Numerical algorithms in computational fluid dynamics on vector computers

Modern vector computers tend to favour certain classes of algorithms (e.g. explicit, Jacobi-type) while other important algorithms, such as implicit ones or Monte Carlo, in their serial versions are not very suitable for these machines. However, restructuring of serial algorithms often enables the user to exploit fully the potential of vector machines, which will often result in remarkable performance improvements. In the following contribution, the vectorization of five well-known algorithms, the explicit-implicit MacCormack scheme, the implicit scheme of Beam and Warming, a boundary-layer algorithm, a Galerkin procedure and a Monte Carlo simulation, for the solution of problems in computational fluid dynamics is discussed and computation times are given.     

Automated domain decomposition for computational fluid dynamics

Automation of flow-field zoning in two-dimensions is an important step towards easing the three-dimensional grid generation bottleneck in computational fluid dynamics. A knowledge-based approach works well, but several aspects of flow-field zoning make the use of such an approach challenging. A proposed model and language to describe the process of zoning a flow field are presented, followed by a discussion of the implementation of EZGrid, a knowledge-based two-dimensional (2-D) flow-field zoner. Results are shown for representative 2-D aerodynamic configurations. Finally, an approach to the evaluation of flow-field zonings is described and used to compare the performance of EZGrid with that of a human expert.     

Asymptotic behavior and best approximation in computational fluid dynamics

Computational fluid dynamics has many successes for the solution of simple standard problems. For relatively complex problems, especially if nonlinear and of mixed type, the computed approximate solutions are mostly of dubious accuracy and credibility. The difficulty appears fundamental. Model studies in one space dimension suggest that most of such discrete problems are poorly posed. The sequence of computed solutions at successively refined meshes need not converge; and apparently “smooth” computed approximations can “converge” to wrong limits with large global errors. For certain discrete formulations the sequence is asymptotic in the sense of displaying minimum error at some fairly large critical mesh Reynolds number (coarse meshes). This error minimum can be as small as those promised by the correct “convergent approximations” at much smaller meshes. Certain behavior of the computed solutions around such a critical mesh Reynolds number help to identify the “best approximation”. Such analytic inferences have been tested and verified in the computational solutions of successively more complex flows governed by Navier-Stokes equations in two space dimensions. The flow fields due to shockwave-laminar-boundary layer interaction were computed with different discrete formulations and various perturbations. The computed “best approximations” differ little and all compare favorably with available experimental data. Some of such formulations give the “best approximations” at reasonably coarse meshes, requiring much smaller computational effort; and should therefore be favorably considered.     

Visualization's role in analyzing computational fluid dynamics data

Visualization has fueled the growth and understanding of many scientific and engineering fields. In computational fluid dynamics, for example, engineers now use numerical calculations to accurately simulate many engineering problems that once required the use of physical experiments involving wind and water tunnels. CFD has come to serve as an instrument in the design of many familiar engineering processes. These developments have produced massive amounts of data for analysis. Feature detection has become a critical tool in understanding key structures within these volumes of data. We briefly discuss the growth of CFD and investigate why feature detection and visualization have become such a vital part of analyzing CFD simulation results.     

Complementing computational fluid dynamics methods with classical analytical techniques

New aerospace vehicle designs must have greater performance and versatility at affordable cost. This requires multi-disciplinary analysis and optimization which in turn requires more accurate and efficient numerical simulation tools. The need for greater accuracy and efficiency of computational fluid dynamics (CFD) tools is further amplified by the industry trend toward distributed computing (e.g. workstation clusters) and away from supercomputers. Complementary analytic methods coupled with traditional CFD approaches offer the means for increased simulation capability by incorporating more essential physics into solution algorithms and reducing reliance on grid density for achieving accuracy. McDonnell Douglas Aerospace has a focused activity directed at improving affordability of CFD tools with complementary analytic techniques and has developed a strong capability. Results have proven very successful. Several examples of ongoing work are discussed, including improved far-field boundary conditions for CFD codes and analytic-based aerodynamic analysis and design optimization methods.     

计算流体力学在化学反应器模拟中的应用进展

计算流体力学(CFD)能够准确地描述流体流动、混合、传热规律,近年来逐渐开始耦合到化学反应中应用于化学工程领域,并表现出巨大潜力。本文综述了CFD在不同化学反应器中针对不同反应体系模拟的基本原理以及应用。相比于传统的面向理想反应器的反应动力学模拟和单纯面向流动传递的CFD模拟方法而言,采用CFD耦合化学反应动力学的方法同时考虑了传递过程和反应过程,能够对非理想化学反应器的操作特性(转化率、选择性、分子量及其分布等)进行模拟、分析与预测,在化工过程强化和化工产品控制方面优势明显。开发新的耦合数学模型和数值算法、考虑亚格子尺度的微观过程和采用直接数值模拟等方法,将是利用CFD深入研究非理想反应器特性的重要方向。     

The use of computational fluid dynamics in TsAGI experimental works

The paper describes methods to calculate the flow around an aircraft model in a wind tunnel. It formulates special boundary conditions to achieve the necessary flow parameters in the control section, as well as to simulate some features of wind tunnel walls, for example, perforation. In order to accelerate the numerical solution convergence, a method for implicit smoothing is suggested allowing the calculation duration to be reduced several times. The cases of practical use of this methodology are given. It is shown that in the conditions of the TsAGI subsonic wind tunnel, it is possible to simulate the effect on the model from the elements of the structure that are missing in this tunnel, for example, the running track. A mathematical model of the European Transonic Windtunnel (ETW) with slotted walls is presented. It is shown that the flow in the reentry affects the main flow in the test section of this tunnel. Data on the effect of the model support in the TsAGI wind tunnel T-128 are given. The peniche height used in the half-model tests has been justified. The conclusion is made that the mathematical model of the wind tunnel is an obligatory part in experimental studies.     

Vorton dynamics: a case study of developing a fluid dynamics model for a vector processor

The raw performance of vector processors such as the CDC CYBER-205 has been well documented. The ability to apply this raw power to ever more complex algebraic algorithms has been reported in [9]. The final step in making computers of this class truly the revolutionary tools they are claimed to be is to develop whole applications that perform at a significant fraction of the raw power. This involves two distinct subclasses of problems. On the one hand, there are those pre-existing applications that must be mapped onto vector processors in such a way that not only is performance maintained, but also a (sometimes vague) set of computational boundary conditions of the user community is satisfied. On the other hand, there are those models which are developed ab initio with machines such as the CYBER-205 in mind. The development of solutions to problems in the former class involves psychology and politics as well as mathematics and computer science. We limit ourselves here to reporting on an example of the latter class, viz. a model to study a particular fluid-dynamic phenomenon, that was specifically designed with the CYBER-205 in mind.     

Recent progress and challenges in exploiting graphics processors in computational fluid dynamics

The progress made in accelerating simulations of fluid flow using GPUs, and the challenges that remain, are surveyed. The review first provides an introduction to GPU computing and programming, and discusses various considerations for improved performance. Case studies comparing the performance of CPU- and GPU-based solvers for the Laplace and incompressible Navier–Stokes equations are performed in order to demonstrate the potential improvement even with simple codes. Recent efforts to accelerate CFD simulations using GPUs are reviewed for laminar, turbulent, and reactive flow solvers. Also, GPU implementations of the lattice Boltzmann method are reviewed. Finally, recommendations for implementing CFD codes on GPUs are given and remaining challenges are discussed, such as the need to develop new strategies and redesign algorithms to enable GPU acceleration.     

Research trends in multibody system dynamics

During the last decade, multibody dynamics was acknowledged as an independent branch of theoretical, computational and applied mechanics around the globe. The research topics have been widened as well as the applications. The research topics are discussed with respect to the subjects and countries dealing with multibody dynamics. A community of multibody dynamicists is identified by their contributions and services to the journal Multibody System Dynamics. Commemorative Contribution.     

Control of convergence in a computational fluid dynamics simulation using ANFIS

Adaptive-network-based fuzzy inference system (ANFIS) was used to control convergence of a computational fluid dynamics (CFD) algorithm. Normalized residuals were used to select the relaxation factors on each iteration of the computation. The ratio between the residual of the current iteration and of the previous iteration was used as a control input. ANFIS was designed to keep the tuning index at or near one throughout the fluid dynamics simulation. The finite volume CFD algorithm SIMPLER was used as the platform for this study. Four different benchmark cases were examined.     

Multi-objective shape optimization using ant colony coupled computational fluid dynamics solver

An adaptation of a parametric ant colony optimization (ACO) to multi-objective optimization (MOO) is presented in this paper. In this algorithm (here onwards called MACO) the concept of MOO is achieved using the reference point (or goal vector) optimization strategy by applying scalarization. This method translates the multi-objective optimization problem to a single objective optimization problem. The ranking is done using ?-dominance with modified L_p metric strategy. The minimization of the maximum distance from the goal vector drives the solution close to the goal vector. A few validation test cases with multi-objectives have been demonstrated. MACO was found to out perform R-NSGA-II for the test cases considered. This algorithm was then integrated with a meshless computational fluid dynamics (CFD) solver to perform aerodynamic shape optimization of an airfoil. The algorithm was successful in reaching the optimum solutions near to the goal vector on one hand. On the other hand the algorithm converged to an optimum outside the boundary specified by the user for the control variables. These make MACO a good contender for multi-objective shape optimization problems.     

Design of a flow-controlled asymmetric droplet splitter using computational fluid dynamics

In this work the design of a segmented flow microfluidic device is presented that allows droplet splitting ratios from 1:1 up to 20:1. This ratio can be dynamically changed on chip by altering an additional oil flow. The design was fabricated in PDMS chips using the standard SU-8 mold technique and does not require any valves, membranes, optics or electronics. To avoid a trial and error approach, fabricating and testing several designs, a computational fluid dynamics model was developed and validated for droplet formation and splitting. The model was used to choose between several variations of the splitting T-junction with the extra oil inlet, as well to predict the additional flow rate needed to split the droplets in various ratios. Experimental and simulated results were in line, suggesting the model’s suitability to optimize future designs and concepts. The resulting asymmetric droplet splitter design opens possibilities for controlled sampling and improved magnetic separation in bio-assay applications.     

Screw and Lie group theory in multibody dynamics

Screw and Lie group theory allows for user-friendly modeling of multibody systems (MBS), and at the same they give rise to computationally efficient recursive algorithms. The inherent frame invariance of such formulations allows to use arbitrary reference frames within the kinematics modeling (rather than obeying modeling conventions such as the Denavit–Hartenberg convention) and to avoid introduction of joint frames. The computational efficiency is owed to a representation of twists, accelerations, and wrenches that minimizes the computational effort. This can be directly carried over to dynamics formulations. In this paper, recursive \(O ( n ) \) Newton–Euler algorithms are derived for the four most frequently used representations of twists, and their specific features are discussed. These formulations are related to the corresponding algorithms that were presented in the literature. Two forms of MBS motion equations are derived in closed form using the Lie group formulation: the so-called Euler–Jourdain or “projection” equations, of which Kane’s equations are a special case, and the Lagrange equations. The recursive kinematics formulations are readily extended to higher orders in order to compute derivatives of the motions equations. To this end, recursive formulations for the acceleration and jerk are derived. It is briefly discussed how this can be employed for derivation of the linearized motion equations and their time derivatives. The geometric modeling allows for direct application of Lie group integration methods, which is briefly discussed.     

Architecture for video coding on a processor with an ARM and DSP cores

This paper aims to describe architecture for video coding on a processor with an ARM and DSP cores. The proposed platform has been designed for MPEG-4 Visual Simple Profile. The obtained results are optimized if compared with these of single-core. The dual-core processors, composed of RISC and DSP, are widely used as the based-band processors of cell phones. The RISC suits for IO control, while DSP is useful for computation. The operational efficiency of the integration of RISC and DSP is outstanding. Video compression requires a great deal of computation, so we take both the feature of coding algorithm and the hardware platform into consideration. We analyze features of key components in video codec and propose the framework, which adopts DMA to shorten the time needed. It is the result of the communication between the dual-cores. The experimental results indicate that during the inter-frame processing, dual-core with DMA can cut down the processing time by 1/4 more than that of single-use of ARM or DSP. Moreover, it can save 3/4 of the time for encode/decode processing in inter-frame. Especially, in respect of motion estimation, the performance rating can be improved by 4 times.