烟雾的快速模拟

在粒子系统方法的基础上,比较了近年来的最新研究成果和实际应用方法,采用旋转纹理片的快速烟雾模拟方法,讨论了纹理片的数据结构、各种参数的设置依据和它们对总体模拟效果的影响,给出了具体的模拟步骤,并且通过不同的设置采构造不同的烟雾模拟场景.最后,给出了实际的计算机模拟效果.     

交错网格结构的涡粒子烟模拟

目的 流体模拟方法中的基于旋度的模拟方法相比于基于速度的模拟方法,能提供较多细节,但是通常难以处理不同的边界条件,比如固体边界和自由表面,而且通常难以保证模拟的稳定性。本文的目的就是为了解决基于旋度的模拟方法的边界问题和稳定性问题。方法 提出一种交错网格结构,在这种网格结构下,旋度分量被错开放置在每个网格的棱的中心点。利用这种网格离散格式,提出了几种修改求解速度场方程组的策略,以应对不同的边界条件。结果 给出多种场景下的流体模拟结果图,以及几种场景下的总动能变化图和时间效率表。结果显示,本文方法能够处理好不同边界条件,并保持模拟的稳定性。结论 本文提出了一种新的涡粒子流体模拟方法,该方法利用一种交错网格结构辅助模拟,在这种新的网格离散格式下,该方法解决了基于旋度的模拟方法的边界问题和稳定性问题。     

Analysis of numerical methods for the simulation of deformable models

Simulating deformable objects based on physical laws has become the most popular technique for modeling textiles, skin, or volumetric soft objects like human tissue. The physical model leads to an ordinary differential equation. Recently, several approaches to fast algorithms have been proposed.In this work, more profound numerical background about numerical stiffness is provided. Stiff equations impose stability restrictions on a numerical integrator. Some one-step and multistep methods with adequate stability properties are presented. For an efficient implementation, the inexact Newton method is discussed. Applications to 2D and 3D elasticity problems show that the discussed methods are faster and give higher-quality solutions than the commonly used linearized Euler method.     

Physical simulation of land vehicles with obstacle avoidance and various terrain interactions

Programming the motions of an autonomous planetary robot moving in an hostile and hazardous environment is a complex task which requires both the construction of nominal motion plans and the anticipation as far as possible of the effects of the interactions existing between the vehicle and the terrain. In this paper we show how physical models and dynamic simulation tools can be used for amending and completing a nominal motion plan provided by a classical geometrical path planner. The purpose of our physical modeller-simulator is to anticipate the dynamic behaviour of the vehicle while executing the nominal motion plan. Then the obtained simulation results can be used to assess and optimize the nominal motion plan. In the first part, we outline the physical models that have been used for modelling the different types of vehicle, of terrain and of vehicle-surface interactions. Then we formulate the motion planning problem through the definition of two basic abstract constructions derived from physical model: the concept of generalized obstacle and the concept of physical target. We show with various examples how it is possible, when using this method, to solve the locomotion problem and the obstacle avoidance problem simultaneously and, furthermore, to provide the human operator with a true force feedback gestural control over the simulated robot.     

建筑物火灾人员疏散的计算机仿真

将建筑物在平面上划分成能反映人员具体位置的几何坐标网格,根据不同人员在不同网格内的移动特性确定其移动速度,建立了描述人员疏散过程的数学模型,用场模拟的方法可以准确得到建筑物疏散时间和人员疏散轨迹,其仿真结果与国外同类软件对比具有较好的精度。     

Dispersion and Dissipation Error in High-Order Runge-Kutta Discontinuous Galerkin Discretisations of the Maxwell Equations

Different time-stepping methods for a nodal high-order discontinuous Galerkin discretisation of the Maxwell equations are discussed. A comparison between the most popular choices of Runge-Kutta (RK) methods is made from the point of view of accuracy and computational work. By choosing the strong-stability-preserving Runge-Kutta (SSP-RK) time-integration method of order consistent with the polynomial order of the spatial discretisation, better accuracy can be attained compared with fixed-order schemes. Moreover, this comes without a significant increase in the computational work. A numerical Fourier analysis is performed for this Runge-Kutta discontinuous Galerkin (RKDG) discretisation to gain insight into the dispersion and dissipation properties of the fully discrete scheme. The analysis is carried out on both the one-dimensional and the two-dimensional fully discrete schemes and, in the latter case, on uniform as well as on non-uniform meshes. It also provides practical information on the convergence of the dissipation and dispersion error up to polynomial order 10 for the one-dimensional fully discrete scheme.     

Eliminating constraint drift in the numerical simulation of constrained dynamical systems

By means of the Udwadia–Kalaba approach we propose an explicit equation of constrained motion developed to simulate constrained dynamical systems without error accumulation due to constraint drift. The basic idea is to embed a small virtual force and a small virtual impulse to the equation of motion, in order to avoid the drift typically experienced in constrained multibody simulations. The embedded correction terms are selected to minimally alter the dynamics in an acceleration and kinetic energy norm sense. The formulation allows one to use a standard ODE solver, avoiding the need for iterative constraint stabilization. The equation is based on the pseudoinverse of a constraint matrix such that it can be used under redundant constraints and kinematic singularities. The proposed method takes into account the finite word-length of the computational environment, and also accommodates possibly inconsistent initial conditions.     

Interactive Procedural Modelling of Coherent Waterfall Scenes

Combining procedural generation and user control is a fundamental challenge for the interactive design of natural scenery. This is particularly true for modelling complex waterfall scenes where, in addition to taking charge of geometric details, an ideal tool should also provide a user with the freedom to shape the running streams and falls, while automatically maintaining physical plausibility in terms of flow network, embedding into the terrain, and visual aspects of the waterfalls. We present the first solution for the interactive procedural design of coherent waterfall scenes. Our system combines vectorial editing, where the user assembles elements to create a waterfall network over an existing terrain, with a procedural model that parametrizes these elements from hydraulic exchanges; enforces consistency between the terrain and the flow; and generates detailed geometry, animated textures and shaders for the waterfalls and their surroundings. The tool is interactive, yielding visual feedback after each edit.     

Splines over regular triangulations in numerical simulation

We investigate the use of smooth spline spaces over regular triangulations as a tool in (isogeometric) Galerkin methods. In particular, we focus on box splines over three-directional meshes. Box splines are multivariate generalizations of univariate cardinal B-splines sharing the same properties. Tensor-product B-splines with uniform knots are a special case of box splines. The use of box splines over three-directional meshes has several advantages compared with tensor-product B-splines, including enhanced flexibility in the treatment of the geometry and stiffness matrices with stronger sparsity. Boundary conditions are imposed in a weak form to avoid the construction of special boundary functions. We illustrate the effectiveness of the approach by means of a selection of numerical examples.     

矩阵变换器输入侧端口受控耗散哈密尔顿算子建模及无源控制

矩阵变换器无中间直流环节,易受电网扰动和负载扰动的影响.针对这一问题,本文设计了矩阵变换器输入侧无源性控制器以改善控制系统特性.首先,在直–交坐标系下建立输入侧的端口受控耗散哈密尔顿(port-controlled Hamiltonian with dissipation,PCHD)算子模型.然后,设计了基于互联和阻尼配置的无源性控制器,用来实现对输入电流快速准确的跟踪.重新配置了系统的平衡点,通过注入阻尼提高系统的收敛速度,并从理论上对闭环系统的渐进稳定性进行了分析.仿真结果表明,系统在非正常工况下仍能保证输入电流为正弦,相比传统偏差修正法,该控制策略具有更好的动态性能和抗干扰能力.     

Collision avoidance in cloth animation

For cloth modeling and animation, we use a physically based model to simulate the dynamic formation of folds, pleats, and wrinkles and the final static appearance of cloth draped over a rigid object. To simulate the behavior of the cloth and its final static appearance on the model, we propose a new collision and self-collision avoidance method to prevent penetration between the cloth and rigid objects and between parts of the cloth. At each time step, we enforce constraints over those grid points about to penetrate other objects. Our method is easier and more robust than conventional methods at representing interaction between the cloth and various objects.     

A novel linearly-weighted gradient smoothing method (LWGSM) in the simulation of fluid dynamics problem

This paper describes a novel linearly-weighted gradient smoothing method (LWGSM). The proposed method is based on irregular cells and thus can be used for problems with arbitrarily complex geometrical boundaries. Based on the analysis about the compactness and the positivity of coefficients of influence of their stencils for approximating a derivative, one favorable scheme (VIII) is selected among total eight proposed discretization schemes. This scheme VIII is successively verified and carefully examined in solving Poisson equations, subjected to changes in the number of nodes, the shapes of cells and the irregularity of triangular cells, respectively. Strong form of incompressible Navier–Stokes equations enhanced with artificial compressibility terms are tackled, in which the spatial derivatives are approximated by consistent and successive use of gradient smoothing operation over smoothing domains at various locations. All the test cases using LWGSM solver exhibits its robust, stable and accurate behaviors. The attained incompressible LWGSM solutions show good agreements with experimental and literature data. Therefore, the proposed LWGSM can be reliably used for accurate solutions to versatile fluid flow problems.     

Numerical simulation of mechanisms of deformation,failure and energy dissipation in porous rock media subjected to wave stresses

The pore characteristics,mineral compositions,physical and mechanical properties of the subarkose sandstones were acquired by means of CT scan,X-ray diffraction and physical tests.A few physical models possessing the same pore characteristics and matrix properties but different porosities compared to the natural sandstones were developed.The 3D finite element models of the rock media with varied porosities were established based on the CT image processing of the physical models and the MIMICS software platf...     

An explicit structure‐preserving numerical scheme for EPDiff

We present a new structure‐preserving numerical scheme for solving the Euler‐Poincaré Differential (EPDiff) equation on arbitrary triangle meshes. Unlike existing techniques, our method solves the difficult non‐linear EPDiff equation by constructing energy preserving, yet fully explicit, update rules. Our approach uses standard differential operators on triangle meshes, allowing for a simple and efficient implementation. Key to the structure‐preserving features that our method exhibits is a novel numerical splitting scheme. Namely, we break the integration into three steps which rely on linear solves with a fixed sparse matrix that is independent of the simulation and thus can be pre‐factored. We test our method in the context of simulating concentrated reconnecting wavefronts on flat and curved domains. In particular, EPDiff is known to generate geometrical fronts which exhibit wave‐like behavior when they interact with each other. In addition, we also show that at a small additional cost, we can produce globally‐supported periodic waves by using our simulated fronts with wavefronts tracking techniques. We provide quantitative graphs showing that our method exactly preserves the energy in practice. In addition, we demonstrate various interesting results including annihilation and recreation of a circular front, a wave splitting and merging when hitting an obstacle and two separate fronts propagating and bending due to the curvature of the domain.     

Time‐Discrete Geodesics in the Space of Shells

Building on concepts from continuum mechanics, we offer a computational model for geodesics in the space of thin shells, with a metric that reflects viscous dissipation required to physically deform a thin shell. Different from previous work, we incorporate bending contributions into our deformation energy on top of membrane distortion terms in order to obtain a physically sound notion of distance between shells, which does not require additional smoothing. Our bending energy formulation depends on the so‐called relative Weingarten map, for which we provide a discrete analogue based on principles of discrete differential geometry. Our computational results emphasize the strong impact of physical parameters on the evolution of a shell shape along a geodesic path.     

Influence of numerical and viscous dissipation on shock wave reflections in supersonic steady flows

Numerical simulations are investigated to describe precisely the shock wave reflections in supersonic steady air flow field. The main objectives are to study the influence of the wedge trailing edge corner angle, of the numerical methods and of the viscous effects on the shock wave reflections and on the hysteresis behavior. The computations are done with different MUSCL-TVD finite volume schemes and the corresponding results are compared. The flow viscosity is also taken into account and comparisons are made between inviscid and viscous flow simulations. The results display the non-negligible influence of the numerical scheme accuracy on the results, mainly on the position and height of the Mach stem, and the relatively weak influence of the flow viscosity on these parameters. Comparisons between numerical results and experimental data have also been done and a good agreement is only observed for small wedge angles mainly due to the three-dimensional effects in the experimental setup.     

A parallel fully coupled implicit domain decomposition method for numerical simulation of microfluidic mixing in 3D

A parallel fully coupled implicit fluid solver based on a Newton–Krylov–Schwarz algorithm is developed on top of the Portable, Extensible Toolkit for Scientific computation for the simulation of microfluidic mixing described by the three-dimensional unsteady incompressible Navier–Stokes equations. The popularly used fractional step method, originally designed for high Reynolds number flows, requires some modification of the inviscid-type pressure boundary condition in order to reduce the divergence error near the wall. On the other hand, the fully coupled approach works well without any special treatment of the boundary condition for low Reynolds number microchannel flows. A key component of the algorithm is an additive Schwarz preconditioner, which is used to accelerate the convergence of a linear Krylov-type solver for the saddle-point-type Jacobian systems. As a test case, we carefully study a three-dimensional passive serpentine micromixer and report the parallel performance of the algorithm obtained on a parallel machine with more than one hundred processors.     

Physically Based Deformable Models in Computer Graphics

Physically based deformable models have been widely embraced by the Computer Graphics community. Many problems outlined in a previous survey by Gibson and Mirtich have been addressed, thereby making these models interesting and useful for both offline and real‐time applications, such as motion pictures and video games. In this paper, we present the most significant contributions of the past decade, which produce such impressive and perceivably realistic animations and simulations: finite element/difference/volume methods, mass‐spring systems, mesh‐free methods, coupled particle systems and reduced deformable models‐based on modal analysis. For completeness, we also make a connection to the simulation of other continua, such as fluids, gases and melting objects. Since time integration is inherent to all simulated phenomena, the general notion of time discretization is treated separately, while specifics are left to the respective models. Finally, we discuss areas of application, such as elastoplastic deformation and fracture, cloth and hair animation, virtual surgery simulation, interactive entertainment and fluid/smoke animation, and also suggest areas for future research.     

A new approach for multistep numerical methods in several frequencies for perturbed oscillators

This article presents a new multi-step numerical method based on φ-function series and designed to integrate forced oscillators with precision. The new algorithm retains the good properties of the MDF_pPC methods while presenting the advantages of greater precision and that of integrating the non-perturbed problem without any discretization error. In addition, this new method permits a single formulation to be obtained from the MDF_pPC schemes independently of the parity of the number of steps, which facilitates the design of a computational algorithm thus permitting improved implementation in a computer.The construction of a new method for accurately integrating the homogenous problem is necessary if a method is sought which would be comparable to the methods based on Scheifele G-function series, very often used when problems of satellite orbital dynamics need to be resolved without discretization error.Greater precision compared to the MDF_pPC methods and other known integrators is demonstrated by overcoming stiff and highly oscillatory problems with the new method and comparing approximations obtained with those calculated by means of other integrators.