Analytic adjoint solutions for the 2-D incompressible Euler equations using the Green's function approach
@article{Lozano2022AnalyticAS, title={Analytic adjoint solutions for the 2-D incompressible Euler equations using the Green's function approach}, author={Carlos Lozano and Jorge Pons{\'i}n}, journal={Journal of Fluid Mechanics}, year={2022}, volume={943} }
Abstract The Green's function approach of Giles and Pierce (J. Fluid Mech., vol. 426, 2001, pp. 327–345) is used to build the lift and drag based analytic adjoint solutions for the two-dimensional incompressible Euler equations around irrotational base flows. The drag-based adjoint solution turns out to have a very simple closed form in terms of the flow variables and is smooth throughout the flow domain, while the lift-based solution is singular at rear stagnation points and sharp trailing…
One Citation
Singularity and Mesh Divergence of Inviscid Adjoint Solutions at Solid Walls
- PhysicsArXiv
- 2022
The mesh divergence problem occurring at subsonic and transonic speeds with the adjoint Euler equations is reviewed and it is shown that the explanation is that the adjointed solution is singular at the wall.
References
SHOWING 1-10 OF 39 REFERENCES
Analytic adjoint solutions for the quasi-one-dimensional Euler equations
- MathematicsJournal of Fluid Mechanics
- 2001
The analytic properties of adjoint solutions are examined for the quasi-one-dimensional Euler equations. For shocked flow, the derivation of the adjoint problem reveals that the adjoint variables are…
Entropy and Adjoint Methods
- Mathematics, Environmental ScienceJ. Sci. Comput.
- 2019
This paper builds the adjoint solution that corresponds to this representation of the drag and investigates its relation to the entropy variables, which are linked to the integrated residual of the entropy transport equation.
On the proper treatment of grid sensitivities in continuous adjoint methods for shape optimization
- MathematicsJ. Comput. Phys.
- 2015
The theory and application of eulerlets
- EngineeringPhysics of Fluids
- 2019
Consider a fixed body in a uniform flow field in the limit as the Reynolds number approaches infinity and the flow field remains steady. Instead of using standard techniques and theory for describing…
Singularity and Mesh Divergence of Inviscid Adjoint Solutions at Solid Walls
- Physics
- 2022
The mesh divergence problem occurring at subsonic and transonic speeds with the adjoint Euler equations is reviewed and it is shown that the explanation is that the adjointed solution is singular at the wall.
On mesh sensitivities and boundary formulas for discrete adjoint-based gradients in inviscid aerodynamic shape optimization
- MathematicsJ. Comput. Phys.
- 2017
Improved- lift and drag estimates using adjoint Euler equations
- Mathematics
- 1999
This paper demonstrates the use of adjoint error analysis to improve the order of accuracy of integral functionals obtained from CFD calculations. Using second order accurate finite element solutions…
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…
Systematic Continuous Adjoint Approach to Viscous Aerodynamic Design on Unstructured Grids
- Mathematics
- 2007
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…