Adaptive mesh refinement for global stability analysis of transitional flows

TL;DR

This paper presents a novel adaptive mesh refinement approach for global stability analysis of incompressible transitional flows, improving accuracy by reducing numerical errors in base flow, direct, and adjoint solutions.

Contribution

It introduces a new AMR methodology tailored for stability analysis, enabling independent mesh design for different flow solutions to enhance accuracy.

Findings

Validated on 2D flow past a circular cylinder

Successfully computed spectra of linearised Navier-Stokes operators

Demonstrated improved accuracy with adaptive meshes

Abstract

In this work, we introduce the novel application of the adaptive mesh refinement (AMR) technique in the global stability analysis of incompressible flows. The design of an accurate mesh for transitional flows is crucial. Indeed, an inadequate resolution might introduce numerical noise that triggers premature transition. With AMR, we enable the design of three different and independent meshes for the non-linear base flow, the linear direct and adjoint solutions. Each of those is designed to reduce the truncation and quadrature errors for its respective solution, which are measured via the spectral error indicator. We provide details about the workflow and the refining procedure. The numerical framework is validated for the two-dimensional flow past a circular cylinder, computing a portion of the spectrum for the linearised direct and adjoint Navier-Stokes operators.