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Sunday, November 15, 2020 | History

3 edition of A preconditioning method for shape optimization governed by the Euler equations found in the catalog.

A preconditioning method for shape optimization governed by the Euler equations

A preconditioning method for shape optimization governed by the Euler equations

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  • 30 Currently reading

Published by Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, National Technical Information Service, distributor in Hampton, VA, [Springfield, Va .
Written in English

    Subjects:
  • Preconditioning.,
  • Compressible flow.,
  • Airfoils.,
  • Computational fluid dynamics.,
  • Discretization (Mathematics),
  • Optimization.

  • Edition Notes

    StatementEyal Arian, Veer N. Vatsa.
    SeriesICASE report -- no. 98-14., [NASA contractor report] -- NASA/CR-1998-206926., NASA contractor report -- NASA CR-206926.
    ContributionsVatsa, Veer N., Institute for Computer Applications in Science and Engineering.
    The Physical Object
    FormatMicroform
    Pagination1 v.
    ID Numbers
    Open LibraryOL15543271M

    Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid ers are used to perform the calculations required to simulate the free-stream flow of the fluid, and the interaction of the fluid (liquids and gases) with surfaces defined by boundary conditions. @article{osti_, title = {Shape Optimization for Navier-Stokes Equations with Algebraic Turbulence Model: Existence Analysis}, author = {Bulicek, Miroslav and Haslinger, Jaroslav and Malek, Josef and Stebel, Jan}, abstractNote = {We study a shape optimization problem for the paper machine headbox which distributes a mixture of water and wood fibers in the paper making process. See, when you're using Euler's method, the assumption there is that you're unable or unwilling to find a symbolic solution to your differential equation, and you just want to estimate the function values of a solution at a few points.


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A preconditioning method for shape optimization governed by the Euler equations Download PDF EPUB FB2

In this paper, the preconditioning method, suggested by Arian and Ta'asan [1] is re-derived for the compressible Euler equations in their conservative form in two space dimensions and is tested numerically for an optimal shape design problem in two dimensions.

The design space is. In this paper, the preconditioning method, suggested by Arian and Ta’asan [1] is re-derived for the compressible Euler equations in their conservative form in two space dimensions and is tested numerically for an optimal shape design problem in two dimensions.

The design space is. Abstract We consider a classical aerodynamic shape optimization problem subject to the compressible Euler flow equations. The gradient of the cost functional with respect to the shape variables is derived with the adjoint method at the continuous by: CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): We consider a classical aerodynamic shape optimization problem subject to the compressible Euler flow equations.

The gradient of the cost functional with respect to the shape variables is derived with the adjoint method at the continuous level. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda). We consider a classical aerodynamic shape optimization problem subject to the compressible Euler flow equations.

The gradient of the cost functional with respect to the shape variables is derived with the adjoint method at the continuous level. Title: A Preconditioning Method for Shape Optimization Governed by the Euler Equations: Authors: Arian, Eyal; Vatsa, Veer: Publication: International Journal of. adshelp[at] The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative Agreement NNX16AC86A.

AIREX: A Preconditioning Method for Shape Optimization Governed by the Euler Equations We consider a classical aerodynamic shape optimization problem subject to the compressible Euler flow equations. The gradient of the cost functional with respect to the shape variables is derived with the adjoint method at the continuous level.

The gradient of the cost functional with respect to the shape variables is derived with the adjoint method at the continuous level. The Hessian (second order derivative of the cost functional with respect to the shape variables) is approximated also at the continuous level, as first introduced by Arian and Ta’asan Author: Eyal Arian and Veer N.

Vatsa. [vatsa] Arian, E., Vatsa, V.: A Preconditioning Method for Shape Optimization Governed by the Euler Equations. International Journal of Computational Fluid Dynam 17–27 () zbMATH CrossRef MathSciNet Google ScholarAuthor: Eval Arian, Angelo Iollo.

In this paper we discuss a numerical approach for the treatment of optimal shape problems governed by the quasi one-dimensional Euler equations. In particular, we focus on flows with embedded shocks.

E. Arian, V.N. Vatsa, A preconditioning method for shape optimization governed by the Euler equations. Technical reportInstitute for Computer Applications in Science and Engineering (ICASE) () Google ScholarCited by: 6.

A preconditioning method for shape optimization governed Non-Parametric Aerodynamic Shape Optimization based on the compressible Euler equations is considered. Shape. A preconditioning method for shape optimization governed by the Euler equations Author: Eyal Arian ; Veer N Vatsa ; Institute for Computer Applications in Science and Engineering.

Arian, V. VatsaA preconditioning method for shape optimization governed by the Euler equations International Journal of Computational Fluid Dynamics, 12 (), pp. Google ScholarCited by: 4. A Preconditioning Method for Shape Optimization Governed by the Euler Equations International Journal of Computational Fluid Dynamics, Vol.

12, No. 1 Admitting the Inadmissible: Adjoint Formulation for Incomplete Cost Functionals in Aerodynamic Optimization. A preconditioning method for shape optimization governed by the Euler equations, Int J Computational Fluid Dynamics,12, (1), pp 17 – 4.

Chiba, K., Obayashi, S. and Nakahashi, K. High-fidelity multidisciplinary design optimization of aerostructural wing shape for regional jet, June23rd AIAA Applied Aerodynamics Cited by: 6.

The study of shape optimization problems encompasses a wide spectrum of academic research with numerous applications to the real world. In this work these problems are treated from both the classical and modern perspectives and target a broad audience of graduate students in pure and applied mathematics, as well as engineers requiring a solid mathematical basis for the solution of practical.

This paper presents applications of an optimization-based multigrid method to state constrained aerodynamic shape optimization problems. The one-shot simultaneous pseudo-time-stepping method has been applied successfully to such problems, reducing the cost of computation up to 70% from that of a traditional gradient method.

However, the number of optimization iterations is comparatively large Cited by: 7. This paper presents a numerical method for constrained aerodynamic shape optimization problems.

It is based on simultaneous pseudo-timestepping in which stationary states are obtained by solving the pseudo-stationary system of equations representing the state, costate, and design equations.

The main advantages of this method are that it blends in nicely with a previously existing pseudo Cited by: the continuous adjoint method for shape optimization problems in viscous compressible flow is carried out in [9–11].

Use of less accurate state and adjoint solutions for Euler equations has also been performed in Iollo et al. [12]. In [13], Ta’asan proposed an approach in which pseudo-time embedding is suggested for theCited by: 8.

A semi-coarsened multigrid algorithm with a point block Jacobi, multi-stage smoother for second-order upwind discretizations of the two-dimensional Euler equations which produces convergence rates independent of grid size for moderate subsonic Mach numbers is by: A preconditioner for this problem is done exactly as in the small disturbance equations using (60)-(62).

It is also possible to construct the preconditioner based on solution of the linearized Euler equations, but is more complicated and unnecessary. Large-scale three-dimensional aerodynamic shape optimization based on the compressible Euler equations is considered.

Shape calculus is used to derive an exact surface formulation of the gradients, enabling the computation of shape gradient information for each surface mesh node without having to calculate further mesh sensitivities.

Special attention is paid to the applicability to large Cited by: One-Shot Pseudo-Time Method for Aerodynamic Shape Optimization Using the Navier-Stokes Equations S.

Hazra1,n2 1 Department of Mathematics, University of Trier, D Trier, Germany 2 Department of Aeronautics and Astronautics, Stanford University, Stanford, CAUSA Abstract. This paper presents a numerical method for aerodynamic shape optimization problems inCited by: 8.

recently, the method has been employed for wing design in the context of complex aircraft configurations [7], [8], using a grid perturbation technique to accommodate the geometry modifications.

Pironneau had earlier initiated studies of the use of control theory for optimum shape design of systems governed by elliptic equations [9], [10].

COVID Resources. Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous and frequently-updated resource results are available from this ’s WebJunction has pulled together information and resources to assist library staff as they consider how to handle coronavirus.

Real-Time PDE-Constrained Optimization, the first book devoted to real-time optimization for systems governed by PDEs, focuses on new formulations, methods, and algorithms needed to facilitate real-time, PDE-constrained optimization. van Leer, B., “Upwind-Difference Methods for Aerodynamic Problems Governed by the Euler Equations,” Proceedings of Large-scale Computations in Fluid Mechanics, Lectures in Applied Mathematics, Vol.

22, pp. – ().Cited by: 4. 2 A. NIGRO., C. DE BARTOLO, R. HARTMANN, F. BASSI 19 KEY WORDS: Discontinuous Galerkin finite element method; Low Mach num ber; Cancellation error; 20 Preconditioning; Euler equations.

21 22 1. INTRODUCTION 23 DG methods have received more and more attention in the last years because of their appealing 24 features that justify the widespread applications of these Size: 1MB.

This paper describes a numerical method for solving the unsteady Euler equation at any speed. In the process of calculating Euler's equation, the control equation in orthogonal curvilinear coordinate system is discretized by the finite -volume scheme based on the center-difference method, and convection flux used Jameson central deference scheme was solved at every pseudo time step, and the Author: De Bao Lei, Zhong Hua Tang, Yan Hui Zheng.

Shape Optimization Governed by the Quasi 1-D Euler Equations Using an Adjoint Methodp. Relaxation Method for 3-D Problems in Supersonic Aerodynamics p. Virtual Zone Navier-Stokes Computations for Oscillating Control Surfaces p.

The Domain Decomposition Method and Compact Discretization for the Navier-Stokes Equations p. The optimization's iterative process is carried out using a multilevel optimization, where each level is produced by agglomeration on the skin mesh.

The method is improved by using an additive multilevel preconditioner. At each optimization iterate, the shape is modified by using transpiration conditions.

is the reference velocity. The details of the preconditioning method can be found in (Weiss ). Continuous adjoint equations.

The steady Euler equations in preconditioned form can be expressed as * T F 0. (8) For many aerodynamic optimization problems.

Preconditioning for linear systems. In linear algebra and numerical analysis, a preconditioner of a matrix is a matrix such that − has a smaller condition number is also common to call = − the preconditioner, rather than, since itself is rarely explicitly available.

In modern preconditioning, the application of = −, i.e., multiplication of a column vector, or a block of column. Numerical Solution of the Euler Equations by Finite Volume Methods terms of third order, and a Runge Kutta time stepping scheme, is shown to yield an e ective method for solving the Euler equations in arbitrary geometric domains.

The method has been used to determine the ow solutions and solutions of the Euler equations at quite. compressibility method for treating variable density incompressible ows with heat transfer. The method could also be viewed as a simpli cation of the preconditioning approach developed by Weiss and Smith,6 who sought to unify arti cial compressibility and low-speed preconditioning approaches into one method for all speeds.

fort in local preconditioning of the Euler equations af- ter the presentation at the AIAA 10th CFD Conference, JuneHonolulu ([I]; for more details see the Ph.D. thesis of W.-T. Lee [2]), and also includes our first re- sults on local preconditioning of the Navier-Stokes equa- by: This question suggests that you can precondition an optimization problem by a simple multiplicative scaling of the variables in the objective function.

However, when I look up literature on preconditioning I see it is typically defined on matrices in the context of solving sets of linear equations. After a review of mathematical models of fluid flow, methods for solving the transonic potential flow equation (of mixed type) are examined.

The central part of the article discusses the formulation and implementation of shock‐capturing schemes for the Euler and Navier–Stokes equations. using the Euler equations. These methods, however, require the determination of analytically and computationally comple.x residual Jacobians due to the conserved flow variables vector and the entire mesh which defines the computational domain.

On structured grids, shape optimization via direct and discrete adjoint approaches for first.A Discontinuous Galerkin Method for Solutions of the Euler Equations on Cartesian Grids with Embedded Geometries Ruibin Qin and Lilia Krivodonova University of Waterloo Waterloo, Ontario Abstract We present a discontinuous Galerkin method (DGM) for solutions of the Euler equa-tions on Cartesian grids with embedded geometries.We first consider the case of a fluid at rest, such that u = 0.

Euler’s equation is then reduced to the equation of hydrostatic balance, ∇p = ρg ⇔ p(x) = ρg x+C, () where C is a constant.

Example The density of mass in the ocean can be considered as constant, ρ 0, and the gravity g = − Size: KB.