Singularity and Mesh Divergence of Inviscid Adjoint Solutions at Solid Walls

TL;DR

This paper investigates the divergence issues of adjoint solutions at solid walls in fluid dynamics, revealing that the singularity originates from the trailing edge rather than previous assumptions, impacting numerical methods at subsonic and transonic speeds.

Contribution

It provides a new analytic explanation for the wall singularity in adjoint solutions, challenging prior conjectures and improving understanding of mesh divergence problems.

Findings

Adjoint solutions are singular at the wall due to trailing edge effects.

The divergence is not caused by previously assumed mechanisms.

Understanding the singularity helps improve numerical stability in simulations.

Abstract

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.