CFD Problems Research Articles

A 2D software system for expedite analysis of CFD problems in complex geometries

ABSTRACTEasyCFD_G, a 2D software tool for fluid dynamics and heat transfer applications, is presented. The underlying physical and numerical principles are described, including mesh generation. The software is based on quadrilateral structured and unstructured meshes, rendering it with great versatility in geometrical terms. Amenable problems include multi‐domain simulations with fluid and solid regions, thermal effects and mixing of different fluids, in stationary or turbulent regime. For illustration, a few example problems are presented, covering different physical situations, including comparison with benchmark data. Due to its versatility, fast learning curve and easy and intuitive utilization, this software tool represents a great value for educational purposes. © 2015 Wiley Periodicals, Inc. Comput. Appl. Eng. Educ. 24:27–38, 2016; View this article online at wileyonlinelibrary.com/journal/cae; DOI 10.1002/cae.21668

Asynchronous partial update of the Restricted Additive Schwarz preconditioner to solve nonlinear CFD problems

This paper presents a method that speeds up the solution of unsteady nonlinear problems. When a Newton–Krylov method is used, the most time-consuming part of the numerical simulation is the solution of the successive linear systems. Generally, there are only slight changes between two consecutive Jacobian matrices. Thus, in order to save computations, it is possible to use the same preconditioning matrix for a few successive linear systems, but the convergence of the Krylov method is slowed down. In the case of a preconditioner based on domain decomposition, one can update only the parts of the preconditioner associated to certain subdomains, keeping the other ones constant. In order to achieve an efficient parallel implementation, we propose to add processes dedicated to the asynchronous update of some parts of the preconditioner. Numerical results are provided for a reaction–diffusion problem and for a model problem based on the lid-driven cavity. They show that this addition of processes can speed up the computation and improve the robustness.

Collaborating CPU and GPU for large-scale high-order CFD simulations with complex grids on the TianHe-1A supercomputer

Programming and optimizing complex, real-world CFD codes on current many-core accelerated HPC systems is very challenging, especially when collaborating CPUs and accelerators to fully tap the potential of heterogeneous systems. In this paper, with a tri-level hybrid and heterogeneous programming model using MPI + OpenMP + CUDA, we port and optimize our high-order multi-block structured CFD software HOSTA on the GPU-accelerated TianHe-1A supercomputer. HOSTA adopts two self-developed high-order compact definite difference schemes WCNS and HDCS that can simulate flows with complex geometries. We present a dual-level parallelization scheme for efficient multi-block computation on GPUs and perform particular kernel optimizations for high-order CFD schemes. The GPU-only approach achieves a speedup of about 1.3 when comparing one Tesla M2050 GPU with two Xeon X5670 CPUs. To achieve a greater speedup, we collaborate CPU and GPU for HOSTA instead of using a naive GPU-only approach. We present a novel scheme to balance the loads between the store-poor GPU and the store-rich CPU. Taking CPU and GPU load balance into account, we improve the maximum simulation problem size per TianHe-1A node for HOSTA by 2.3×, meanwhile the collaborative approach can improve the performance by around 45% compared to the GPU-only approach. Further, to scale HOSTA on TianHe-1A, we propose a gather/scatter optimization to minimize PCI-e data transfer times for ghost and singularity data of 3D grid blocks, and overlap the collaborative computation and communication as far as possible using some advanced CUDA and MPI features. Scalability tests show that HOSTA can achieve a parallel efficiency of above 60% on 1024 TianHe-1A nodes. With our method, we have successfully simulated an EET high-lift airfoil configuration containing 800M cells and China's large civil airplane configuration containing 150M cells. To our best knowledge, those are the largest-scale CPU–GPU collaborative simulations that solve realistic CFD problems with both complex configurations and high-order schemes.

Computational steering of CFD simulations using a grid computing environment

Simulation of complex phenomena is usually a long computing process and it has been traditionally performed in batch mode on large high performance computing (HPC) systems. However, advances in computer processing and networking capabilities can now be used to monitor and alter simulation parameters whilst it is running. This process is called computational steering. By combining this capability with advanced communication tools, it is now possible for a group of scientists located across the world to work collaboratively while visualising on-going simulations. This raise the possibility that researches can now share their experience and promote new ideas and solutions by exploring collaboratively the solution space of a complex simulation. In this paper, a collaborative computational steering environment specialised to solve CFD problems is presented.

ON A RIEMANN SOLVER FOR THREE-DIMENSIONAL RANS

The exact analytical expression for a system of both eigenvalues and right/left eigenvectors of a Jacobian matrix for the inviscid part of a two-equations differential closure 3D RANS operator split along a curvilinear coordinate is derived. Two CFD problems are considered, namely, supersonic flow over a flat plate and supersonic flow over a compression corner with separation. It is shown that application of the exact system of eigenvalues and eigenvectors to realization of the Roe approach for approximate solution of Riemann problem results in increase in convergence rate, better stability, and higher accuracy of a steady-state solution in comparison with those in the case of an approximate system.

Model Adaptation Enriched with an Anisotropic Mesh Spacing for Nonlinear Equations: Application to Environmental and CFD Problems

Goal of this paper is to suitably combine a model with an anisotropic mesh adaptation for the numerical simulation of nonlinear advection-diffusion-reaction sys- tems and incompressible flows in ecological and environmental applications. Using the reduced-basis method terminology, the proposed approach leads to a noticeable compu- tational saving of the online phase with respect to the resolution of the reference model on nonadapted grids. The search of a suitable adapted model/mesh pair is to be meant, instead, in an offline fashion. AMS subject classifications: 65N15, 65N50, 65J15, 35J60

Model Adaptation Enriched with an Anisotropic Mesh Spacing for Nonlinear Equations: Application to Environmental and CFD Problems

Model Adaptation Enriched with an Anisotropic Mesh Spacing for Nonlinear Equations: Application to Environmental and CFD Problems

Asynchronous Partial Update of Domain Decomposition Preconditioners to Solve Nonlinear CFD Problems

In this paper, we propose a numerical strategy to speed up the implicit solution of unsteady nonlinear problems arising from fluid dynamics. This strategy consists in a partial update of a domain decomposition preconditioner used in the Newton-Krylov method that solves the nonlinear problem of each time step. The underlying principle of the proposed method is that, usually, there is only slight changes between two consecutive Jacobian matrices. Consequently, it is possible to use the same preconditioner for few Newton iterations, or, even better, to partially update it. We propose to add some processes dedicated to the asynchronous update of the subdomains parts of the preconditioner. Numerical results for the lid-driven cavity are provided, they show that this addition of processes can speed up the computation in a super linear way.

Noisy 한 CFD 결과에 대한 구속조건을 고려한 EGO 방법 연구

Efficient Global Optimization (EGO) method is a global optimization technique which can select the next sample point automatically by infill sampling criteria (ISC) and search for the global minimum with less samples than what the conventional global optimization method needs. ISC function consists of the predictor and mean square error (MSE) provided from the kriging model which is a stochastic metamodel. Also the constrained EGO method can minimize the objective function dealing with the constraints under EGO concept. In this study the constrained EGO method applied to the RAE2822 airfoil shape design formulated with the constraint. But the noisy CFD data caused the kriging model to fail to depict the true function. The distorted kriging model would make the EGO deviate from the correct search. This distortion of kriging model can be handled with the interpolation(p=free) kriging model. With the interpolation(p=free) kriging model, however, the search of EGO solution was stalled in the narrow feasible region without the chance to update the objective and constraint functions. Then the accuracy of EGO solution was not good enough. So the three-step search method was proposed to obtain the accurate global minimum as well as prevent from the distortion of kriging model for the noisy constrained CFD problem.

Determining the parametric effectiveness of a CAD model

The motivation for this paper is to present an approach for rating the quality of the parameters in a computer-aided design model for use as optimization variables. Parametric Effectiveness is computed as the ratio of change in performance achieved by perturbing the parameters in the optimum way, to the change in performance that would be achieved by allowing the boundary of the model to move without the constraint on shape change enforced by the CAD parameterization. The approach is applied in this paper to optimization based on adjoint shape sensitivity analyses. The derivation of parametric effectiveness is presented for optimization both with and without the constraint of constant volume. In both cases, the movement of the boundary is normalized with respect to a small root mean squared movement of the boundary. The approach can be used to select an initial search direction in parameter space, or to select sets of model parameters which have the greatest ability to improve model performance. The approach is applied to a number of example 2D and 3D FEA and CFD problems.

A GPU Accelerated Red-Black SOR Algorithm for Computational Fluid Dynamics Problems

GPUs are high performance co-processors of CPU for scientific computing including CFD. We present an optimistic shared memory allocation strategy to solve 2D CFD problems using Red-Black SOR method on GPU with CUDA (Compute Unified Device Architecture). Lid-driven results are compared with the benchmark data. The speed up ratio of same problem size by using NVDIA GTX480 and Intel Core-Dual 3.0GHz processor is discussed, the performance of GPU is 120 times faster than the sequential code on CPU with the problem size of 756756. Based on this work, we conclude that using the memory hierarchy properly has a key role in improving the computational performance of GPU.

Coupled heat transfer modes for calculation of cooling load through hollow concrete building walls

A CFD model was developed to study thermal performance of hollow cement wall constructions of buildings under hot summer conditions. The approach employed couples conjugate, laminar natural convective flow of a viscous fluid in hollow building blocks with long-wave radiation between the cavity sides. Realistic boundary conditions were employed at the outdoor and indoor surfaces of the wall. A state-of-art building energy simulation program, ESP-r, was used to determine the outdoor thermal environment that included solar radiation, equivalent temperature of the surroundings and convective heat transfer coefficient. The CFD problem is put into dimensionless formulation and solved numerically by means of the control-volume approach. The study yielded comprehensive, detailed quantitative estimates of temperature, stream function and heat flux throughout the wall domain. A detailed parametric study showed that using a wider cavity within a building block does not necessarily reduce heat flux through the block. Radiation heat transfer between cavity sides may account for a significant fraction of heat flux through the block and neglecting its effect can lead to errors that could be as large as 46%. The geometry of the hollow blocks was demonstrated to affect the heat flux by as much as 30%.

A study of gridless method with dynamic clouds of points for solving unsteady CFD problems in aerodynamics

AbstractWhen solving unsteady computational fluid dynamics problems in aerodynamics with a gridless method, a cloud of points is usually required to be regenerated due to its accommodation to moving boundaries. In order to handle this problem conveniently, a fast dynamic cloud method based on Delaunay graph mapping strategy is proposed in this paper. A dynamic cloud method makes use of algebraic mapping principles and therefore points can be accurately redistributed in the flow field without any iteration. In this way, the structure of the gridless clouds is not necessarily changed so that the clouds regeneration can be avoided successfully. The spatial derivatives of the mathematical modeling of the flow are directly determined by using weighted least‐squares method in each cloud of points, and then numerical fluxes can be obtained. A dual time‐stepping method is further implemented to advance the two‐dimensional Euler equations in arbitrary Lagarangian–Eulerian formulation in time. Finally, unsteady transonic flows over two different oscillating airfoils are simulated with the above method and results obtained are in good agreement with the experimental data. Copyright © 2009 John Wiley & Sons, Ltd.

Active aeroelastic control over a four control surface wing model

This paper describes the procedure implemented to design, develop and test an aeroelastic control system installed on a forward swept wing of the aeroelastic demonstrator X-DIA. A control method directly based on Nissim aerodynamic energy concept has been chosen. Two different modeling techniques have been adopted for the calculation of generalized aerodynamic forces, such as doublet lattice method and computational fluid dynamics and the obtained results are finally compared. The latter approach, applied to better estimate the control surfaces effectiveness, requires the capability to correctly model the control surface rotation and the grid deformation, usually addressed as non-trivial problems in CFD based aeroelastic analysis. A genetic algorithm optimization technique has been adopted to state and refine all the control gains.

Unconditionally convergent nonlinear solver for hyperbolic conservation laws with S-shaped flux functions

This paper addresses the convergence properties of implicit numerical solution algorithms for nonlinear hyperbolic transport problems. It is shown that the Newton–Raphson (NR) method converges for any time step size, if the flux function is convex, concave, or linear, which is, in general, the case for CFD problems. In some problems, e.g., multiphase flow in porous media, the nonlinear flux function is S-shaped (not uniformly convex or concave); as a result, a standard NR iteration can diverge for large time steps, even if an implicit discretization scheme is used to solve the nonlinear system of equations. In practice, when such convergence difficulties are encountered, the current time step is cut, previous iterations are discarded, a smaller time step size is tried, and the NR process is repeated. The criteria for time step cutting and selection are usually based on heuristics that limit the allowable change in the solution over a time step and/or NR iteration. Here, we propose a simple modification to the NR iteration scheme for conservation laws with S-shaped flux functions that converges for any time step size. The new scheme allows one to choose the time step size based on accuracy consideration only without worrying about the convergence behavior of the nonlinear solver. The proposed method can be implemented in an existing simulator, e.g., for CO 2 sequestration or reservoir flow modeling, quite easily. The numerical analysis is confirmed with simulation studies using various test cases of nonlinear multiphase transport in porous media. The analysis and numerical experiments demonstrate that the modified scheme allows for the use of arbitrarily large time steps for this class of problems.

HEGDE'S INTERFACE NUMERICAL TECHNIQUE FOR RESOLVING QUASI-ONE-DIMENSIONAL NOZZLE FLOWS

Faster convergence, better accuracy and improved stability of the solutions to fluid flow and heat transfer problems in CFD reduce the computational cost and time. The numerical solutions to partial differential equations governing the physical flow and heat phenomena, using computer software and hardware, have been obtained by various techniques which have been refined over the years. The numerical techniques have obtained the base in finite difference method (FDM) approximations derived from Taylor series expansion. Because of linearization, FDM approximations have truncation error creeping into the values of the partial derivatives, which projects an unrealistic picture of the final outcome of results in terms of accuracy, convergence and stability. As the prime objective of this paper, the minimization of truncation error is attempted with the aid of the interface theory (briefly described in the appendix) used as a computational treatment tool. In simple terms, the interface theory provides an optimal solution to all variables in a linear indeterminate system with redundancy in unknowns. The effort has converged in the form of Hegde's interface numerical technique (HINT), which is demonstrated on a quasi-one-dimensional nozzle flow, the physical behavior of which is described by the Navier–Stokes equation considered specific to the said case. HINT could successfully match the results of MacCormack's predictor–corrector method as far as the accuracy is concerned, but with less computational effort and higher productivity. To the knowledge of the authors, HINT may be considered both original and different for its kind in the vast developments in CFD.

A hyperbolic model for convection-diffusion transport problems in CFD: Numerical analysis and applications

In this paper we present a numerical study of the hyperbolic model for convection-diffusion transport problems that has been recently proposed by the authors [16]. This model avoids the infinite speed paradox, inherent to the standard parabolic model and introduces a new parameter τ called relaxation time. This parameter plays the role of an “inertia” for the movement of the pollutant. The analysis presented herein is twofold: first, we perform an accurate study of the 1D steady-state equations and its numerical solution. We compare the solution of the hyperbolic model with that of the parabolic model and we analyze the influence of the relaxation time on the solution. On the other hand, we explore the possibilities of the proposed model for real-world applications. With this aim we solve an example concerning the evolution of a pollutant being spilled in the harbor of A Coruña (northwest of Spain, EU).

An improved parallel hybrid bi-conjugate gradient method suitable for distributed parallel computing

An improved parallel hybrid bi-conjugate gradient method (IBiCGSTAB(2) method, in brief) for solving large sparse linear systems with nonsymmetric coefficient matrices is proposed for distributed parallel environments. The method reduces five global synchronization points to two by reconstructing the BiCGSTAB(2) method in [G.L.G. Sleijpen, H.A. van der Vorst, Hybrid bi-conjugate gradient methods for CFD problems, in: M. Hafez, K. Oshima (Eds.), Computational Fluid Dynamics Review 1995, John Wiley & Sons Ltd, Chichester, 1995, pp. 457–476] and the communication time required for the inner product can be efficiently overlapped with useful computation. The cost is only slightly increased computation time, which can be ignored, compared with the reduction of communication time. Performance and isoefficiency analysis shows that the IBiCGSTAB(2) method has better parallelism and scalability than the BiCGSTAB(2) method. Numerical experiments show that the scalability can be improved by a factor greater than 2.5 and the improvement in parallel communication performance approaches 60%.

Inexact Newton Dogleg Methods

The dogleg method is a classical trust-region technique for globalizing Newton's method. While it is widely used in optimization, including large-scale optimization via truncated-Newton approaches, its implementation in general inexact Newton methods for systems of nonlinear equations can be problematic. In this paper, we first outline a very general dogleg method suitable for the general inexact Newton context and provide a global convergence analysis for it. We then discuss certain issues that may arise with the standard dogleg implementational strategy and propose modified strategies that address them. Newton-Krylov methods have provided important motivation for this work, and we conclude with a report on numerical experiments involving a Newton-GMRES dogleg method applied to benchmark CFD problems.

Solution of industrial CFD problems with structured Boltzmann approach

AbstractA new algorithm and acorresponding software package are developed that contain a fast tensor algorithm for the deterministic solution of the Boltzmann equation. The domain space discretisation performed with the Delaunay grid and the velocity space discretisation is performed with the tensor grid, and benefits with multilinear decomposition. This algorithm is also implemented for GPGPU processors, which allows to reach very high computational performance. The memory and complexity requirements are comparable with most Navier‐Stockes solvers, however we solve the Boltzmann equation with chemical reactions. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)