# Systematic Continuous Adjoint Approach to Viscous Aerodynamic Design on Unstructured Grids

@article{Castro2007SystematicCA, title={Systematic Continuous Adjoint Approach to Viscous Aerodynamic Design on Unstructured Grids}, author={Carlos Castro and Carlos Lozano and Francisco Palacios and E. Zuazua}, journal={AIAA Journal}, year={2007}, volume={45}, pages={2125-2139} }

DOI: 10.2514/1.24859 A continuous adjoint approach to aerodynamic design for viscous compressible flow on unstructured grids is developed. Sensitivity gradients arecomputed using tools ofshapedeformation of boundaryintegrals. Theresulting expressions involve second-order derivatives of the flow variables that require numerical solvers with greater than second-order accuracy. A systematic way of reducing the order of these terms is presented. The accuracy of the sensitivity derivatives is…

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## References

SHOWING 1-10 OF 32 REFERENCES

Aerodynamic design optimization on unstructured grids with a continuous adjoint formulation

- Engineering
- 1997

Continuous Adjoint Method for Unstructured Grids

- Engineering
- 2008

Adjoint-based shape optimization methods have proven to be computationally efficient for aerodynamic problems. The majority of the studies on adjoint methods have used structured grids to discretize…

Aerodynamic Shape Optimization of Complete Aircraft Configurations using Unstructured Grids

- Engineering
- 2004

This study has developed and validated a continuous adjoint formulation for unstructured grids for complex configurations and initiated a CAD based geometry handling process to support single and multidisciplinary analysis and design.

Numerical solution of the Euler equations by finite volume methods using Runge Kutta time stepping schemes

- Physics
- 1981

A new combination of a finite volume discretization in conjunction with carefully designed dissipative terms of third order, and a Runge Kutta time stepping scheme, is shown to yield an effective…

IMPLICIT SOLUTION OF THE NAVIER-STOKES EQUATIONS ON UNSTRUCTURED MESHES

- Computer Science
- 1997

An algorithm for the solution of the Navier-Stokes equations on unstructured meshes is described that employs a coupled algebraic multigrid (AMG) method to accelerate a two-sweep point implicit Gauss-Siedel relaxation scheme.

Adjoint equations in CFD: duality, boundary conditions and solution behaviour

- Mathematics
- 1997

The first half of this paper derives the adjoint equations for inviscid and viscous compressible flow, with the emphasis being on the correct formulation of the adjoint boundary conditions and…

A COMPARISON OF THE CONTINUOUS AND DISCRETE ADJOINT APPROACH TO AUTOMATIC AERODYNAMIC OPTIMIZATION

- Computer Science, Mathematics
- 2000

The objective is to study the trade-off between the complexity of the discretization of the adjoint equation for both the continuous and discrete approach, the accuracy of the resulting estimate of the gradient, and its impact on the computational cost to approach an optimum solution.

The design and application of upwind schemes on unstructured meshes

- Computer Science, Physics
- 1989

Cell-centered and mesh-vertex upwind finite-volume schemes are developed which utilize multi-dimensional monotone linear reconstruction procedures which differ from existing algorithms (even on structured meshes).

2-D Euler Shape Design on Nonregular Flows Using Adjoint Rankine-Hugoniot Relations

- Mathematics
- 2009

Optimal Shape Design (OSD) aims at flnding the minimum of a functional by controlling the Partial Difierential Equation (PDE) modeling the ∞ow using surface (domain boundaries) deformation…

Recent developments in high order K-exact reconstruction on unstructured meshes

- Physics
- 1993

This paper presents recent improvements in high-order K-exact reconstruction on unstructured meshes. The new reconstruction procedures are incorporated into a basic upwind finite-volume scheme…