BROADCAST: A high-order compressible CFD toolbox for stability and sensitivity using Algorithmic Differentiation

TL;DR

BROADCAST is an open-source CFD toolbox that uses Algorithmic Differentiation to accurately compute high-order derivatives, enabling advanced stability and sensitivity analyses of compressible flows.

Contribution

It introduces a high-order, open-source CFD toolkit that integrates Algorithmic Differentiation for precise derivative extraction and stability analysis of compressible flows.

Findings

Validated on cylinder flow at low Mach number

Applied to hypersonic boundary layer stability

Demonstrates accurate derivative and sensitivity computations

Abstract

The evolution of any complex dynamical system is described by its state derivative operators. However, the extraction of the exact N-order state derivative operators is often inaccurate and requires approximations. The open-source CFD code called BROADCAST discretises the compressible Navier-Stokes equations and then extracts the linearised Nderivative operators through Algorithmic Differentiation (AD) providing a toolbox for laminar flow dynamic analyses. Furthermore, the gradients through adjoint derivation are extracted either by transposition of the linearised operator or through the backward mode of the AD tool. The software includes base-flow computation and linear global stability analysis via eigen-decomposition of the linearised operator or via singular value decomposition of the resolvent operator. Sensitivity tools as well as weakly nonlinear analysis complete the package. The numerical method for the spatial discretisation of the equations consists of a finite-difference high-order shock-capturing scheme applied within a finite volume framework on 2D curvilinear structured grids. The stability and sensitivity tools are demonstrated on two cases: a cylinder flow at low Mach number and a hypersonic boundary layer.