Application of Graphics Processor Unit Computing Resources to Solution of Incompressible Fluid Dynamics Problems

Many problems in Computational Electromagnetics (CEM) and Computational Fluid Dynamics (CFD) require millions of grid cells to properly represent the physics. Advances in parallel computing, both in hardware and software, make it feasible to solve such large scale simulations in a timely manner. The objective of this paper is to describe some of the recent work at Rockwell in performing parallel computing for providing quick-turnaround solutions to problems in CFD, CEM and other computational disciplines.

In this paper we apply a reduced basis framework for the computation of flow bifurcation (and stability) problems in fluid dynamics. The proposed method aims at reducing the complexity and the computational time required for the construction of bifurcation and stability diagrams. The method is quite general since it can in principle be specialized to a wide class of nonlinear problems, but in this work we focus on an application in incompressible fluid dynamics at low Reynolds numbers. The validation of the reduced order model with the full order computation for a benchmark cavity flow problem is promising.

In the past several years, domain decomposition has been a very popular topic, partly because of the poten tial of parallelization. Although numerous theories and algorithms have been developed for model elliptic problems, they are only recently starting to be tested on realistic applications. This paper investigates the applica tion of some of these methods to two model problems in computational fluid dynamics: two-dimensional con vection-diffusion problems and the incompressible driven cavity flow problem. Our approach is the con struction and analysis of efficient preconditioners for the interface operator to be used in the iterative solution of the interface solution. For the convection-diffusion problems, we discuss the effect of the convection term and its discretization on the performance of some of the preconditioners. For the driven cavity problem, we dis cuss the effectiveness of a class of boundary probe preconditioners.

The correct modeling for processes involving convection, without introducing excessive artificial damping while retaining high accuracy, stability, boundedness and simplicity of implementation continues being nowadays a challenging task for CFD practitioners. The objective of this study is to present and evaluate the performance of two new upwinding schemes, namely SDPUS-C1 and EPUS, for nonlinear convection term discretization. Both SDPUS-C1 and EPUS schemes satisfy the TVD principle of Harten and are based on the NVD formulation of Leonard. Firstly, a description of the schemes is presented and then the numerical results are provided for one- and two-dimensional hyperbolic conservation laws. Finally, as an application, the SDPUS-C1 and EPUS schemes are employed for the simulation of two-dimensional incompressible fluid flows involving moving free surfaces. The numerical experiments show that the proposed upwinding schemes perform very well.

Multiphase flow simulations are essential methods for providing information such as the evolution of phase fraction (gas, liquid and solid), velocities, pressure, temperature and flow regimes at every time during a process. Dynamic flow simulations also help reservoir, drilling, and production engineers to develop a proper well design. DamBreak problem is one of the most well-known problems in computational fluid dynamics (CFD); it is a dynamic hydraulic phenomena and the numerical simulation requires sophisticated mathematical modeling. OpenFOAM, is used to run CFD simulations in this thesis.;One of the main issues in CFD is that the simulations are time-consuming. In this work, will use artificial intelligence (AI) to predict the behavior of the system at each time-step of the process at a lower run time. DamBreak problem is defined base on a two-dimensional rectangular tank with a barrier at the bottom, the liquid column (water in this study) at the left side of the tank behind the wall. As soon as the wall collapse, the water will pour down, resulting in complicated fluid dynamics. The main data-set, generated by OpenFOAM flow simulations, is used for building the smart proxy model (SPM), using the network toolbox in MATLAB. Neural network (NN) is applied with feed-forward back propagation method and the training algorithm is Levenberg Marquardt.;Results indicate that the smart proxy can run 3 seconds of the DamBreak process, which takes 8 hours of computational time with 4 processors when is done by using OpenFOAM, takes less than 2 minutes using the developed SPM on one processor. SPM is also capable of predicting the CFD results in non-cascading condition and up to around 40 time-steps in cascading condition with acceptable error (less than %10).

Numerical algorithms in computational fluid dynamics on vector computers

Computational Fluid Dynamics (CFD) is widely used by polymer processing industries in order to evaluate polymeric fluid flows. A successful computational code must provide reliable predictions (modeling) in a fast and efficient way (simulation). In this work, a new approach to solve the governing equations of viscoelastic fluid flows is proposed. It is based on the finite-volume method with collocated arrangement of the variables, using high-order approximations for the linear and nonlinear average fluxes in the interfaces and for the nonlinear terms obtained from the discretization of the constitutive equations. The approximations are coupled to the Weighted Essentially Non-Oscillatory (WENO) scheme to avoid oscillations in the solution. The Oldroyd-B model is used to describe the rheological behavior of the viscoelastic fluid. The average values of the variables in the volumes are used during the resolution, and the point values are recovered in the post-processing step by deconvolution of the average values. The nonlinear system, resulting from the discretization of the equations, is solved simultaneously using a Newton-like method. The obtained solutions are oscillation-free and accurate, demonstrated by the application on a classic problem in computational fluid dynamics, the slip-stick flow.

Wind profile prediction at different scales plays a crucial role for efficient operation of wind turbines and wind power prediction. This problem can be approached in two different ways: one is based on statistical signal processing techniques and both linear and nonlinear models can be employed either separately or combined together for profile prediction; on the other hand, wind/atmospheric flow analysis is a classical problem in computational fluid dynamics (CFD) in applied mathematics, which employs various numerical methods and algorithms, although it is an extremely time-consuming process with high computational complexity. In this work, a new method is proposed based on synergy's between the signal processing approach and the CFD approach, by alternating the operations of a quaternion-valued least mean square (QLMS) algorithm and the large eddy simulation (LES) in CFD. As demonstrated by simulation results, the proposed method has a much lower computational complexity while maintaining a comparable prediction result.

SUMMARYThe solution of problems in computational fluid dynamics (CFD) represents a classical field for the application of advanced numerical methods. Many different approaches were developed over the years to address CFD applications. Good examples are finite volumes, finite differences (FD), and finite elements (FE) but also newer approaches such as the lattice‐Boltzmann (LB), smooth particle hydrodynamics or the particle finite element method. FD and LB methods on regular grids are known to be superior in terms of raw computing speed, but using such regular discretization represents an important limitation in dealing with complex geometries. Here, we concentrate on unstructured approaches which are less common in the GPU world. We employ a nonstandard FE approach which leverages an optimized edge‐based data structure allowing a highly parallel implementation. Such technique is applied to the ‘convection‐diffusion’ problem, which is often considered as a first step towards CFD because of similarities to the nonconservative form of the Navier–Stokes equations. In this regard, an existing highly optimized parallel OpenMP solver is ported to graphics hardware based on the OpenCL platform. The optimizations performed are discussed in detail. A number of benchmarks prove that the GPU‐accelerated OpenCL code consistently outperforms the OpenMP version. Copyright © 2011 John Wiley & Sons, Ltd.

The numerical simulation of incompressible viscous flows using primitive variable formulation requires that the pressure be obtained by solving the pressure Poisson equation (PPE). It is mentioned in the literature on incompressible flows [1,2] that when all the pressure boundary conditions are of Neumann type, then the pressure compatibility condition (PCC) has to be satisfied for guaranteeing the existence of solution. The main aim of this paper is to show that the PCC is not an important issue as has been claimed in the literature [1–3]. On the other hand, it will be shown that the crucial issue, in numerical simulation of incompressible viscous flows, is to ensure solenoidality of the velocity field accurately. We will further show that the accuracy of solenoidality depends on the choice of pressure boundary conditions. The demonstration is based on the computation for 2-D lid-driven cavity problem for Re=100 on 1292 uniform grid.

Casting computational fluid mechanics into a convex quadratic optimization framework

The study of hydrodynamics and thermal characteristics inside a lid‐driven cavity has been one of the most captivating problems in computational fluid dynamics. In this numerical work, the mixed convection phenomenon inside a two‐dimensional, tall lid‐driven cavity with top and bottom lids moving in opposite directions, +x and –x, respectively, has been explored for non‐Newtonian power‐law fluids. The cavity contains a uniformly heated equilateral triangular obstacle at its geometric center. Numerical experimentation is performed for a range of flow governing parameters, such as aspect ratio (0.25, 0.5, and 0.75), Prandtl number (1, 50, and 100) Richardson number (0.1, 1, and 10), power‐law index (0.6–1.4) and Grashof number of 104. The physical perceptions of the cavity are explained by using streamline and isotherm contours. The fluid movement is limited adjacent to the moving wall concerning the Richardson number at the lower Prandtl number. With a rise in the aspect ratio of the cavity, the flow‐pattern becomes more dispersed inside the cavity. Heat transfer enhancement is observed at a lower aspect ratio equal to 0.25.

Lattice-Boltzmann methods are being increasingly used to solve problems in computational fluid dynamics. The combination of robustness and simplicity has made it the method of choice for problems involving fluid flow through geometrically complex structures. Progress in several areas is summarized in a recent review article [1]. In this paper I will focus on applications of the lattice-Boltzmann method to simulations of particle-fluid suspensions. Since the basic principles of the method have already been described [2, 3], the focus of this article will be a review of recent developments and a discussion of some of the fine points that arise in practical applications of the method. In particular I will contrast the accuracy and complexity of different solid-fluid boundary conditions, discuss the application of an external pressure gradient, and describe additional complications arising from particle motion.

Grid Adaption Based on Modified Anisotropic Diffusion Equations Formulated in the Parametric Domain

Two problems in computational fluid dynamics are studied in the context of transonic small-disturbance theory - namely, (1) how to speed up the convergence for currently available iterative procedures, and (2) how a shock-fitting method may be adapted to existing relaxation procedures with minimal alterations in computer programming and storage requirements. The paper contributes to a clarification of error analyses for sequence transformations based on the power method (including also the nonlinear transforms of Aitken, Shanks, and Wilkinson), and to developing a cyclic iterative procedure applying the transformations. Examples testing the procedure for a model Dirichlet problem and for a transonic airfoil problem show that savings in computer time by a factor of three to five are generally possible, depending on accuracy requirements and the particular iterative procedure used.-