Results 1  10
of
108
Optimum aerodynamic design using the NavierStokes equations
 Theoretical and Computational Fluid Dynamics
, 1998
"... The ultimate success of an aircraft design depends on the resolution of complex multidisciplinary tradeo s between factors such as aerodynamic eciency, structural weight, stability and control, and ..."
Abstract

Cited by 148 (49 self)
 Add to MetaCart
(Show Context)
The ultimate success of an aircraft design depends on the resolution of complex multidisciplinary tradeo s between factors such as aerodynamic eciency, structural weight, stability and control, and
A Perspective on Computational Algorithms for Aerodynamic Analysis and Design
 Progress in Aerospace Sciences
, 2001
"... This paper exam nes the use of computational fluid dynamics as a tool for aircraft design. It addresses the requirements for effective industrial use, and tradeoffs between modeling accuracy and computational costs. Essential elements of algorithm design are discussed in detail, together with a uni ..."
Abstract

Cited by 57 (20 self)
 Add to MetaCart
(Show Context)
This paper exam nes the use of computational fluid dynamics as a tool for aircraft design. It addresses the requirements for effective industrial use, and tradeoffs between modeling accuracy and computational costs. Essential elements of algorithm design are discussed in detail, together with a unified approach to the design of shock capturing schemes. Finally, the paper discusses the use of techniques drawn from control theory to determine optimal aerodynamic shapes. In the future multidisciplinary analysis and optimization should be combined to take account of the tradeoffs in the overall performance of the complete system
Algebraic flux correction I. Scalar conservation laws. Chapter 6 in the first edition of this book
, 2005
"... Abstract This chapter is concerned with the design of highresolution finite element schemes satisfying the discrete maximum principle. The presented algebraic flux correction paradigm is a generalization of the fluxcorrected transport (FCT) methodology. Given the standard Galerkin discretization ..."
Abstract

Cited by 44 (23 self)
 Add to MetaCart
(Show Context)
Abstract This chapter is concerned with the design of highresolution finite element schemes satisfying the discrete maximum principle. The presented algebraic flux correction paradigm is a generalization of the fluxcorrected transport (FCT) methodology. Given the standard Galerkin discretization of a scalar transport equation, we decompose the antidiffusive part of the discrete operator into numerical fluxes and limit these fluxes in a conservative way. The purpose of this manipulation is to make the antidiffusive term local extremum diminishing. The available limiting techniques include a family of implicit FCT schemes and a new linearitypreserving limiter which provides a unified treatment of stationary and timedependent problems. The use of Anderson acceleration makes it possible to design a simple and efficient quasiNewton solver for the constrained Galerkin scheme. We also present a linearized FCT method for computations with small time steps. The numerical behavior of the proposed algorithms is illustrated by a grid convergence study for convectiondominated transport problems and anisotropic diffusion equations. 1
Spectral Difference Method for Unstructured Grids II: Extension to the Euler Equations
, 2006
"... An efficient, highorder, conservative method named the spectral difference method has been developed recently for conservation laws on unstructured grids. It combines the best features of structured and unstructured grid methods to achieve highcomputational efficiency and geometric flexibility; it ..."
Abstract

Cited by 39 (25 self)
 Add to MetaCart
(Show Context)
An efficient, highorder, conservative method named the spectral difference method has been developed recently for conservation laws on unstructured grids. It combines the best features of structured and unstructured grid methods to achieve highcomputational efficiency and geometric flexibility; it utilizes the concept of discontinuous and highorder local representations to achieve conservation and high accuracy; and it is based on the finitedifference formulation for simplicity. The method is easy to implement since it does not involve surface or volume integrals. Universal reconstructions are obtained by distributing solution and flux points in a geometrically similar manner for simplex cells. In this paper, the method is further extended to nonlinear systems of conservation laws, the Euler equations. Accuracy studies are performed to numerically verify the order of accuracy. In order to capture both smooth feature and discontinuities, monotonicity limiters are implemented, and tested for several problems in one and two dimensions. The method is more efficient than the discontinuous Galerkin and spectral volume methods for unstructured grids. KEY WORDS: Highorder; conservation laws; unstructured grids; spectral difference; spectral collocation method; Euler equations.
Aerodynamic Shape Optimization Techniques Based On Control Theory
 Control Theory, CIME (International Mathematical Summer
, 1998
"... This paper review the formulation and application of optimization techniques based on control theory for aerodynamic shape design in both inviscid and viscous compressible flow . The theory is applied to a system defined by the partial differential equations of the flow, with the boundary shape acti ..."
Abstract

Cited by 36 (25 self)
 Add to MetaCart
This paper review the formulation and application of optimization techniques based on control theory for aerodynamic shape design in both inviscid and viscous compressible flow . The theory is applied to a system defined by the partial differential equations of the flow, with the boundary shape acting as the control. The Frechet derivative of the cost function is determined via the solution of an adjoint partial differential equation, and the boundary shape is then modified in a direction of descent. This process is repeated until an optimum solution is approached. Each design cycle requires the numerical solution of both the flow and the adjoint equations, leading to a computational cost roughly equal to the cost of two flow solutions. Representative results are presented for viscous optimization of transonic wingbody combinations and inviscid optimization of complex configurations.
Positive schemes and shock modelling for compressible flows
 International Journal for Numerical Methods in Fluids
, 1995
"... A unified theory of nonoscillatory finite volume schemes for both structured and unstructured meshes is developed in two parts. In the first part, a theory of local extremum diminishing (LED) and essentially local extremum diminishing (ELED) schemes is developed for scalar conservation laws. This l ..."
Abstract

Cited by 33 (2 self)
 Add to MetaCart
(Show Context)
A unified theory of nonoscillatory finite volume schemes for both structured and unstructured meshes is developed in two parts. In the first part, a theory of local extremum diminishing (LED) and essentially local extremum diminishing (ELED) schemes is developed for scalar conservation laws. This leads to symmetric and upstream limited positive (SLIP and USLIP) schemes which can be formulated on either structured or unstructured meshes. The second part examines the application of similar ideas to the treatment of systems of conservation laws. An analysis of discrete shock structure leads to conditions on the numerical flux such that stationary discrete shocks can contain a single interior point. The simplest formulation which meets these conditions is a convective upwind and split pressure (CUSP) scheme, in which the coefficient of the pressure differences is fully determined by the coefficient of convective diffusion. Numerical results are presmted which confirm the properties of these schemes. KEY WORDS computational aerodynamics; shock capturing; positive schemes 1.
Preconditioned Multigrid Methods for Compressible Flow Calculations on Stretched Meshes
 J. Comput. Phys
, 1997
"... this paper are not intended for preconditioning in the limit of incompressibility. For typical viscous meshes, the Mach number remains sufficiently large, even in the cells near the wall, that the tip of the vorticity footprint remains distinguishable from the origin as in Fig. 7a. For most boundary ..."
Abstract

Cited by 33 (10 self)
 Add to MetaCart
(Show Context)
this paper are not intended for preconditioning in the limit of incompressibility. For typical viscous meshes, the Mach number remains sufficiently large, even in the cells near the wall, that the tip of the vorticity footprint remains distinguishable from the origin as in Fig. 7a. For most boundary layer cells, the Mach number is large enough that even the vorticity footprint is clustered well away from the origin as in Fig. 8a. The interaction between the preconditioner and multigrid algorithm is critical, since the preconditioner is chiefly responsible for damping the convective modes and the coarsening strategy is essential to damping the acoustic modes.
Highresolution FEMFCT schemes for multidimensional conservation laws
"... The fluxcorrectedtransport paradigm is generalized to implicit finite element schemes and nonlinear systems of hyperbolic conservation laws. In the scalar case, a nonoscillatory loworder method of upwind type is derived by elimination of negative offdiagonal entries of the discrete transport ope ..."
Abstract

Cited by 28 (16 self)
 Add to MetaCart
(Show Context)
The fluxcorrectedtransport paradigm is generalized to implicit finite element schemes and nonlinear systems of hyperbolic conservation laws. In the scalar case, a nonoscillatory loworder method of upwind type is derived by elimination of negative offdiagonal entries of the discrete transport operator. The difference between the discretizations of high and low order is decomposed into a sum of skewsymmetric antidiffusive fluxes. An iterative flux limiter independent of the time step is proposed for implicit schemes. The nonlinear antidiffusion is incorporated into the solution in the framework of a defect correction scheme preconditioned by the monotone loworder operator. In the case of a hyperbolic system, the global Jacobian matrix is assembled edgebyedge without resorting to numerical integration. Its loworder counterpart is constructed by rendering all offdiagonal blocks positive definite or adding scalar artificial diffusion proportional to the spectral radius of the Roe matrix. The coupled equations are solved in a segregated manner within an outer defect correction loop equipped with a blockdiagonal preconditioner. After a suitable synchronization, the correction factors evaluated for an arbitrary set of indicator variables are applied to the antidiffusive fluxes which are inserted into the global defect vector. The performance of the new algorithm is illustrated by numerical examples for scalar transport problems and the compressible Euler equations. Key Words: convectiondominated flows; hyperbolic conservation laws; flux correction; finite elements; implicit timestepping 1
AdjointBased Control of a New Eulerian Network Model of Air Traffic Flow
, 2006
"... An Eulerian network model for air traffic flow in the National Airspace System is developed and used to design flow control schemes which could be used by Air Traffic Controllers to optimize traffic flow. The model relies on a modified version of the Lighthill–Whitham–Richards (LWR) partial differe ..."
Abstract

Cited by 22 (4 self)
 Add to MetaCart
(Show Context)
An Eulerian network model for air traffic flow in the National Airspace System is developed and used to design flow control schemes which could be used by Air Traffic Controllers to optimize traffic flow. The model relies on a modified version of the Lighthill–Whitham–Richards (LWR) partial differential equation (PDE), which contains a velocity control term inside the divergence operator. This PDE can be related to aircraft count, which is a key metric in air traffic control. An analytical solution to the LWR PDE is constructed for a benchmark problem, to assess the gridsize required to compute a numerical solution at a prescribed accuracy. The Jameson–Schmidt–Turkel (JST) scheme is selected among other numerical schemes to perform simulations, and evidence of numerical convergence is assessed against this analytical solution. Linear numerical schemes are discarded because of their poor performance. The model is validated against actual air traffic data (ETMS data), by showing that the Eulerian description enables good aircraft count predictions, provided a good choice of numerical parameters is made. This model is then embedded as the key constraint in an optimization problem, that of maximizing the throughput at a destination airport while maintaining aircraft density below a legal threshold in a set of sectors of the airspace. The optimization problem is solved by constructing the adjoint problem of the linearized network control problem, which provides an explicit formula for the gradient. Constraints are enforced using a logarithmic barrier. Simulations of actual air traffic data and control scenarios involving several airports between Chicago and the U.S. East Coast demonstrate the feasibility of the method.
Dirichlet problems for some HamiltonJacobi equations with inequality constraints
 SIAM J. CONTROL OPTIM
, 2008
"... We use viability techniques for solving Dirichlet problems with inequality constraints (obstacles) for a class of Hamilton–Jacobi equations. The hypograph of the “solution” is defined as the “capture basin” under an auxiliary control system of a target associated with the initial and boundary condit ..."
Abstract

Cited by 17 (5 self)
 Add to MetaCart
(Show Context)
We use viability techniques for solving Dirichlet problems with inequality constraints (obstacles) for a class of Hamilton–Jacobi equations. The hypograph of the “solution” is defined as the “capture basin” under an auxiliary control system of a target associated with the initial and boundary conditions, viable in an environment associated with the inequality constraint. From the tangential condition characterizing capture basins, we prove that this solution is the unique “upper semicontinuous ” solution to the Hamilton–Jacobi–Bellman partial differential equation in the BarronJensen/Frankowska sense. We show how this framework allows us to translate properties of capture basins into corresponding properties of the solutions to this problem. For instance, this approach provides a representation formula of the solution which boils down to the Lax–Hopf formula in the absence of constraints.