Procedural Synthesis using Vortex Particle Method for Fluid Simulation

We propose a fast and effective technique to improve sub‐grid visual details of the grid based fluid simulation. Our method procedurally synthesizes the flow fields coming from the incompressible Navier‐Stokes solver and the vorticity fields generated by vortex particle method for sub‐grid turbulence. We are able to efficiently animate smoke which is highly turbulent and swirling with small scale details. Since this technique does not solve the linear system in high‐resolution grids, it can perform fluid simulation more rapidly. We can easily estimate the influence of turbulent and swirling effect to the fluid flow.     

A Hybrid Lagrangian/Eulerian Collocated Velocity Advection and Projection Method for Fluid Simulation

We present a hybrid particle/grid approach for simulating incompressible fluids on collocated velocity grids. Our approach supports both particle-based Lagrangian advection in very detailed regions of the flow and efficient Eulerian grid-based advection in other regions of the flow. A novel Backward Semi-Lagrangian method is derived to improve accuracy of grid based advection. Our approach utilizes the implicit formula associated with solutions of the inviscid Burgers’ equation. We solve this equation using Newton's method enabled by C¹ continuous grid interpolation. We enforce incompressibility over collocated, rather than staggered grids. Our projection technique is variational and designed for B-spline interpolation over regular grids where multiquadratic interpolation is used for velocity and multilinear interpolation for pressure. Despite our use of regular grids, we extend the variational technique to allow for cut-cell definition of irregular flow domains for both Dirichlet and free surface boundary conditions.     

拼接网格通量守恒插值算法研究

提出一种通用的拼接网格通量守恒算法应用于拼接网格"找重"过程,为拼接网格预处理提供了高效、可靠的插值方法。该算法灵活利用图形学中"多边形裁剪"原理和曲线积分公式得到拼接面上相交多边形及其面积,算法实现复杂度低,简单并健壮性较好,能够通用于结构网格和非结构网格问题。实验结果表明在大网格量、复杂拼接区域时该拼接网格插值计算方法仍能得到较理想的结果。     

Interactive Visualization of Flood and Heavy Rain Simulations

In this paper, we present a real‐time technique to visualize large‐scale adaptive height fields with C ‐continuous surface reconstruction. Grid‐based shallow water simulation is an indispensable tool for interactive flood management applications. Height fields defined on adaptive grids are often the only viable option to store and process the massive simulation data. Their visualization requires the reconstruction of a continuous surface from the spatially discrete simulation data. For regular grids, fast linear and cubic interpolation are commonly used for surface reconstruction. For adaptive grids, however, there exists no higher‐order interpolation technique fast enough for interactive applications. Our proposed technique bridges the gap between fast linear and expensive higher‐order interpolation for adaptive surface reconstruction. During reconstruction, no matter if regular or adaptive, discretization and interpolation artifacts can occur, which domain experts consider misleading and unaesthetic. We take into account boundary conditions to eliminate these artifacts, which include water climbing uphill, diving towards walls, and leaking through thin objects. We apply realistic water shading with visual cues for depth perception and add waves and foam synthesized from the simulation data to emphasize flow directions. The versatility and performance of our technique are demonstrated in various real‐world scenarios. A survey conducted with domain experts of different backgrounds and concerned citizens proves the usefulness and effectiveness of our technique.     

Using interpolation to improve path planning: The Field D* algorithm

We present an interpolation‐based planning and replanning algorithm for generating low‐cost paths through uniform and nonuniform resolution grids. Most grid‐based path planners use discrete state transitions that artificially constrain an agent's motion to a small set of possible headings (e.g., 0, π/4, π/2, etc.). As a result, even “optimal” grid‐based planners produce unnatural, suboptimal paths. Our approach uses linear interpolation during planning to calculate accurate path cost estimates for arbitrary positions within each grid cell and produce paths with a range of continuous headings. Consequently, it is particularly well suited to planning low‐cost trajectories for mobile robots. In this paper, we introduce a version of the algorithm for uniform resolution grids and a version for nonuniform resolution grids. Together, these approaches address two of the most significant shortcomings of grid‐based path planning: the quality of the paths produced and the memory and computational requirements of planning over grids. We demonstrate our approaches on a number of example planning problems, compare them to related algorithms, and present several implementations on real robotic systems.     

A block LU-SGS implicit unsteady incompressible flow solver on hybrid dynamic grids for 2D external bio-fluid simulations

A hybrid dynamic grid generation technique for two-dimensional (2D) morphing bodies and a block lower-upper symmetric Gauss-Seidel (BLU-SGS) implicit dual-time-stepping method for unsteady incompressible flows are presented for external bio-fluid simulations. To discretize the complicated computational domain around 2D morphing configurations such as fishes and insect/bird wings, the initial grids are generated by a hybrid grid strategy firstly. Body-fitted quadrilateral (quad) grids are generated first near solid bodies. An adaptive Cartesian mesh is then generated to cover the entire computational domain. Cartesian cells which overlap the quad grids are removed from the computational domain, and a gap is produced between the quad grids and the adaptive Cartesian grid. Finally triangular grids are used to fill this gap. During the unsteady movement of morphing bodies, the dynamic grids are generated by a coupling strategy of the interpolation method based on ‘Delaunay graph’ and local remeshing technique. With the motion of moving/morphing bodies, the grids are deformed according to the motion of morphing body boundaries firstly with the interpolation strategy based on ‘Delaunay graph’ proposed by Liu and Qin. Then the quality of deformed grids is checked. If the grids become too skewed, or even intersect each other, the grids are regenerated locally. After the local remeshing, the flow solution is interpolated from the old to the new grid. Based on the hybrid dynamic grid technique, an efficient implicit finite volume solver is set up also to solve the unsteady incompressible flows for external bio-fluid dynamics. The fully implicit equation is solved using a dual-time-stepping approach, coupling with the artificial compressibility method (ACM) for incompressible flows. In order to accelerate the convergence history in each sub-iteration, a block lower-upper symmetric Gauss-Seidel implicit method is introduced also into the solver. The hybrid dynamic grid generator is tested by a group of cases of morphing bodies, while the implicit unsteady solver is validated by typical unsteady incompressible flow case, and the results demonstrate the accuracy and efficiency of present solver. Finally, some applications for fish swimming and insect wing flapping are carried out to demonstrate the ability for 2D external bio-fluid simulations.     

Parametric interpolation of the moment matrix in surface integral equation formulation

In the analysis of electromagnetic scattering and radiation from objects of arbitrary shape using the method of moments (MoM), it is desirable to fill the impedance (or moment) matrix efficiently so that larger size problems can be solved. This article describes a general MoM technique in which the matrix is filled by spatial interpolation with respect to a parametrized electrical separation between source and test elements. The parametrization is accomplished such that the same algorithm also provides frequency interpolation, thus facilitating efficient computations over a wide frequency band. The spatial interpolation method is illustrated by application to the analysis of radiation from tunable microstrip patch antennas over multiple frequency bands. By specializing the interpolation scheme to a surface integral equation formulation that employs rooftop basis functions on a grid of rectangular cells, it is shown that the interpolation method results in considerable reduction of the storage and CPU time requirements. ©1999 John Wiley & Sons, Inc. Int J RF and Microwave CAE 9: 474–489, 1999.     

Numerical construction of optimal adaptive grids in two spatial dimensions

This article concerns a new procedure to generate a solution-adaptive grid for convection dominated problems in two spatial dimensions based on finite element approximations. The procedure extends a one-dimensional equidistribution principle which minimizes the interpolation error in appropriate norms. The idea in extending such a technique to two spatial dimensions is to select two directions which can reflect the physics of the problems, and then the one-dimensional equidistribution principle is applied to the chosen directions. The final grids generated are connected through a sweep-line based unstructured grid technique. Model problems considered are the two-dimensional convection-diffusion problems where boundary and interior layers occur. Numerical results of model problems illustrating the efficiency of the proposed scheme are presented. Comparisons of the solutions with an existing scheme will also be provided.     

Fast, memory-efficient cell location in unstructured grids for visualization

Applying certain visualization techniques to datasets described on unstructured grids requires the interpolation of variables of interest at arbitrary locations within the dataset's domain of definition. Typical solutions to the problem of finding the grid element enclosing a given interpolation point make use of a variety of spatial subdivision schemes. However, existing solutions are memory- intensive, do not scale well to large grids, or do not work reliably on grids describing complex geometries. In this paper, we propose a data structure and associated construction algorithm for fast cell location in unstructured grids, and apply it to the interpolation problem. Based on the concept of bounding interval hierarchies, the proposed approach is memory-efficient, fast and numerically robust. We examine the performance characteristics of the proposed approach and compare it to existing approaches using a number of benchmark problems related to vector field visualization. Furthermore, we demonstrate that our approach can successfully accommodate large datasets, and discuss application to visualization on both CPUs and GPUs.     

Efficient Smoke Simulation on Curvilinear Grids

We present an efficient approach for performing smoke simulation on curvilinear grids. Our technique is based on a fast unconditionally‐stable advection algorithm and on a new and efficient solution to enforce mass conservation. It uses a staggered‐grid variable arrangement, and has linear cost on the number of grid cells. Our method naturally integrates itself with overlapping‐grid techniques, lending to an efficient way of producing highly‐realistic animations of dynamic scenes. Compared to approaches based on regular grids traditionally used in computer graphics, our method allows for better representation of boundary conditions, with just a small increment in computational cost. Thus, it can be used to evaluate aerodynamic properties, possibly enabling unexplored applications in computer graphics, such as interactive computation of lifting forces on complex objects. We demonstrate the effectiveness of our approach, both in 2‐D and 3‐D, through a variety of high‐quality smoke animations.     

GCLgrid: A three-dimensional geographical curvilinear grid library for computational seismology

We developed a general library for handling a class of objects we call geographical curvilinear grids (GCLgrids). A GCLgrid is a distorted, uniform grid that is georeferenced. The GCLgrid library is implemented in an object oriented system with methods that relate points in the grid to a geographic reference frame. A simple example is a spherical shell divided along latitude, longitude, and depth, but more elaborate shapes can use the same interface. Scalar and vector fields are derived from the base grid through inheritance. Two algorithms are the core of this library. First, we use the Direction Set method to search for a location in space from a starting point. This algorithm converges reasonably fast if the grid is not extremely distorted. Second, we interpolate the grid using methods known from finite element analysis. A Jacobian matrix for an 8-node cube is computed to transform a distorted cube into a unit one. Shape functions for the standard cube are used to compute interpolation coefficients. Once the interpolation coefficients are computed, we can interpolate n-element vectors almost as quickly as scalar data. We show an application of the library to travel time table calculation at regional distances. Our table interpolator was found to be 10 times faster than one based on the tau-p method and is expected to be several orders of magnitude faster than 3D ray-tracing methods. Travel time interpolation errors are reduced significantly by tabulating delay times relative to a homogenous reference model instead of absolute times. This allows much coarser grids to be used at large scales comparing to one using total time.     

混合重叠网格通信优化算法

重叠网格技术广泛应用在复杂外型和运动边界问题的流场数值模拟中.本文在并行重叠网格隐式挖洞算法实现的基础上,提出了笛卡尔辅助网格和多块结构网格的混合重叠网格方法.通过笛卡尔辅助网格实现重叠网格洞边界和网格插值关系的快速建立.通过定义重叠区域网格权重、部件网格与背景网格绑定的方法,建立了混合网格的并行分配模式,有效减少重叠插值信息在各进程间的通信,实现计算负载和通信负载在各个进程的均匀分配.测试表明该方法可应用于数千万量级的重叠网格系统,可扩展至千核规模,高效的实现多个物体构成的复杂网格系统的重叠关系建立.     

Electrostatic and magnetostatic particle simulation models in three dimensions

Electrostatic and magnetostatic particle simulation models have been developed and tested for a magnetically confined plasma near thermal equilibrium. The model makes use of a three-dimensional grid elongated in the direction of a magnetic field to simulate plasma confinement devices. Linear interpolation is used on a two-dimensional grid perpendicular to a magnetic field while quadratic or cubic interpolation is used in the direction of the magnetic field. It is found that energy conservation is good and the fluctuation spectra for the electric and magnetic fields agree with theoretical predictions. The model presented here may be used as an alternative method to simulate a laboratory device along with the hybrid model which makes use of the combination of a two-dimensional spatial grid and an eigenfunction expansion along the main magnetic field.     

A FV-TD electromagnetic solver using adaptive Cartesian grids

A second-order finite-volume (FV) method has been developed to solve the time-domain (TD) Maxwell equations, which govern the dynamics of electromagnetic waves. The computational electromagnetic (CEM) solver is capable of handling arbitrary grids, including structured, unstructured, and adaptive Cartesian grids, which are topologically arbitrary. It is argued in this paper that the adaptive Cartesian grid is better than a tetrahedral grid for complex geometries considering both efficiency and accuracy. A cell-wise linear reconstruction scheme is employed to achieve second-order spatial accuracy. Second-order time accuracy is obtained through a two-step Runge-Kutta scheme. Issues on automatic adaptive Cartesian grid generation such as cell-cutting and cell-merging are discussed. A multi-dimensional characteristic absorbing boundary condition (MDC-ABC) is developed at the truncated far-field boundary to reduce reflected waves from this artificial boundary. The CEM solver is demonstrated with several test cases with analytical solutions.     

一种基于密度和网格的簇心可确定聚类算法

以网格化数据集来减少聚类过程中的计算复杂度,提出一种基于密度和网格的簇心可确定聚类算法.首先网格化数据集空间,以落在单位网格对象里的数据点数表示该网格对象的密度值,以该网格到更高密度网格对象的最近距离作为该网格的距离值;然后根据簇心网格对象同时拥有较高的密度和较大的距离值的特征,确定簇心网格对象,再通过一种基于密度的划分方式完成聚类;最后,在多个数据集上对所提出算法与一些现有聚类算法进行聚类准确性与执行时间的对比实验,验证了所提出算法具有较高的聚类准确性和较快的执行速度.     

Balancing conflicting requirements for grid and particle decomposition in continuum-Lagrangian solvers

Load balancing strategies for hybrid solvers that involve grid based partial differential equation solution coupled with particle tracking are presented in this paper. A typical Message Passing Interface (MPI) based parallelization of grid based solves are done using a spatial domain decomposition while particle tracking is primarily done using either of the two techniques. One of the techniques is to distribute the particles to MPI ranks to whose grid they belong to while the other is to share the particles equally among all ranks, irrespective of their spatial location. The former technique provides spatial locality for field interpolation but cannot assure load balance in terms of number of particles, which is achieved by the latter. The two techniques are compared for a case of particle tracking in a homogeneous isotropic turbulence box as well as a turbulent jet case. A strong scaling study is performed to more than 32,000 cores, which results in particle densities representative of anticipated exascale machines. The use of alternative implementations of MPI collectives and efficient load equalization strategies are studied to reduce data communication overheads.     

A Practical Method for High‐Resolution Embedded Liquid Surfaces

Combining high‐resolution level set surface tracking with lower resolution physics is an inexpensive method for achieving highly detailed liquid animations. Unfortunately, the inherent resolution mismatch introduces several types of disturbing visual artifacts. We identify the primary sources of these artifacts and present simple, efficient, and practical solutions to address them. First, we propose an unconditionally stable filtering method that selectively removes sub‐grid surface artifacts not seen by the fluid physics, while preserving fine detail in dynamic splashing regions. It provides comparable results to recent error‐correction techniques at lower cost, without substepping, and with better scaling behavior. Second, we show how a modified narrow‐band scheme can ensure accurate free surface boundary conditions in the presence of large resolution mismatches. Our scheme preserves the efficiency of the narrow‐band methodology, while eliminating objectionable stairstep artifacts observed in prior work. Third, we demonstrate that the use of linear interpolation of velocity during advection of the high‐resolution level set surface is responsible for visible grid‐aligned kinks; we therefore advocate higher‐order velocity interpolation, and show that it dramatically reduces this artifact. While these three contributions are orthogonal, our results demonstrate that taken together they efficiently address the dominant sources of visual artifacts arising with high‐resolution embedded liquid surfaces; the proposed approach offers improved visual quality, a straightforward implementation, and substantially greater scalability than competing methods.     

Multi-thread implementations of the lattice Boltzmann method on non-uniform grids for CPUs and GPUs

Two multi-thread based parallel implementations of the lattice Boltzmann method for non-uniform grids on different hardware platforms are compared in this paper: a multi-core CPU implementation and an implementation on General Purpose Graphics Processing Units (GPGPU). Both codes employ second order accurate compact interpolation at the interfaces, coupling grids of different resolutions. Since the compact interpolation technique is both simple and accurate, it produces almost no computational overhead as compared to the lattice Boltzmann method for uniform grids in terms of node updates per second. To the best of our knowledge, the current paper presents the first study on multi-core parallelization of the lattice Boltzmann method with inhomogeneous grid spacing and nested time stepping for both CPUs and GPUs.     

Second-order, exact charge conservation for electromagnetic particle-in-cell simulation in complex geometry

A second-order, exact charge-conserving algorithm for accumulating charge and current on the spatial grid for electromagnetic particle-in-cell (EM-PIC) simulation in bounded geometry is presented. The algorithm supports standard EM-PIC exterior boundary conditions and complex internal conductors on non-uniform grids. Boundary surfaces are handled by smoothly transitioning from second to first-order weighting within half a cell of the boundary. When a particle is exactly on the boundary surface (either about to be killed, or just created), the weighting is fully first-order. This means that particle creation and particle/surface interaction models developed for first-order weighting do not need to be modified. An additional feature is the use of an energy-conserving interpolation scheme from the electric field on the grid to the particles. Results show that high-density, cold plasmas with ωpeΔt∼1, and Δx/λD?1, can be modeled with reasonable accuracy and good energy conservation. This opens up a significant new capability for explicit simulation of high-density plasmas in high-power devices.     

Full Wave Modelling of Light Propagation and Reflection

The propagation and reflection of electromagnetic waves in a three‐dimensional environment is simulated, and realistic images are produced using the resulting light distributions and reflectance functions. A finite difference time domain method is employed to advance the electric and magnetic fields in a scene. Surfaces containing wavelength scaled structures are created, the interaction of the electromagnetic waves with these nano‐structured materials is calculated, and the sub‐surface interference and diffraction effects are modelled. The result is a reflectance function with wavelength composition and spatial distribution properties that could not have been predicted using classic computer graphic ray tracing approaches. The techniques are employed to reproduce demonstrations of simple interference and diffraction effects, and to create computer‐generated pictures of a Morpho butterfly.