Streamwise computation of duct flows

A computational method is presented to calculate momentum and energy transport in two-dimensional viscous compressible duct flows. The flow in the duct is partitioned into finite streams. The difference equations are then obtained by applying momentum and energy conservation principles directly to the individual streams. The method is applicable to laminar and turbulent flows.     

Computation of three-dimensional parabolic laminar flows

A simple yet accurate method for computing three-dimensional parabolic laminar flow of an incompressible, viscous fluid in a constant area duct is presented. The boundary-layer type nonlinear equations of motion are solved numerically using finite differences and the variable mesh technique. Results of the present calculations are compared with experimental and previous theoretical data for flow through square and rectangular ducts; the agreement is satisfactory.     

Transition prediction for three-dimensional flows using parallel computation

A computational method to predict transition lines for general three-dimensional configurations is presented. The method consists of a coupled program system including a 3D Navier-Stokes solver, a transition module, a boundary layer code and a stability code. The newly developed transition module has been adapted to be used with parallel computation to account for the high computational demand for three-dimensional configurations. Detailed computations have been performed to show the ability of the Navier-Stokes code to provide three-dimensional boundary layer data of high accuracy needed for the stability analysis. A comprehensive investigation on general computational and parallel performance identifies the numerical effort for the transition prediction method. The procedure has been validated comparing the numerical results with experiments for the flow around an inclined prolate spheroid. Feasibility studies on generic transport aircraft have been performed to show the code’s capability to predict transition lines on general complex geometries.     

The numerical computation of turbulent flows

The paper reviews the problem of making numerical predictions of turbulent flow. It advocates that computational economy, range of applicability and physical realism are best served at present by turbulence models in which the magnitudes of two turbulence quantities, the turbulence kinetic energy $\text{k}$ and its dissipation rate ?, are calculated from transport equations solved simultaneously with those governing the mean flow behaviour. The width of applicability of the model is demonstrated by reference to numerical computations of nine substantially different kinds of turbulent flow.     

Parallel finite-element computation of 3D flows

The authors describe their work on the massively parallel finite-element computation of compressible and incompressible flows with the CM-200 and CM-5 Connection Machines. Their computations are based on implicit methods, and their parallel implementations are based on the assumption that the mesh is unstructured. Computations for flow problems involving moving boundaries and interfaces are achieved by using the deformable-spatial-domain/stabilized-space-time method. Using special mesh update schemes, the frequency of remeshing is minimized to reduce the projection errors involved and also to make parallelizing the computations easier. This method and its implementation on massively parallel supercomputers provide a capability for solving a large class of practical problems involving free surfaces, two-liquid interfaces, and fluid-structure interactions     

Parallel computation of three-dimensional nonlinear magnetostatic problems

We describe a general-purpose parallel code for computing accurate solutions to large computationally demanding, 3D, nonlinear magnetostatic problems. The code, CORAL, is based on a volume integral equation formulation. Using an IBM SP parallel computer and iterative solution methods, we successfully solved the dense linear systems inherent in such formulations. A key component of our work was the use of the PETSc library, which provides parallel portability and access to the latest linear algebra solution technology. Copyright © 1999 John Wiley & Sons, Ltd.     

Numerical computation of transient coaxial entry tube flows

A numerical program was developed to compute transient laminar flows in two dimensions including multicomponent mixing and chemical reaction. The program can compute both incompressible flows and compressible flows at all speeds, and it is applied to describe transient and steady state solutions for low subsonic, coaxial entry, tube flows. Single component, non-reacting flows comprise most of the solutions, but one steady state solution is presented for trace concentration constituents engaging in a second order reaction. Numerical stability was obtained by adding at each calculation point a correction for numerical diffusion errors caused by truncation of the Taylor series used to finite difference the conservation equations. Transient computations were made for fluids initially at rest, then subjected to step velocity inputs that were uniform across each region of the entry plane and were held constant throughout the computation period. For center tube to annulus velocity ratios of 0.5 and 2.0, the bulk fluid in the tube initially moved in plug flow, but strong radial flows developed near the injection plane which moved the fluid into the high shear region between the jets and away from the tube wall. The entrance flows penetrated the bulk flow until steady state was attained. A computation with only the center jet flowing developed a recirculation vortex in the annulus that propagated downstream. The calculation of steady state reacting flows showed formation of a third specie in the mixing zone. Both short and long tube solutions are presented.     

On two- and three-dimensional expansion flows

This paper gives consideration to incompressible Newtonian flows through two- and three-dimensional expansions. Through a time-stepping scheme, steady-state solutions are sought for both small and large expansion ratios. The flow structure in the two-dimensional case can be significantly different from that of the three-dimensional equivalent, depending on the expansion ratio. Both lip and salient corner vortices are reported, and comparisons are made against available experimental data.     

Operator splitting methods for the computation of reacting flows

If the modeling of the chemistry of a reacting flow system is to consider more than a simple, one-step, global reaction the attainment of a numerical solution of the relevant governing equations is generally jeopardised by the problem of stiffness. In the present work a general approach to overcoming the stiffness hazard is presented. It makes use of operator-splitting techniques, the novel feature being that splitting of the chemical source terms themselves is permitted, with the aid of a new chemical splitting parameter. For the case of elliptic flow with a unimolecular reversible chemical reaction a convergence analysis provides an insight into the conditions under which a converged solution will be obtained. The existence of an optimum value of the chemical splitting parameter indicates the possibility of accelerating convergence. Finally, calculated results for some test problems, involving linear and nonlinear chemical kinetic models, illustrate the viability and usefulness of methods based on the new approach.     

GPGPU computation and visualization of three-dimensional cellular automata

This paper presents a general-purpose simulation approach integrating a set of technological developments and algorithmic methods in cellular automata (CA) domain. The approach provides a general-purpose computing on graphics processor units (GPGPU) implementation for computing and multiple rendering of any direct-neighbor three-dimensional (3D) CA. The major contributions of this paper are: the CA processing and the visualization of large 3D matrices computed in real time; the proposal of an original method to encode and transmit large CA functions to the graphics processor units in real time; and clarification of the notion of top-down and bottom-up approaches to CA that non-CA experts often confuse. Additionally a practical technique to simplify the finding of CA functions is implemented using a 3D symmetric configuration on an interactive user interface with simultaneous inside and surface visualizations. The interactive user interface allows for testing the system with different project ideas and serves as a test bed for performance evaluation. To illustrate the flexibility of the proposed method, visual outputs from diverse areas are demonstrated. Computational performance data are also provided to demonstrate the method’s efficiency. Results indicate that when large matrices are processed, computations using GPU are two to three hundred times faster than the identical algorithms using CPU.     

Review of numerical computation of compressible flows with artificial interfaces

In Computational Fluid Dynamics, it is very often to use a composite grid for various purposes including easy meshing of a complex geometry, parallel computing, local mesh refinement, or treating different flows with different physical models, and using different numerical methods. All these methods have a common feature: they have internal artificial interfaces at which one needs to define interface conditions. In this paper, we first give a review on the current status of this subject with emphasis on compressible flows. Then two problems will be discussed in details. The first is for the overlapping grid approach due to its wide popularity for treating complex geometry and for parallel computing. The second is concerned with continuum/DSMC matching since this is a hot topic of current interest. A two dimensional computation is also performed to study the transmission of a shock wave across an overlapping grid interface.     

Characteristic lines for two- and three-dimensional flows

An algorithm based on the method of characteristics for one-dimensional flow is generalized to apply to multidimensional flow. InN dimensions the method has 2N+2 ordinary differential equations defined on a unique set of 2N+1 characteristic lines, modulo the appropriate rotation group.     

Particle partitioning strategies for the parallel computation of solid-liquid flows

The numerical investigation of the interaction of large, solid particles with fluids is an important area of research for many manufacturing processes. Such studies frequently lead to models that are very large and require the use of parallel solution techniques. This paper presents the results of a parallel implementation of a serial code for the direct numerical simulation of solid-liquid flows. The base code is a serial, arbitrary Lagrangian-Eulerian (ALE) formulation of the equations of motion, which views that particles as solid bodies are embedded into the flow domain. This particular model poses some interesting difficulties for domain decomposition type approaches for parallel solutions. In particular, it is not fully understood how the partitioning of the particles among the subdomains influences the performance of parallel solvers. We present several strategies for the partitioning of the solid particles, focusing on the effectiveness of these techniques in terms of parallel speedup and efficiency.     

Parallel 3D computation of unsteady flows around circular cylinders

In this article we present parallel 3D finite element computation of unsteady incompressible flows around circular cylinders. We employ stabilized finite element formulations to solve the Navier-Stokes equations on a thinking machine CM-5 supercomputer. The time integration is based on an implicit method, and the coupled, nonlinear equations generated every time step are solved iteratively, with an element-vector based evaluation technique. This strategy enables us to carry out these computations with millions of coupled, nonlinear equations, and thus resolve the flow features in great detail. At Reynolds number 300 and 800, our results indicate strong 3D features arising from the instability of the columnar vortices forming the Karman street. At Re = 10 000 we employ a large eddy simulation (LES) turbulence model.     

Parallel multigrid finite volume computation of three-dimensional thermal convection

A parallel implementation of the finite volume method for three-dimensional, time-dependent, thermal convective flows is presented. The algebraic equations resulting from the finite volume discretization, including a pressure equation which consumes most of the computation time, are solved by a parallel multigrid method. A flexible parallel code has been implemented on the Intel Paragon, the Cray T3D, and the IBM SP2 by using domain decomposition techniques and the MPI communication software. The code can use 1D, 2D, or 3D partitions as required by different geometries, and is easily ported to other parallel systems. Numerical solutions for air (Prandtl number Pr = 0.733) with various Rayleigh numbers up to 10⁷ are discussed.     

Efficient computation of Morse-Smale complexes for three-dimensional scalar functions

The Morse-Smale complex is an efficient representation of the gradient behavior of a scalar function, and critical points paired by the complex identify topological features and their importance. We present an algorithm that constructs the Morse-Smale complex in a series of sweeps through the data, identifying various components of the complex in a consistent manner. All components of the complex, both geometric and topological, are computed, providing a complete decomposition of the domain. Efficiency is maintained by representing the geometry of the complex in terms of point sets.     

Implicit multigrid computation of unsteady flows past cylinders of square cross-section

An implicit, multigrid scheme has been extended to treat unsteady flows using the concept of temporal subiteration (or dual-time stepping, as it sometimes is called). The efficiency and accuracy of the subiterated, multigrid approach has been discussed in a previous paper. Here, the scheme is applied to compute the unsteady flow past fixed cylinders of square cross-section at moderate Reynolds numbers. The observed pattern of periodic vortex shedding is computed and the dimensionless frequency of this phenomenon (the Strouhal number) is compared with experimentally determined values. Results of coupled aeroelastic computations also are presented that illustrate a hysteresis phenomenon as the structural frequency is varied.     

Efficient blocking probability computation of complex traffic flows for network dimensioning

Computing or estimating link blocking probabilities is a fundamental ingredient in network design and engineering. While in traditional telephone networks this was easily done by Erlang's formula, it became much harder in today's complex networks that carry very heterogeneous traffic. We present a simple, efficient method to estimate the blocking probability and link utilization for general multirate, heterogeneous traffic, where the individual bandwidth demands may aggregate in complex, nonlinear ways. The estimation is derived without adopting conventional performance modeling assumptions, such as Poisson arrivals or exponential holding times, thus allowing non-standard behaviour patterns, including special phenomena of IP networks, such as self-similarity. Despite its generality, our estimation maintains an optimally tight exponent and is capable of handling apparently very different cases in a unified way. The approach also makes it possible to make estimations under incomplete information. We show that the results are easily applicable for fast, robust link dimensioning, especially in case of complex traffic patterns, under partial information. Moreover, it is very well fitted for embedding into network level optimization tasks, due in part to simplicity and in part to convexity properties.     

The computation of massively separated flows using compressible vorticity confinement methods

Vorticity confinement methods have been shown to be very effective in the computation of flows involving the convection of thin vortical layers. These are the only Eulerian methods whereby simulations of these layers remain very thin and persist long distances without significant dissipation. Initially developed by Steinhoff and co-workers for incompressible flow, these methods have been used successfully to predict complex flows, particularly involving helicopter rotors. Recently, the method has been extended to a compressible finite-volume form, which will enable the methods to be used for a much broader class of problems. In this paper, we examine the ability of the compressible vortex confinement methodology to handle an important class of vortex-dominated flows involving massive separation from bluff bodies. We evaluate the effectiveness of the method by comparisons with experimental data and available state-of-the-art computations. An important conclusion of the present work is that vortex confinement applied to massively separated flows, without modeling the viscous terms and on an essentially inviscid grid, can result in a reasonable approximation to turbulent separated flows. The computed flow structures and velocity profiles were in good agreement with time-averaged values of the data and with LES simulations even though the confinement approach utilized more than a factor of 50 fewer cells in the computation (20,000 compare to more the 1 million). The success of the method for these classes of flows may be attributed to the accurate calculation of the rotational inviscid flow which dominates the convection of the large-scale flow structures.     

Calculations of axisymmetric swirling flows by the use of parabolic type equations

Numerical solutions of boundary layer like equations are presented for steady, axisymmetric swirling flows in a pipe; the fluid is incompressible. Calculations were performed for combinations of two parameters; Wa and Ω are the velocity on the axis and the swirl strength at the upstream boundary, respectively. One of the solutions was in qualitative agreement, over some axial distance, with earlier Navier-Stokes calculations obtained by the authors.