The Experts below are selected from a list of 33174 Experts worldwide ranked by ideXlab platform
Xin Zhang - One of the best experts on this subject based on the ideXlab platform.
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A generalized sound Extrapolation Method for turbulent flows
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2018Co-Authors: Siyang Zhong, Xin ZhangAbstract:Sound Extrapolation Methods are often used to compute acoustic far-field directivities using near-field flow data in aeroacoustics applications. The results may be erroneous if the volume integrals...
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a sound Extrapolation Method for aeroacoustics far field prediction in presence of vortical waves
Journal of Fluid Mechanics, 2017Co-Authors: Siyang Zhong, Xin ZhangAbstract:Off-surface integral solutions to an inhomogeneous wave equation based on acoustic analogy could suffer from spurious wave contamination when volume integrals are ignored for computation efficiency and vortical/turbulent gusts are convected across the integration surfaces, leading to erroneous far-field directivity predictions. Vortical gusts often exist in aerodynamic flows and it is inevitable their effects are present on the integration surface. In this work, we propose a new sound Extrapolation Method for acoustic far-field directivity prediction in the presence of vortical gusts, which overcomes the deficiencies in the existing Methods. The Euler equations are rearranged to an alternative form in terms of fluctuation variables that contains the possible acoustical and vortical waves. Then the equations are manipulated to an inhomogeneous wave equation with source terms corresponding to surface and volume integrals. With the new formulation, spurious monopole and dipole noise produced by vortical gusts can be suppressed on account of the solenoidal property of the vortical waves and a simple convection process. It is therefore valid to ignore the volume integrals and preserve the sound properties. The resulting new acoustic inhomogeneous convected wave equations could be solved by means of the Green’s function Method. Validation and verification cases are investigated, and the proposed Method shows a capacity of accurate sound prediction for these cases. The new Method is also applied to the challenging airfoil leading edge noise problems by injecting vortical waves into the computational domain and performing aeroacoustic studies at both subsonic and transonic speeds. In the case of a transonic airfoil leading edge noise problem, shocks are present on the airfoil surface. Good agreements of the directivity patterns are obtained compared with direct computation results.
Siyang Zhong - One of the best experts on this subject based on the ideXlab platform.
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A generalized sound Extrapolation Method for turbulent flows
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2018Co-Authors: Siyang Zhong, Xin ZhangAbstract:Sound Extrapolation Methods are often used to compute acoustic far-field directivities using near-field flow data in aeroacoustics applications. The results may be erroneous if the volume integrals...
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a sound Extrapolation Method for aeroacoustics far field prediction in presence of vortical waves
Journal of Fluid Mechanics, 2017Co-Authors: Siyang Zhong, Xin ZhangAbstract:Off-surface integral solutions to an inhomogeneous wave equation based on acoustic analogy could suffer from spurious wave contamination when volume integrals are ignored for computation efficiency and vortical/turbulent gusts are convected across the integration surfaces, leading to erroneous far-field directivity predictions. Vortical gusts often exist in aerodynamic flows and it is inevitable their effects are present on the integration surface. In this work, we propose a new sound Extrapolation Method for acoustic far-field directivity prediction in the presence of vortical gusts, which overcomes the deficiencies in the existing Methods. The Euler equations are rearranged to an alternative form in terms of fluctuation variables that contains the possible acoustical and vortical waves. Then the equations are manipulated to an inhomogeneous wave equation with source terms corresponding to surface and volume integrals. With the new formulation, spurious monopole and dipole noise produced by vortical gusts can be suppressed on account of the solenoidal property of the vortical waves and a simple convection process. It is therefore valid to ignore the volume integrals and preserve the sound properties. The resulting new acoustic inhomogeneous convected wave equations could be solved by means of the Green’s function Method. Validation and verification cases are investigated, and the proposed Method shows a capacity of accurate sound prediction for these cases. The new Method is also applied to the challenging airfoil leading edge noise problems by injecting vortical waves into the computational domain and performing aeroacoustic studies at both subsonic and transonic speeds. In the case of a transonic airfoil leading edge noise problem, shocks are present on the airfoil surface. Good agreements of the directivity patterns are obtained compared with direct computation results.
Wei Shyy - One of the best experts on this subject based on the ideXlab platform.
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a least square Extrapolation Method for the a posteriori error estimate of the incompressible navier stokes problem
International Journal for Numerical Methods in Fluids, 2005Co-Authors: Marc Garbey, Wei ShyyAbstract:A posteriori error estimators are fundamental tools for providing confidence in the numerical computation of PDEs. To date, the main theories of a posteriori estimators have been developed largely in the finite element framework, for either linear elliptic operators or non-linear PDEs in the absence of disparate length scales. On the other hand, there is a strong interest in using grid refinement combined with Richardson Extrapolation to produce CFD solutions with improved accuracy and, therefore, a posteriori error estimates. But in practice, the effective order of a numerical Method often depends on space location and is not uniform, rendering the Richardson Extrapolation Method unreliable. We have recently introduced (Garbey, 13th International Conference on Domain Decomposition, Barcelona, 2002; 379–386; Garbey and Shyy, J. Comput. Phys. 2003; 186:1–23) a new Method which estimates the order of convergence of a computation as the solution of a least square minimization problem on the residual. This Method, called least square Extrapolation, introduces a framework facilitating multi-level Extrapolation, improves accuracy and provides a posteriori error estimate. This Method can accommodate different grid arrangements. The goal of this paper is to investigate the power and limits of this Method via incompressible Navier Stokes flow computations. Copyright © 2005 John Wiley & Sons, Ltd.
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a least square Extrapolation Method for improving solution accuracy of pde computations
Journal of Computational Physics, 2003Co-Authors: Marc Garbey, Wei ShyyAbstract:Richardson Extrapolation (RE) is based on a very simple and elegant mathematical idea that has been successful in several areas of numerical analysis such as quadrature or time integration of ODEs. In theory, RE can be used also on PDE approximations when the convergence order of a discrete solution is clearly known. But in practice, the order of a numerical Method often depends on space location and is not accurately satisfied on different levels of grids used in the Extrapolation formula. We propose in this paper a more robust and numerically efficient Method based on the idea of finding automatically the order of a Method as the solution of a least square minimization problem on the residual. We introduce a two-level and three-level least square Extrapolation Method that works on nonmatching embedded grid solutions via spline interpolation. Our least square Extrapolation Method is a post-processing of data produced by existing PDE codes, that is easy to implement and can be a better tool than RE for code verification. It can be also used to make a cascade of computation more numerically efficient. We can establish a consistent linear combination of coarser grid solutions to produce a better approximation of the PDE solution at a much lower cost than direct computation on a finer grid. To illustrate the performance of the Method, examples including two-dimensional turning point problem with sharp transition layer and the Navier-Stokes flow inside a lid-driven cavity are adopted.
C Arakawa - One of the best experts on this subject based on the ideXlab platform.
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incompressible navier stokes solver using Extrapolation Method suitable for massively parallel computing
Computational Mechanics, 1999Co-Authors: Katsuhiro Shimano, C ArakawaAbstract:The authors propose combination of the coupled Method and the Extrapolation Method as a numerical technique suitable for calculation of an incompressible flow on a massively parallel computer. In the coupled Method, the momentum equations and the continuity equation are directly coupled, and velocity components and pressure values are simultaneously updated. It is very simple and efficiently parallelized. The Extrapolation Method is an accelerative technique predicting a converged solution from a sequence of intermediate solutions generated by an iterative procedure. When it is implemented on a parallel computer, it is expected to retain good accelerative property even for fine granularity in contrast to the multigrid Method. In this paper three existing versions of the Extrapolation Method, ROLE, MPE and ROGE, are reviewed, and LWE, a new version developed by the authors, is presented. Then, ROLE and LWE are applied to numerical analysis of Poisson's equation on a Fujitsu AP1000 and its results are shown. The mathematical proof that the Extrapolation Method, which is based on the linear theory, is applicable to an iterative procedure solving nonlinear equations is presented. Then the code consisting of the coupled Method and the Extrapolation Method is implemented on a Fujitsu AP1000 to solve two simple 2-D steady flows. Accelerative property of the Extrapolation Method is discussed, and suitability of the code to massively parallel computing is demonstrated.
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incompressible navier stokes solver with Extrapolation Method suitable for massively parallel computing application of Extrapolation Method to linear equation
Jsme International Journal Series B-fluids and Thermal Engineering, 1997Co-Authors: Kenjiro Shimano, C ArakawaAbstract:A massively parallel computer, which has a large number of processors, is expected to become the main instrument for scientific numerical analysis including the CFD field. It has been pointed out that efficiency of parallel computing becomes worse when the number of processors increases and granularity comes to fine. Therefore an accelerative technique should be introduced to achieve nearly maximum performance of the massively parallel computer. Some researchers have used the multigrid Method, but this technique turned out to be inappropriate for parallel computing of very fine granularity because efficiency rapidly worsens. The purpose of this study is to propose a numerical technique suitable for calculation of incompressible flow on massively parallel computer. In this regard, we choose an Extrapolation Method as the accelerative technique, which perdicts converged solutions from a suquence of intermediate solutions and is expected to retain its accelerative property for fine granularity. Three existing Extrapolation Methods ROLE, MPE, ROGE and newly developed LWE are discussed. Furthermore, ROLE and LWE are applied to numerical analysis of Poisson's equation and the results are discussed.
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Application of Extrapolation Method to incompressible N-S equations on massively parallel computer
Fifteenth International Conference on Numerical Methods in Fluid Dynamics, 1Co-Authors: Kenjiro Shimano, C ArakawaAbstract:We chose the Extrapolation Method ROLE as the acceleration technique implemented on massively parallel computers. Theoretical discussion was given on applicability of the Extrapolation Method to a nonlinear system of equations by considering behavior of a nonlinear mapping. Then the Extrapolation Method was introduced to the coupled Method solving incompressible N-S equations on AP1000. The maximum speed-up by Extrapolation reached about 1.5∼1.9 and it hardly depended on the number of processors. It was concluded that the Extrapolation Method which retained its accelerative property even for fine granularity was an appropriate choice for massively parallel computation.
Marc Garbey - One of the best experts on this subject based on the ideXlab platform.
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a least square Extrapolation Method for the a posteriori error estimate of the incompressible navier stokes problem
International Journal for Numerical Methods in Fluids, 2005Co-Authors: Marc Garbey, Wei ShyyAbstract:A posteriori error estimators are fundamental tools for providing confidence in the numerical computation of PDEs. To date, the main theories of a posteriori estimators have been developed largely in the finite element framework, for either linear elliptic operators or non-linear PDEs in the absence of disparate length scales. On the other hand, there is a strong interest in using grid refinement combined with Richardson Extrapolation to produce CFD solutions with improved accuracy and, therefore, a posteriori error estimates. But in practice, the effective order of a numerical Method often depends on space location and is not uniform, rendering the Richardson Extrapolation Method unreliable. We have recently introduced (Garbey, 13th International Conference on Domain Decomposition, Barcelona, 2002; 379–386; Garbey and Shyy, J. Comput. Phys. 2003; 186:1–23) a new Method which estimates the order of convergence of a computation as the solution of a least square minimization problem on the residual. This Method, called least square Extrapolation, introduces a framework facilitating multi-level Extrapolation, improves accuracy and provides a posteriori error estimate. This Method can accommodate different grid arrangements. The goal of this paper is to investigate the power and limits of this Method via incompressible Navier Stokes flow computations. Copyright © 2005 John Wiley & Sons, Ltd.
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a least square Extrapolation Method for improving solution accuracy of pde computations
Journal of Computational Physics, 2003Co-Authors: Marc Garbey, Wei ShyyAbstract:Richardson Extrapolation (RE) is based on a very simple and elegant mathematical idea that has been successful in several areas of numerical analysis such as quadrature or time integration of ODEs. In theory, RE can be used also on PDE approximations when the convergence order of a discrete solution is clearly known. But in practice, the order of a numerical Method often depends on space location and is not accurately satisfied on different levels of grids used in the Extrapolation formula. We propose in this paper a more robust and numerically efficient Method based on the idea of finding automatically the order of a Method as the solution of a least square minimization problem on the residual. We introduce a two-level and three-level least square Extrapolation Method that works on nonmatching embedded grid solutions via spline interpolation. Our least square Extrapolation Method is a post-processing of data produced by existing PDE codes, that is easy to implement and can be a better tool than RE for code verification. It can be also used to make a cascade of computation more numerically efficient. We can establish a consistent linear combination of coarser grid solutions to produce a better approximation of the PDE solution at a much lower cost than direct computation on a finer grid. To illustrate the performance of the Method, examples including two-dimensional turning point problem with sharp transition layer and the Navier-Stokes flow inside a lid-driven cavity are adopted.
