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69
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 ..."
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Cited by 107 (45 self)
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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 ..."
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Cited by 37 (19 self)
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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
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 ..."
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Cited by 34 (24 self)
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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 ..."
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Cited by 30 (25 self)
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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.
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 ..."
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Cited by 17 (7 self)
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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.
Aerodynamic Shape Optimization of Wings including Planform Variations
 AIAA paper 20030210, 41st Aerospace Sciences Meeting & Exhibit
, 2003
"... This paper describes the formulation of optimization techniques based on control theory for aerodynamic shape design in inviscid compressible flow modelled by the Euler equations. The design methodology has been extended to include wing planform optimization ..."
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Cited by 15 (13 self)
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This paper describes the formulation of optimization techniques based on control theory for aerodynamic shape design in inviscid compressible flow modelled by the Euler equations. The design methodology has been extended to include wing planform optimization
Comparison of Several Spatial Discretizations for the NavierStokes Equations
 of 10 American Institute of Aeronautics and Astronautics
, 1989
"... Grid convergence studies for subsonic and transonic flows over airfoils are presented in order to compare the accuracy of several spatial discretizations for the compressible Navier–Stokes equations. The discretizations include the following schemes for the inviscid fluxes: (1) secondorderaccurate ..."
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Cited by 12 (6 self)
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Grid convergence studies for subsonic and transonic flows over airfoils are presented in order to compare the accuracy of several spatial discretizations for the compressible Navier–Stokes equations. The discretizations include the following schemes for the inviscid fluxes: (1) secondorderaccurate centered differences with thirdorder matrix numerical dissipation, (2) the secondorder convective upstream split pressure scheme (CUSP), (3) thirdorder upwindbiased differencing with Roe’s fluxdifference splitting, and (4) fourthorder centered differences with thirdorder matrix numerical dissipation. The first three are combined with secondorder differencing for the grid metrics and viscous terms. The fourth discretization uses fourthorder differencing for the grid metrics and viscous terms, as well as higherorder approximations near boundaries and for the numerical integration used to calculate forces and moments. The results indicate that the discretization using higherorder approximations for all terms is substantially more accurate than the others, producing less than two percent numerical error in lift and drag components on grids with less than 13,000 nodes for subsonic cases and less than 18,000 nodes for transonic cases. Since the cost per grid node of all of the discretizations studied is comparable, the higherorder discretization produces solutions of a given accuracy much more efficiently than the others. c ○ 2000 Academic Press Key Words: aerodynamics; Navier–Stokes equations; finitedifference methods; higherorder methods.
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 ..."
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Cited by 12 (3 self)
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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.
Acceleration of Convergence to a Periodic Steady State in Turbomachinery Flows
 AIAA paper 010152, AIAA 39th Aerospace Sciences Meeting
, 2001
"... This paper present s at echnique usedt o accelerat et he convergence ofunst eady calculat ions oft imeperiodic flowst o a periodic st eady st at e. The basis oft he procedure is t e use of t e discret e Fouriert sform int ime, and is similart ot he harmonic balance proceduret hat has been pursued ..."
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Cited by 12 (11 self)
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This paper present s at echnique usedt o accelerat et he convergence ofunst eady calculat ions oft imeperiodic flowst o a periodic st eady st at e. The basis oft he procedure is t e use of t e discret e Fouriert sform int ime, and is similart ot he harmonic balance proceduret hat has been pursued by Hallet . al. Thet echnique is amenablet o parallel processing, and convergence accelerat t echniques such as mult grid and implicit residual averaging. The comput at ional e#ciency oft his met hod is compared wit h dual t imest epping algorit hms. Sample calculat ions are provided, and a comparison bet ween solutI s wit varying t mporal resolutI is present d. The result show tat t e comput al e#ciency of t e harmonic balance t chnique is largely a funct of t et emporal resolut ion. Init ial experiment s confirmt he promise oft he harmonic balance met hodt o achieve significant reduct ions in comput at ional cost .
Accelerating ThreeDimensional NavierStokes Calculations
, 1997
"... This paper addresses the widely observed breakdown in multigrid performance for turbulent ..."
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Cited by 10 (3 self)
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This paper addresses the widely observed breakdown in multigrid performance for turbulent