Search results

1 – 10 of over 2000
Book part
Publication date: 13 December 2013

Victor Aguirregabiria and Arvind Magesan

We derive marginal conditions of optimality (i.e., Euler equations) for a general class of Dynamic Discrete Choice (DDC) structural models. These conditions can be used to…

Abstract

We derive marginal conditions of optimality (i.e., Euler equations) for a general class of Dynamic Discrete Choice (DDC) structural models. These conditions can be used to estimate structural parameters in these models without having to solve for approximate value functions. This result extends to discrete choice models the GMM-Euler equation approach proposed by Hansen and Singleton (1982) for the estimation of dynamic continuous decision models. We first show that DDC models can be represented as models of continuous choice where the decision variable is a vector of choice probabilities. We then prove that the marginal conditions of optimality and the envelope conditions required to construct Euler equations are also satisfied in DDC models. The GMM estimation of these Euler equations avoids the curse of dimensionality associated to the computation of value functions and the explicit integration over the space of state variables. We present an empirical application and compare estimates using the GMM-Euler equations method with those from maximum likelihood and two-step methods.

Details

Structural Econometric Models
Type: Book
ISBN: 978-1-78350-052-9

Keywords

Article
Publication date: 8 August 2008

S.A. Mohamed

The aim of the paper is to achieve textbook multigrid efficiency for some flow problems.

Abstract

Purpose

The aim of the paper is to achieve textbook multigrid efficiency for some flow problems.

Design/methodology/approach

The steady incompressible Euler equations are decoupled into elliptic and hyperbolic subsystems. Numerous classical FAS‐MG algorithms are implemented and tested for convergence. A full multigrid algorithm that costs less than 10 work units (WUs) is sufficient to reduce the algebraic error below the discretization error. A new algorithm “NUVMGP” is introduced. A two‐step iterative procedure is adopted. First, given the pressure gradient, the convection equations are solved on the computational grid for the velocity components by performing one Gauss‐Seidel iteration ordered in the flow direction. second, a linear multigrid (MG) cycle for Poisson's equation is performed to update pressure values.

Findings

It is found that algorithm “NUVMGP‐FMG” requires less than 6 WU to attain the target solution. The convergence rates are independent on both the mesh size and the approximation order.

Research limitations/implications

Lexicographic Gauss‐Seidel using downstream ordering is a good solver for the advection terms and provides excellent smoothing rates for relaxation. But it is complicated to maintain downstream ordering in case the flow directions change with location.

Originality/value

Although the scope of this work is limited to rectangular domains, finite difference schemes, and incompressible Euler equation, the same approaches can be extended for other flow problems. However, such relatively simple problems may provide deep understanding of the ideal convergence behavior of MG and accumulate experience to detect unacceptable performance and regain the optimal one.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 18 no. 6
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 24 May 2013

Michiel H. Straathof, Giampietro Carpentieri and Michel J.L. van Tooren

An aerodynamic shape optimization algorithm is presented, which includes all aspects of the design process: parameterization, flow computation and optimization. The…

Abstract

Purpose

An aerodynamic shape optimization algorithm is presented, which includes all aspects of the design process: parameterization, flow computation and optimization. The purpose of this paper is to show that the Class‐Shape‐Refinement‐Transformation method in combination with an Euler/adjoint solver provides an efficient and intuitive way of optimizing aircraft shapes.

Design/methodology/approach

The Class‐Shape‐Transformation method was used to parameterize the aircraft shape and the flow was computed using an in‐house Euler code. An adjoint solver implemented into the Euler code was used to compute the required gradients and a trust‐region reflective algorithm was employed to perform the actual optimization.

Findings

The results of two aerodynamic shape optimization test cases are presented. Both cases used a blended‐wing‐body reference geometry as their initial input. It was shown that using a two‐step approach, a considerable improvement of the lift‐to‐drag ratio in the order of 20‐30 per cent could be achieved. The work presented in this paper proves that the CSRT method is a very intuitive and effective way of parameterizating aircraft shapes. It was also shown that using an adjoint algorithm provides the computational efficiency necessary to perform true three‐dimensional shape optimization.

Originality/value

The novelty of the algorithm lies in the use of the Class‐Shape‐Refinement‐Transformation method for parameterization and its coupling to the Euler and adjoint codes.

Details

Engineering Computations, vol. 30 no. 4
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 7 March 2016

Nikita Ageev and Alexander Pavlenko

This study aims to decrease the aerodynamic drag of the body of revolution at supersonic speeds. Supersonic area rule is widely used in modern supersonic aircraft design…

Abstract

Purpose

This study aims to decrease the aerodynamic drag of the body of revolution at supersonic speeds. Supersonic area rule is widely used in modern supersonic aircraft design. Further reduction of the aerodynamic drag is possible in the framework of Euler and Reynolds averaged Navier–Stokes (RANS) equations. Sears–Haack body of revolution shape variation, which decreased its aerodynamic drag in compressible inviscid and viscous gas flow at Mach number of 1.8 under constraint of the volume with lower bound equal to volume of initial body, was numerically investigated.

Design/methodology/approach

Calculations were carried out in two-dimensional axisymmetric mode in the framework of Euler and RANS with SST model with compressibility correction equations at structured multiblock meshes. Variation of the radius as function of the longitudinal coordinate was given as a polynomial third-order spline through five uniformly distributed points. Varied parameters were increments of the radius of the body at points that defined spline. Drag coefficient was selected as an objective function. Parameter combinations corresponding to the objective function minimum under volume constraint were obtained by mixed-integer sequential quadratic programming at second-order polynomial response surface and IOSO algorithm.

Findings

Improving variations make front part of the body become slightly blunted, transfer part of volume from front part of the body to back part and generate significant back face. In the framework of RANS, the best variation decreases aerodynamic drag by approximately 20 per cent in comparison with Sears–Haack body.

Practical implications

The results can be applied for the aerodynamic design of the bullets and projectiles. The second important application is knowledge of the significance of the difference between linearized slender body theory optimization results and optimization results obtained by modern computational fluid dynamics (CFD) optimization techniques.

Social implications

Knowledge about the magnitude of the difference between linearized slender body theory optimization results and optimization results obtained by modern CFD optimization techniques can stimulate further research in related areas.

Originality/value

The optimization procedure and optimal shapes obtained in the present work are directly applicable to the design of small aerodynamic drag bodies.

Details

Aircraft Engineering and Aerospace Technology: An International Journal, vol. 88 no. 2
Type: Research Article
ISSN: 1748-8842

Keywords

Article
Publication date: 24 May 2013

Hong Wang, Jyri Leskinen, Dong‐Seop Lee and Jacques Périaux

The purpose of this paper is to investigate an active flow control technique called Shock Control Bump (SCB) for drag reduction using evolutionary algorithms.

Abstract

Purpose

The purpose of this paper is to investigate an active flow control technique called Shock Control Bump (SCB) for drag reduction using evolutionary algorithms.

Design/methodology/approach

A hierarchical genetic algorithm (HGA) consisting of multi‐fidelity models in three hierarchical topological layers is explored to speed up the design optimization process. The top layer consists of a single sub‐population operating on a precise model. On the middle layer, two sub‐populations operate on a model of intermediate accuracy. The bottom layer, consisting of four sub‐populations (two for each middle layer populations), operates on a coarse model. It is well‐known that genetic algorithms (GAs) are different from deterministic optimization tools in mimicking biological evolution based on Darwinian principle. In HGAs process, each population is handled by GA and the best genetic information obtained in the second or third layer migrates to the first or second layer for refinement.

Findings

The method was validated on a real life optimization problem consisting of two‐dimensional SCB design optimization installed on a natural laminar flow airfoil (RAE5243). Numerical results show that HGA is more efficient and achieves more drag reduction compared to a single population based GA.

Originality/value

Although the idea of HGA approach is not new, the novelty of this paper is to combine it with mesh/meshless methods and multi‐fidelity flow analyzers. To take the full benefit of using hierarchical topology, the following conditions are implemented: the first layer uses a precise meshless Euler solver with fine cloud of points, the second layer uses a hybrid mesh/meshless Euler solver with intermediate mesh/clouds of points, the third layer uses a less fine mesh with Euler solver to explore efficiently the search space with large mutation span.

Details

Engineering Computations, vol. 30 no. 4
Type: Research Article
ISSN: 0264-4401

Keywords

Article
Publication date: 1 February 1995

N.R. ALURU, K.H. LAW, P.M. PINSKY and R.W. DUTTON

A mathematical analysis of the time‐dependent multi‐dimensional Hydrodynamic model is performed to determine the well‐posed boundary conditions for semiconductor device…

Abstract

A mathematical analysis of the time‐dependent multi‐dimensional Hydrodynamic model is performed to determine the well‐posed boundary conditions for semiconductor device simulation. The number of independent boundary conditions that need to be specified at electrical contacts of a semi‐conductor device are derived. Using the classical energy method, a mathematical relation among the physical parameters is established to define the well‐posed boundary conditions for the problem. Several possible sets of boundary conditions are given to illustrate the proper boundary conditions. Natural boundary conditions that can be specified are obtained from the boundary integrals of the weak‐form finite element formulations. An example is included to illustrate the importance of well‐posedness of the boundary conditions for device simulation.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, vol. 14 no. 2/3
Type: Research Article
ISSN: 0332-1649

Article
Publication date: 1 January 1992

GABRIELE ENGL and PETER RENTROP

We present results of a mathematical model for the gas flow in an internal combustion engine consisting of a single cylinder with an inlet and outlet pipe. In order to…

Abstract

We present results of a mathematical model for the gas flow in an internal combustion engine consisting of a single cylinder with an inlet and outlet pipe. In order to achieve optimal performance of the engine the dependence of the gas flow on physical parameters such as pipe dimensions and valve geometry need to be understood. A system of ordinary differential equations (in time t) with discontinuous right‐hand side describes the gas properties in the cylinder, whereas the gas flow in each pipe is modelled by the Euler equations, a system of hyperbolic partial differential equations. The explicit method of Euler and a TVD scheme are used for solving these equations. However, since the coupling of the pipe equations with the o.d.e. system in the cylinder on one side and atmospheric gas properties on the other appeared to be a main problem, we concentrate on appropriate coupling conditions. The numerical techniques involve discretization in space and time, and we present different methods of discrete coupling. As a main result we show that the various coupling methods lead to quite different numerical solutions. Therefore, a careful treatment of the coupling conditions is crucial.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 2 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 January 1939

F.R. Shanley

MOST of the structural analysis problems that have resulted from the use of “thin‐walled” construction seem to fall into two general classes: Stress distribution and…

1110

Abstract

MOST of the structural analysis problems that have resulted from the use of “thin‐walled” construction seem to fall into two general classes: Stress distribution and buckling. Even these classes cannot be entirely separated, as the stress distribution can be greatly affected by buckling phenomena. A thorough understanding of the general principles of buckling (or structural instability) is therefore essential for efficient and safe design of modern aircraft structures.

Details

Aircraft Engineering and Aerospace Technology, vol. 11 no. 1
Type: Research Article
ISSN: 0002-2667

Article
Publication date: 14 October 2020

Zhijian Duan and Gongnan Xie

The discontinuous Galerkin finite element method (DGFEM) is very suited for realizing high order resolution approximations on unstructured grids for calculating the…

Abstract

Purpose

The discontinuous Galerkin finite element method (DGFEM) is very suited for realizing high order resolution approximations on unstructured grids for calculating the hyperbolic conservation law. However, it requires a significant amount of computing resources. Therefore, this paper aims to investigate how to solve the Euler equations in parallel systems and improve the parallel performance.

Design/methodology/approach

Discontinuous Galerkin discretization is used for the compressible inviscid Euler equations. The multi-level domain decomposition strategy was used to deal with the computational grids and ensure the calculation load balancing. The total variation diminishing (TVD) Runge–Kutta (RK) scheme coupled with the multigrid strategy was employed to further improve parallel efficiency. Moreover, the Newton Block Gauss–Seidel (GS) method was adopted to accelerate convergence and improve the iteration efficiency.

Findings

Numerical experiments were implemented for the compressible inviscid flow problems around NACA0012 airfoil, over M6 wing and DLR-F6 configuration. The parallel acceleration is near to a linear convergence. The results indicate that the present parallel algorithm can reduce computational time significantly and allocate memory reasonably, which has high parallel efficiency and speedup, and it is well-suited to large-scale scientific computational problems on multiple instruction stream multiple data stream model.

Originality/value

The parallel DGFEM coupled with TVD RK and the Newton Block GS methods was presented for hyperbolic conservation law on unstructured meshes.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 31 no. 5
Type: Research Article
ISSN: 0961-5539

Keywords

Article
Publication date: 1 January 1993

J.‐Y. TRÉPANIER, M. REGGIO and D. AIT‐ALI‐YAHIA

An implicit method for the solution of transonic flows modelled by the time‐dependent Euler equations is presented. The method is characterized by a robust linearization…

Abstract

An implicit method for the solution of transonic flows modelled by the time‐dependent Euler equations is presented. The method is characterized by a robust linearization for first‐ and second‐order versions of Roe's flux‐difference splitting scheme, an implicit treatment of the boundary conditions and the implementation of an adaptive grid strategy for global efficiency. The performance of the method is investigated for the GAMM test circular‐arc bump configuration and for the RAE 2822 aerofoil.

Details

International Journal of Numerical Methods for Heat & Fluid Flow, vol. 3 no. 1
Type: Research Article
ISSN: 0961-5539

Keywords

1 – 10 of over 2000