Nonlinear Elimination in Aerodynamic
Analysis and Design Optimization

Context

Why is the Problem So Difficult?

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Why Aren’t These Difficulties Fatal?

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Capacitance Matrices and Fast Solvers

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Transpiration Modeling of Boundary Movement

Transpiration Boundary Conditions

“One Term” Transpiration

“Two Term” Transpiration

Two Term Flux Box Argument

Mixed Transpiration

The Engineering Optimization Experience

Mathematical Aerodynamic Optimization Issues

Airfoil Geometries for Multipoint Airfoil Drag Minimization

Drag Rise Curves for Multipoint Airfoil Drag Minimization

Sensitivity of Design to Constraint Specification Minimize the Maximum Mach Number

Typical Constraints for Wing Design

Wind Tunnel Drag Rises For Conventional and Optimized Wing

Multipoint Design Optimization Using TRANAIR

Geometry Parameterizations for Airfoil Design

Airfoil Drag Minimization With Spline Mode Shapes vs. Curvature Variables

Airfoil Drag Minimization

Universal Lagrangian Optimization Formulation

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TRANAIR Multipoint Design Flow Chart

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Design Prediction About Solution With Shock

Airfoil Design Least Squares Case

Convergence Of Various Globalization Methods For Inviscid Airfoil Design

Target Pressure Distributions For Viscous And Challenging Inviscid Cases

Convergence Of Globalization Methods For Challenging Design Least Squares Case

Convergence Of Various Globalization Methods For Viscous Airfoil Design

Convergence Of Various Globalization Methods For Separated Viscous Airfoil Design

Summary And Future Developments