• Corpus ID: 246063419

Singularity and Mesh Divergence of Inviscid Adjoint Solutions at Solid Walls

@article{Lozano2022SingularityAM,
  title={Singularity and Mesh Divergence of Inviscid Adjoint Solutions at Solid Walls},
  author={Carlos Lozano and Jorge Pons{\'i}n},
  journal={ArXiv},
  year={2022},
  volume={abs/2201.08129}
}
The mesh divergence problem occurring at subsonic and transonic speeds with the adjoint Euler equations is reviewed. By examining a recently derived analytic adjoint solution, it is shown that the explanation is that the adjoint solution is singular at the wall. The wall singularity is caused by the adjoint singularity at the trailing edge, but not in the way it was previously conjectured. 
Analytic adjoint solutions for the 2-D incompressible Euler equations using the Green's function approach
TLDR
The Green's function approach of Giles and Pierce is used to build the lift and drag based analytic adjoint solutions for the two-dimensional incompressible Euler equations around irrotational base flows, and the drag-based adjoint solution turns out to have a very simple closed form in terms of the flow variables.

References

SHOWING 1-10 OF 30 REFERENCES
Anomalous Mesh Dependence of Adjoint Solutions Near Walls in Inviscid Flows Past Configurations with Sharp Trailing Edges
We show that 2D and 3D inviscid continuous and discrete drag and lift adjoint solutions past sharp trailing edges are generically strongly mesh dependent at and near the wall and do not converge as
Watch Your Adjoints! Lack of Mesh Convergence in Inviscid Adjoint Solutions
It has been long known that 2D and 3D inviscid adjoint solutions are generically singular at sharp trailing edges. In this paper, a concurrent effect is described by which wall boundary values of 2...
Analytic adjoint solutions for the quasi-one-dimensional Euler equations
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
Analytic adjoint solutions for the 2-D incompressible Euler equations using the Green's function approach
TLDR
The Green's function approach of Giles and Pierce is used to build the lift and drag based analytic adjoint solutions for the two-dimensional incompressible Euler equations around irrotational base flows, and the drag-based adjoint solution turns out to have a very simple closed form in terms of the flow variables.
Adjoint equations in CFD: duality, boundary conditions and solution behaviour
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
Entropy and Adjoint Methods
  • C. Lozano
  • Mathematics, Environmental Science
    J. Sci. Comput.
  • 2019
TLDR
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.
Systematic Continuous Adjoint Approach to Viscous Aerodynamic Design on Unstructured Grids
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
Numerical solution of the Euler equations by finite volume methods using Runge Kutta time stepping schemes
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
...
...