A parallel, high-order discontinuous Galerkin code for laminar and turbulent flows

In this study we present a solution method for the compressible Navier-Stokes equations as well as the Reynolds-averaged Navier-Stokes equations (RANS) based on a discontinuous Galerkin (DG) space discretisation. For the turbulent computations we use the standard Wilcox k-ω or the Spalart-Allmaras model in order to close the RANS system. We currently apply either a local discontinuous Galerkin (LDG) or one of the Bassi-Rebay formulations (BR2) for the discretisation of second-order viscous terms. Both approaches (LDG and BR2) can be advanced explicitly as well as implicitly in time by classical integration methods. The boundary is approximated in a continously differentiable fashion by curved elements not to spoil the high-order of accuracy in the interior of the flow field.Computations are performed for the circular cylinder, the flat plate and classical airfoil sections like NACA0012. We compare our obtained results with experimental and computational data as well as analytical (boundary layer) predictions for the flat plate. The excellent parallelisation characteristics of the scheme are demonstrated, achieved by hiding communication latency behind computation.     

Large-scale solutions of three-dimensional compressible flows using the parallel N3S-MUSCL solver

We are concerned here with the parallelisation of the N3S-MUSCL industrial code which aims to solve the three-dimensional compressible Navier–Stokes equations by implementing a mixed finite element/finite volume formulation on unstructured tetrahedral meshes. Defining a good strategy for the parallelisation of an unstructured mesh based solver is a challenge, particularly when one aims at reaching a high level of performance while maintaining portability of the source code between scalar, vector and parallel machines. The parallelisation strategy adopted in this study combines mesh partitioning techniques and a message-passing programming model. The targeted parallel architectures are of MIMD type.     

Parallel DYNEMO: Meso-Scopic Traffic Flow Simulation on Large Networks

Traffic flow simulation is recently being applied to types of studies which require at the same time a large study area and models deeper than macroscopic assignments. Examples are investigations of the effects dynamic route guidance over large networks and the coupling with environmental models on large domains. The computational complexity can be reduced first by moving from microscopic to mesoscopic traffic flow models of the Payne-Cremer type. Where still more computing power is needed, parallelisation of the model may offer a solution. This paper describes a particular mesoscopic traffic flow model and its parallelisation undertaken in the ESPRIT project SIMTRAP. A new two step decomposition strategy is detailed along with its implementation using the message passing model PVM. The resulting speed-up is reported, drawing on both theoretical considerations and on measurements taken in the SIMTRAP demonstrator applications. The paper concludes with lessons learned from the experiments and directions for future work.     

Accelerated catadioptric omnidirectional view image unwrapping processing using GPU parallelisation

Catadioptric omnidirectional view sensors have found increasing adoption in various robotic and surveillance applications due to their 360° field of view. However, the inherent distortion caused by the sensors prevents their direct utilisations using existing image processing techniques developed for perspective images. Therefore, a correction processing known as “unwrapping” is commonly performed. However, the unwrapping process incurs additional computational loads on central processing units. In this paper, a method to reduce this burden in the computation is investigated by exploiting the parallelism of graphical processing units (GPUs) based on the Compute Unified Device Architecture (CUDA). More specifically, we first introduce a general approach of parallelisation to the said process. Then, a series of adaptations to the CUDA platform is proposed to enable an optimised usage of the hardware platform. Finally, the performances of the unwrapping function were evaluated on a high-end and low-end GPU to demonstrate the effectiveness of the parallelisation approach.     

Computational challenges of viscous incompressible flows

Over the past 30 years, numerical methods and simulation tools for incompressible flows have been advanced as a subset of the computational fluid dynamics (CFD) discipline. Although incompressible flows are encountered in many areas of engineering, simulation of compressible flow has been the major driver for developing computational algorithms and tools. This is probably due to the rather stringent requirements for predicting aerodynamic performance characteristics of flight vehicles, while flow devices involving low-speed or incompressible flow could be reasonably well designed without resorting to accurate numerical simulations. As flow devices are required to be more sophisticated and highly efficient, CFD tools become increasingly important in fluid engineering for incompressible and low-speed flow. This paper reviews some of the successes made possible by advances in computational technologies during the same period, and discusses some of the current challenges faced in computing incompressible flows.     

SAC—A Functional Array Language for Efficient Multi-threaded Execution

We give an in-depth introduction to the design of our functional array programming language SaC, the main aspects of its compilation into host machine code, and its parallelisation based on multi-threading. The language design of SaC aims at combining high-level, compositional array programming with fully automatic resource management for highly productive code development and maintenance. We outline the compilation process that maps SaC programs to computing machinery. Here, our focus is on optimisation techniques that aim at restructuring entire applications from nested compositions of general fine-grained operations into specialised coarse-grained operations. We present our implicit parallelisation technology for shared memory architectures based on multi-threading and discuss further optimisation opportunities on this level of code generation. Both optimisation and parallelisation rigorously exploit the absence of side-effects and the explicit data flow characteristic of a functional setting.     

Implicit methods for viscous incompressible flows

Numerical methods and simulation tools for incompressible flows have been advanced largely as a subset of the computational fluid dynamics (CFD) discipline. Especially within the aerospace community, simulation of compressible flows has driven most of the development of computational algorithms and tools. This is due to the high level of accuracy desired for predicting aerodynamic performance of flight vehicles. Conversely, low-speed incompressible flow encountered in a wide range of fluid engineering problems has not typically required the same level of numerical accuracy. This practice of tolerating relatively low-fidelity solutions in engineering applications for incompressible flow has changed. As the design of flow devices becomes more sophisticated, a narrower margin of error is required. Accurate and robust CFD tools have become increasingly important in fluid engineering for incompressible and low-speed flow. Accuracy depends not only on numerical methods but also on flow physics and geometry modeling. For high-accuracy solutions, geometry modeling has to be very inclusive to capture the elliptic nature of incompressible flow resulting in large grid sizes. Therefore, in this article, implicit schemes or efficient time integration schemes for incompressible flow are reviewed from a CFD tool development point of view. Extension of the efficient solution procedures to arbitrary Mach number flows through a unified time-derivative preconditioning approach is also discussed. The unified implicit solution procedure is capable of solving low-speed compressible flows, transonic, as well as supersonic flows accurately and efficiently. Test cases demonstrating Mach-independent convergence are presented.     

p-period maximal dynamic flows in a network

Given a network with a source and a destination vertices, fixed traversal times, time-dependent capacities of edges, and permissible held-over periods at the vertices. The p-period maximal dynamic flow problem is to find the maximal flow that can be transferred from the source to the destination within p periods of time. The paper presents an ulgorithm for the solution of this problem, reviews previous results for simpler cases and reports on some limited computational experience.     

Parallel Task for Parallelising Object-Oriented Desktop Applications

With the arrival of multi-cores for mainstream desktop systems, developers must invest the effort of parallelising their applications in order to benefit from these systems. However, the structure of these interactive desktop applications is noticeably different from the traditional batch-like applications of the engineering and scientific fields. We present Parallel Task (short ParaTask), a solution to assist the parallelisation of object-oriented applications, with the unique feature of including support for the parallelisation of graphical user interface applications. In the simple, but common, cases concurrency is introduced with a single keyword. ParaTask sets itself apart from the many existing object-oriented parallelisation approaches by integrating different task types into the same model and its careful adherence to object-oriented principles. Due to the wide variety of parallelisation needs, ParaTask provides intuitive support for dependence handling, non-blocking notification and exception handling in an asynchronous environment as well as supporting a flexible task scheduling runtime (currently work-sharing, work-stealing and a combination of the two are supported). The performance is excellent compared to traditional Java parallelisation approaches, shown using a variety of different workloads.     

CFD for incompressible flows at NASA Ames

Over the past 30 years, numerical methods and simulation tools for incompressible flows have been advanced as a subset of the computational fluid dynamics (CFD) discipline. Although incompressible flows are encountered in many areas of engineering, the simulation of compressible flows has driven most of the development of computational algorithms and tools at NASA Ames Research Center. This is due to the stringent requirements for predicting aerodynamic performances of flight vehicles. Conversely, low-speed incompressible flow through or past flow devices did not require the same numerical accuracy. This practice of tolerating relatively low-fidelity solutions in engineering applications has changed, as the design of low-speed flow devices have become more sophisticated, along with more strict efficiency requirements. Accurate and robust CFD tools have become increasingly important in fluid engineering for incompressible and low-speed flow. This paper reviews advances in computational technologies for incompressible flow simulation developed at Ames, and some engineering successes brought about by these advances made during the same period. Additionally, some of the current challenges faced in computing incompressible flows are presented.     

Minimal-cost network flow problems with variable lower bounds on arc flows

The minimal-cost network flow problem with fixed lower and upper bounds on arc flows has been well studied. This paper investigates an important extension, in which some or all arcs have variable lower bounds. In particular, an arc with a variable lower bound is allowed to be either closed (i.e., then having zero flow) or open (i.e., then having flow between the given positive lower bound and an upper bound). This distinctive feature makes the new problem NP-hard, although its formulation becomes more broadly applicable, since there are many cases where a flow distribution channel may be closed if the flow on the arc is not enough to justify its operation. This paper formulates the new model, referred to as MCNF-VLB, as a mixed integer linear programming, and shows its NP-hard complexity. Furthermore, a numerical example is used to illustrate the formulation and its applicability. This paper also shows a comprehensive computational testing on using CPLEX to solve the MCNF-VLB instances of up to medium-to-large size.     

On reduction of computational cost of imitation Monte Carlo algorithms for modeling rarefied gas flows

This article describes Monte Carlo methods and algorithms for the Boltzmann equation for rarefied gases problems in the case of large-scale flow areas. We consider imitation or continuous-time Monte Carlo methods where frequencies of interactions of pairs of particles depend on the difference of the coordinates of particles. The question about reduction of computational costs of algorithms is examined using the specificity of the problem. First, algorithms of an approximated method are constructed, analyzed, and implemented. This method is obtained by using splitting (over groups of particles) of the operator in master equations system. Second, we investigate the fictitious collisions technique, where the upper bound for the number of interacting pairs is specified. The plane Poiseuille flow (in the field of external forces) problem, the heat transfer problem, and the temperature discontinuity propagation problem are numerically solved using the developed algorithms. Asymptotical estimates of the computational costs are confirmed with the data of the computational processes and the comparative properties of the later are fixed. The suggested algorithms of the method with splitting allow parallelization of a certain type.     

A fine grid finite element computation of two-dimensional high Reynolds number flows

A velocity—pressure integrated, mixed interpolation, Galerkin finite element computation of the Navier-Stokes equations using fine grids, is presented. In the method, the velocity variables were interpolated using complete quadratic shape functions: and the pressure was interpolated using linear shape functions defined on a triangular element, which is contained inside the quadratic element for velocity variables. Comprehensive computational results for a cavity flow for Reynolds number of 400 through 10,000 and a laminar backward-facing step flow for Reynolds number of 100 through 900 are presented in this paper. Many high Reynolds number flows involve convection dominated motion as well as diffusion dominated motion (such as the fluid motion inside the subtle pressure driven recirculation zones where the local Reynolds number may become vanishingly small) in the flow domain. The computational results for both of the fluid motions compared favorably with the high accuracy finite difference computational results and/or experimental data available.     

Automatic code generation of overlapped communications in a parallelisation tool

This paper addresses the exploitation of overlapping communication with calculation within parallel FORTRAN 77 codes for computational fluid dynamics (CFD) and computational structured dynamics (CSD). The obvious objective is to overlap interprocessor communication with calculation on each processor in a distributed memory parallel system and so improve the efficiency of the parallel implementation. A general strategy for converting synchronous to overlapped communication is presented together with tools to enable its automatic implementation in FORTRAN 77 codes. This strategy is then implemented within the parallelisation toolkit, CAPTools, to facilitate the automatic generation of parallel code with overlapped communications. The success of these tools are demonstrated on two codes from the NAS-PAR and PERFECT benchmark suites. In each case, the tools produce parallel code with overlapped communications which is as good as that which could be generated manually. The parallel performance of the codes also improve in line with expectation.     

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.     

A computational scheme in generalized coordinates for viscous incompressible flows

This paper presents a computational scheme suitable for analyzing viscous incompressible flows in generalized curvilinear coordinate system. The scheme is based on finite volume algorithm with an overlapping staggered grid. The pseudo-diffusive terms arising from the coordinate transformation are treated as source terms. The system of nonlinear algebraic equations is solved by a semi-implicit procedure based upon line-relaxation and a generalization of Patankar's pressure correction algorithm. Examples of the application of the algorithm to flow in convergent channels, developing flow in a U-bend, and flow past backward facing step, are given. In addition, the case of flow past backward facing step is analyzed in detail, and the computed flowfields are found to be in close agreement with previous experimental and numerical results for expansion ratio (defined as the ratio of step height to channel height) of 0.5. The results are summarized in the form of a correlation relating the primary separation length, Reynolds number and expansion ratio.     

Low Reynolds number turbulent flows around a dynamically shaped airfoil

A computational investigation for flows surrounding a dynamically shaped airfoil, at a chord Reynolds number of 78,800, is conducted along with a parallel experimental effort. A piezo-actuated flap on the upper surface of a fixed airfoil is adopted for active control. The actuation frequency focused on is 500 Hz. The computational framework consists of a multi-block, moving grid technique, the eⁿ-based laminar-turbulent transition model, the two-equation turbulence closure, and a pressure-based flow solver. The moving grid technique, which handles the geometric variations in time, employs the transfinite interpolation scheme with a spring network approach. Comparing the experimental and computational results for pressure and velocity fields, implications of the detailed flap geometry, the flapping amplitude, turbulence modeling, and grid distributions on the flow structure are assessed. The effect of the flap movement on the separation location and vortex dynamics is also investigated.     

Phenomena peculiar to underexpanded flows in supersonic micronozzles

In the present study, the characteristics of supersonic flows in micronozzles are experimentally and computationally investigated for Reynolds numbers ranging from 618 to 5560. In the experiments, the flows are created in a rectangular contoured nozzle whose heights at its throat and exit are 286 and 500 μm, respectively. The number-density distribution along the nozzle centerline is measured using the laser-induced fluorescence technique under an underexpanded condition for each Reynolds number. The experimental results reveal that the underexpanded flow expands along the streamwise direction in a range where the cross-sectional area of the nozzle is constant although the flow in such a range has been believed to be compressed owing to friction. The results also reveal that the unexpected range where the flow expands extends with a decrease in Reynolds number. In the computations, the Navier–Stokes equations are solved numerically. The computational results agree very well with the experimental results; i.e., the computational code used in the present study is validated by the experiments. By using the computational results, the reason for the appearance of the phenomena peculiar to supersonic micronozzle flows is discussed. As a result, it is found that information about the back pressure under which the flow is underexpanded can reach into the inside of a micronozzle. Such a property induces the unexpected phenomena observed in the experiments.     

A fixed-grid model for simulation of a moving body in free surface flows

A two-dimensional computer model is developed to simulate free surface flow interaction with a moving body. The model is based on the cut-cell technique in a fixed-grid system. In this model, a body is approximated by the partial cell treatment (PCT), in which an irregular body is represented by the volumetric fraction of solid in Cartesian cells. The body motion is tracked by Lagrangian method whereas the fluid motion around the body is solved by Eulerian method. The concept of “locally relative stationary (LRS)” is introduced in this study. In the LRS method, a source term is added locally to the conventional continuity equation on body surfaces to take account of body motions, which subsequently affects the computational results of fluid pressure and flow velocity around the body. The LRS method is incorporated into an earlier Reynolds averaged Navier-Stokes (RANS) equations model developed by Lin and Liu [A numerical study of breaking waves in the surf zone. J Fluid Mech 1998;359:239-64]. The new model is capable of simulating generic turbulent free surface flows and their interaction with a moving body or multiple moving bodies. A series of numerical experiments have been conducted to verify the accuracy of the model for simulation of moving body interaction with a free surface flow. These tests include the generation of a solitary wave with the prescribed wave paddle movements, water exit and water impact and entry of a horizontal circular cylinder, fluid sloshing in a horizontally excited tank, and the acceleration/deceleration of an elliptical cylinder near a water surface. Excellent agreements are obtained when numerical results are compared to available analytical, experimental, and other numerical results. The model is a simple-to-implement computational tool for simulating a moving body in turbulent free surface flows.