焰,采用分形插值的方法,增强湍流火焰的边缘细节。实验结果表明：该方法实现简单,仿真速度快,显示的动画效果真实,并且是元条件稳定的。     

Liquid sloshing in rectangular road containers

A study of liquid behaviour in rectangular road containers undergoing a turning or braking manoeuvre is presented and discussed. The steady-state solution in terms of liquid heights, forces and overturning moments is derived analytically from the hydrostatic equations. The transient response of the liquid is obtained via numerical solution of the continuity, Navier-Stokes and free-surface equations. The governing equations are discretized in a Eulerian mesh and solved with respect to the nondimensional primitive variables together with the boundary conditions at rigid walls and the free surface using a modified marker-and-cell technique. Such an approach allows one to take into account all basic nonlinearities proper to the sloshing problem and to obtain the damped frequencies and magnitudes of the sloshing parameters. The present study is a contribution to the overall dynamics of coupled “vehicle-liquid” systems performing some road manoeuvres.     

三维实时云建模与渲染在工业仿真中的应用

在云建模方面,提出一种基于物理仿真和艺术可控性相结合的方法,利用Navier-Stokes流体动力学公式描述单一云朵的聚散和运动,通过盒子的堆积来描述云朵的初始轮廓,最终在盒子内部按流体动力学规律填充粒子生成三维云模型.为了满足实时性要求,在可编程图形芯片上求解Navier-Stokes等式,以便利用图形芯片的并行处理能力加快求解速度.在云的实时渲染方面,基于太阳光照方向和天气状况提出了一种简单的光照模型,大幅度地提高了云的渲染速度.此外,还提出一种改进的环状Impostor技术来提高大范围云层的渲染速度,并通过Shader编程的方法解决了应用Impostor技术到Alpha融合场景中所出现的问题.基于所描述的理论模型,利用三维图形API开发了一套三维云仿真系统,并广泛应用于各种工业仿真和科技娱乐展示项目中,取得了较好的效果.利用该方法生成的云模型具有真实感强、渲染速度快等特点.     

Characteristic-based operator-splitting finite element method for Navier-Stokes equations

A new finite element method, which is the characteristic-based operator-splitting (CBOS) algorithm, is developed to solve Navier-Stokes (N-S) equations. In each time step, the equations are split into the diffusive part and the convective part by adopting the operator-splitting algorithm. For the diffusive part, the temporal discretization is performed by the backward difference method which yields an implicit scheme and the spatial discretization is performed by the standard Galerkin method. The convective...     

PVM平台下粗网格修正与拼接网格相匹配解超声速底部流场

§１．引言 飞行器设计时,为了对一些复杂的流场,如激波－粘性层干扰、底部回流区、喷流干扰等有一个定量、定性的认识,常借助于完全的Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程求解,但这往往需要大量的运行时间．尤其当流场中存在波与波的强干扰、强烈的双曲－椭圆混合区,且计算网格密集时,产生极大的数值“刚性”,大大影响了收敛速度,导致无法承受的计算耗时． 数值实践使人们认识到,大部分用来求解离散化偏微分方程的数值迭代方法都能有效地消除高频误差分量,而在消除低频误差分量方面却差强人意．计算中正是这些顽固的低频误差严重影响…     

Penalty solution of the Navier-Stokes equatiosn

The penalty method can advantageously be employed with a finite difference formulation in terms of the primitive variables to solve the Navier-Stokes equations, provided a MAC-type grid is used; a conventional grid yields very poor results. For iterative methods of solution, a succession of solutions with increasing penalties is preferable to the use of a large constant penalty. The method can be extended to three dimensions.     

Analysis and application of a parallel spectral element method for the solution of the Navier-Stokes equations

We present an analysis of the parallel spectral element method for solution of the unsteady incompressible Navier-Stokes equations in general three-dimensional geometries. The approach combines high-order spatial discretizations with iterative solution techniques in a way which exploits with high efficiency the currently available medium-grained distributed-memory parallel computers. Measured performance analysis on the Intel vector hypercubes and example Navier-Stokes calculations demonstrate that parallel processing can now be considered an effective fluid mechanics analysis tool.     

A numerical flow simulation based on the rate form of the equation of state

A finite-difference numerical method of solution for the unsteady, incompressible Navier-Stokes equations using primitive variables is presented. The rate form of the equation of state is used for the calculation of pressure. This form of the equation of state is well-suited for use with the unsteady form of the conservation equations (mass, momentum and energy). An implicit algorithm is used for the time integration for greater numerical stability. This method is used to solve a known benchmark problem in steady-state natural convection as a test of steady-state accuracy. The results of the simulation are compared to the benchmark.