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AIAA Aviation Forum

作者： Piperni, Pat Talukder, Maahi M. Clarkson Univ Dept Mech & Aeronaut Engn Potsdam NY 13699 USA

ISBN: (数字)9781624105982

ISBN: (纸本)9781624105982

Elliptic grid generation equations based on the Laplacian operator have the well-known property of clustering the mesh near convex boundaries and declustering it near concave boundaries. In prior work, a new differential operator was derived and presented to address this issue. This new operator retains the strong smoothing properties of the Laplacian without the latter's adverse curvature effects. In the work presented here, a number of solvers and preconditioners are evaluated to accelerate the convergence of the numerical solution of this newoperator. The results of this evaluation are presented herein, along with the methodology to linearize the equations and set up the numerical solution using finite differences. The efficiency of the solution process is demonstrated with applications to two-dimensional airfoil meshes.

关键词： Two Dimensional Airfoil Poisson Boltzmann Equation Poisson's Equation Iterative Solution Finite Difference Approximation Conjugate Gradient Method Mesh Generation Finite Element Method multigrid algorithm Aspect Ratio

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Pressure Bifurcation Phenomenon on Supersonic Blowing Trailing Edges

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AIAA JOURNAL 2019年第1期57卷 153-164页

作者： Martinez-Cava, Alejandro Wang, Yinzhu de Vicente, Javier Valero, Eusebio Tech Univ Madrid Sch Aeronaut & Space Engn Plaza Cardenal Cisneros 3 E-28040 Madrid Spain Tech Univ Madrid Sch Aeronaut & Space Engn Appl Math Plaza Cardenal Cisneros 3 E-28040 Madrid Spain

Turbine blades operating in transonic-supersonic regime develop a complex shock wave system at the trailing edge: a phenomenon that leads to unfavorable pressure perturbations downstream and can interact with other turbine stages. Understanding the fluid behavior of the area adjacent to the trailing edge is essential in order to determine the parameters that have influence on these pressure fluctuations. Colder flow, bled from the high-pressure compressor, is often purged at the trailing edge to cool the thin blade edges, affecting the flow behavior and modulating the intensity and angle of the shock waves system. However, this purge flow can sometimes generate nonsymmetrical configurations due to a pressure difference that is provoked by the injected flow. In this work, a combination of Reynolds-averaged Navier-Stokes simulations and a global stability analysis is employed to explain the physical reasons of this flow bifurcation. By analyzing the features that naturally appear in the flow and become dominant for some value of the parameters involved in the problem, an antisymmetrical global mode, which is related to the sudden geometrical expansion of the trailing-edge slot, is identified as the main mechanism that forces the changes in the flow topology.

关键词： Trailing Edges Shock Waves Supersonic Flow over a Flat Plate Turbine Blades Incompressible Flow Shear Layers Prandtl Meyer Expansion Fan Strouhal Number Turbulence Models multigrid algorithm

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A Study of p-multigrid Approach for the High Order FR/CPR Method

A Study of p-multigrid Approach for the High Order FR/CPR Me...

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AIAA Aviation Forum and Exposition

作者： Jourdan, Eduardo Wang, Z. J. Univ Kansas Dept Aerosp Engn 2120 Learned Hall Lawrence KS 66045 USA

ISBN: (数字)9781624105890

ISBN: (纸本)9781624105890

This paper addresses the use of the p-multigrid acceleration technique in high-order simulations. Different choices of smoothers for lower level discretization solvers are investigated, such as the 3rd-order explicit Runge-Kutta scheme, the non-linear block LU-SGS solver and the matrix-free GMRES method. Moreover, different choices for the coarsest level of discretization in the p-multigrid method are evaluated. The FR/CPR method is used as the spatial discretization scheme and the flow of interest is modeled by the Navier-Stokes equations. Test cases include two-dimensional (2-D) and three-dimensional (3-D) flow problems, covering viscous and inviscid simulations. Dual time stepping is used in order to perform unsteady simulations and the performance is measured in terms of CPU time, cycles and memory use. The results indicated a comparable total CPU cost between the p-multigrid algorithm and the LU-SGS implicit solver for an unsteady 3-D p4 simulation, whereas the memory footprint of the LU-SGS method is eight times higher.

关键词： multigrid Methods multigrid algorithm Navier Stokes Equations Turbulent Flow NACA 0012 Computational Fluid Dynamics Freestream Mach Number Finite Element Method No Slip Condition Conservation Equations

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Progress in CFD Discretizations algorithms and Solvers for Aerodynamic Flows

Progress in CFD Discretizations Algorithms and Solvers for A...

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AIAA Aviation Forum and Exposition

作者： Mavriplis, Dimitri J. Univ Wyoming Dept Mech Engn Laramie WY 82071 USA

ISBN: (数字)9781624105890

ISBN: (纸本)9781624105890

An overview of developments in computational fluid dynamic discretizations and solution techniques for aerodynamic applications over the past five to six year time frame is given in this paper. We begin with a survey of community efforts that have contributed to advancing the state-of-the-art of computational aerodynamics. Subsequently, an overview of developments in Reynolds-averaged Navier-Stokes (RANS) methods is given, including the use of higher-order discretizations. This is followed by a look at recent developments in scale-resolving methods from an algorithmic point of view. The paper concludes with prospects for further advances towards long term milestones and Grand Challenge projects as outlined in the CFD2030 report.

关键词： Incompressible Flow Reynolds Averaged Navier Stokes Aerodynamic Configurations Adaptive Mesh Refinement Detached Eddy Simulation High Performance Computing FaSTAR multigrid algorithm Finite Volume Method Lattice Boltzmann Approach

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Optimal multi-block mesh generation for CFD 55

Optimal multi-block mesh generation for CFD

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55th AIAA Aerospace Sciences Meeting

作者： Ali, Zaib Caleb Dhanasekaran, P. Tucker, Paul G. Watson, Rob Shahpar, Shahrokh Department of Engineering University of Cambridge CambridgeCB2 1PX United Kingdom Aerothermal Design System CFD Methods DSE Rolls-Royce plc. DerbyDE24 8BJ United Kingdom

ISBN: (数字)9781624104473

ISBN: (纸本)9781624104473

An assessment of various automatic block topology generation techniques for creating structured meshes has been performed. The objective is to find out optimal blocking methods for generating meshes suitable for flow simulations. The comparison has been carried out using an adjoint based error analysis of the meshes generated by these block topologies. Different objective functions and numerical schemes have been used for this assessment. It is found that, in general, the medial axis based approaches provide optimal blocking and yields better accuracy in computing the functional of interest. This is because the medial axis based methods produce meshes which have better flow alignment specially in case of internal flows. The adjoint based error indicator has also been used to implicitly adapt the block boundaries in the regions of large error. © 2017 by Rolls-Royce plc, UK, Zaib Ali, P. Caleb Chanasekaran, Paul G. Tucker, Rob Watson, Shahrokh Shahpar. Published by the American Institute of Aeronautics and Astronautics, Inc.

关键词： Mesh Generation Internal Flows Computing Mach Number multigrid algorithm Pressure Coefficient Turbomachinery Flow Equations Shear Layers Advection

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Scalable solution strategies for stabilized finite-element flow solvers on unstructured meshes 55

Scalable solution strategies for stabilized finite-element f...

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55th AIAA Aerospace Sciences Meeting

作者： Ahrabi, Behzad R. Mavriplis, Dimitri J. Department of Mechanical Engineering University of Wyoming LaramieWY82071 United States

ISBN: (数字)9781624104473

ISBN: (纸本)9781624104473

The objective of the present study is to investigate and develop robust, efficient, and scalable multilevel solution strategies and preconditioning techniques for stabilized finite-element flow solvers. The proposed solution strategy is essentially a p-multigrid approach in which the solution on the mesh with lowest polynomial degree (p=1) is solved using a preconditioned Newton-Krylov method. Seeking robustness, the Newton-Krylov methods are commonly preconditioned using incomplete factorization methods such as ILU(k). However, it is well known that these methods are not scalable. To overcome this problem, we have developed an implicit line preconditioner which can be properly distrusted among processing elements, without affecting the convergence behavior of the linear system and the non-linear path. The lines are extracted from a stiffness matrix based on strong connections. To improve the robustness of the implicit-line relaxation, a dual CFL strategy, with a lower CFL number in the preconditioner matrix, has been developed. In this study, we also employ an algebraic multigrid (AMG) preconditioner and augment it with the dual-CFL strategy. To reach high-order discretizations, a set of hierarchical basis functions are employed and a non-linear p-multigrid approach is developed. In order to test the performance of the newly developed algorithms, a new flow solver for two and three dimensional mixed-element unstructured meshes has been developed in which the Reynolds averaged Navier-Stokes (RANS) equations and negative Spalart-Almaras (SA) turbulence model are discretized, in a coupled form, using the Streamline Upwind Petrov-Galerkin (SUPG) scheme. Several two- and three-dimensional numerical examples including turbulent flows over the 30P30N three element airfoil and a wing-body-tail configuration from the 4th AIAA Drag Prediction Workshop are presented in which the performance of the implicit line relaxation and algebraic multigrid preconditioners are compared w

关键词： Compressible Flow Reynolds Averaged Navier Stokes Galerkin Finite Element Method Airfoil Turbulence Models multigrid Methods Aerodynamic Simulation multigrid algorithm Lift Coefficient High Performance Computing

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MrDIRECT: a multilevel robust DIRECT algorithm for global optimization problems

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JOURNAL OF GLOBAL OPTIMIZATION 2015年第2期62卷 205-227页

作者： Liu, Qunfeng Zeng, Jinping Yang, Gang Dongguan Univ Technol Sch Comp Dongguan 523808 Peoples R China

Although DIRECT global optimization algorithm quickly gets close to the basin of the optimum, it often takes much longer to refine the solution to a high degree of accuracy. This behavior of DIRECT is similar to the "smooth mode phenomenon" encountered when solving linear systems discretized from partial differential equation (PDE). In the case of PDE, this smooth mode phenomenon can be eliminated efficiently by the multigrid algorithm in which the PDE solver is applied at different levels of discretization. In this paper we adapt the multigrid approach to a robust version of DIRECT algorithm, obtaining a "multilevel" robust DIRECT (MrDIRECT) algorithm. Although additional parameters are needed, our numerical results show that MrDIRECT is insensitive to the parameters, and the parameters setting proposed in this paper performs very well on the tested sets of benchmark problems, in terms of the speed with which the global optimum is found to a high degree of accuracy.

关键词： Global optimization Multilevel algorithm multigrid algorithm DIRECT algorithm Multilevel partition

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Global optimization by multilevel partition

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JOURNAL OF GLOBAL OPTIMIZATION 2015年第1期61卷 47-69页

作者： Liu, Qunfeng Zeng, Jinping Dongguan Univ Technol Sch Comp Dongguan 523808 Peoples R China

Partition-based algorithms, such as the DIRECT algorithm, are popular algorithms for solving global optimization problems. However, these algorithms often have an eventually inefficient behavior due to much more costs requirement to obtain a solution with higher accuracy. In this paper, we present an algorithm framework for bound constrained global optimization problems based on a multilevel partition strategy. This multilevel partition strategy can be regarded as a combination of the basic partition strategy and the multigrid algorithm, which is one of the best algorithms to solve partial differential equation. Our basic idea is to combine the multigrid algorithm with the partition-based algorithm to improve the eventually inefficient behavior of the partition-based algorithm. First, we provide a general framework of the partition-based algorithms which include the DIRECT algorithm as a special case. Then we present a strategy to build the subproblem at the coarse level. This strategy is easy to implement and brings no more computational costs. Under mild conditions, we show that the sequence generated by the proposed global optimization algorithm framework converges to the global optimum. Finally, we employ the original DIRECT algorithm to build a specific global optimization algorithm based on multilevel partition and compare it with the original DIRECT algorithm. Our numerical results show that obtained algorithm improves significantly the eventually inefficient behavior of the original DIRECT algorithm when the required accuracy is high.

关键词： Global optimization Partition-based algorithm multigrid algorithm DIRECT algorithm

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Local Discontinuous Galerkin Methods for the Functionalized Cahn-Hilliard Equation

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JOURNAL OF SCIENTIFIC COMPUTING 2015年第3期63卷 913-937页

作者： Guo, Ruihan Xu, Yan Xu, Zhengfu Univ Sci & Technol China Sch Math Sci Hefei 230026 Anhui Peoples R China Michigan Technol Univ Dept Math Sci Houghton MI 49931 USA

In this paper, we develop a local discontinuous Galerkin (LDG) method for the sixth order nonlinear functionalized Cahn-Hilliard (FCH) equation. We address the accuracy and stability issues from simulating high order stiff equations in phase-field modeling. Within the LDG framework, various boundary conditions associated with the background physics can be naturally implemented. We prove the energy stability of the LDG method for the general nonlinear case. A semi-implicit time marching method is applied to remove the severe time step restriction () for explicit methods. The adaptive capability of the LDG method allows for capturing the interfacial layers and the complicated geometric structures of the solution with high resolution. To enhance the efficiency of the proposed approach, the multigrid (MG) method is used to solve the system of linear equations resulting from the semi-implicit temporal integration at each time step. We show numerically that the MG solver has mesh-independent convergence rates. Numerical simulation results for the FCH equation in two and three dimensions are provided to illustrate that the combination of the LDG method for spatial approximation, semi-implicit temporal integration with the MG solver provides a practical and efficient approach when solving this family of problems.

关键词： Functionalized Cahn-Hilliard equation Local discontinuous Galerkin method multigrid algorithm Stability

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Efficient Numerical Techniques for Simulating a Rotorcraft Flow Field with Overlapping Grids

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AIAA JOURNAL 2015年第5期53卷 1372-1383页

作者： Yang, Xiaoquan Yang, Aiming Si, Jiangtao Commercial Aircraft Corp China Shanghai Aircraft Design & Res Inst Gen Configurat & Aerodynam Dept Shanghai 201210 Peoples R China Fudan Univ Dept Mech & Engn Sci Shanghai 200433 Peoples R China Fudan Univ Shanghai 200433 Peoples R China

We propose efficient and accurate techniques for simulating a time-periodic, unsteady rotorcraft flow. The Reynolds-averaged Navier-Stokes equations are solved on overlapping grids using a multigrid method and time spectral method. A new implementation of the multigrid algorithm for overlapping grids is proposed to accelerate hovering and forward-flight computations. Using the time-lagged periodic boundary condition, the time spectral method is combined with the multigrid scheme to significantly improve the simulation efficiency of a helicopter rotor in forward flight. The resulting equations are solved by the implicit lower-upper symmetric-Gauss-Seidel scheme. Some hovering and forward-flight cases are simulated, and the results are compared with experimental data, demonstrating the high efficiency and accuracy of the proposed method.

关键词： Rotorcrafts Reynolds Averaged Navier Stokes multigrid algorithm Navier Stokes Solver Helicopter Rotor Turbulence Models Aerodynamic Shape Optimization Computational Fluid Dynamics Aspect Ratio Vortex Shedding

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