Efficient Functional-Based Adaptation for CFD Applications

TL;DR

This paper introduces a new efficient method for functional-based adaptation in CFD that uses a sparse approximate inverse of the Jacobian, reducing computational costs compared to traditional adjoint methods.

Contribution

The paper proposes a novel approach using a sparse approximate inverse for functional-based adaptation, avoiding the need for multiple adjoint solutions and simplifying implementation.

Findings

The method effectively adapts solutions for functionals of pressure and entropy.

It reduces computational cost by recycling the approximate inverse for multiple functionals.

Results demonstrate comparable accuracy to traditional adjoint-based adaptation.

Abstract

Adjoint methods have gained popularity in recent years for driving adaptation procedures which aim to reduce error in solution functionals. While adjoint methods have been proven effective for functional-based adaptation, the practical implementation of an adjoint method can be quite burdensome since code developers constantly need to ensure and maintain a dual consistent discretization as updates are made. Also, since most engineering problems consider multiple functionals, an adjoint solution must be obtained for each functional of interest which can increase the overall computational cost significantly. In this paper, an alternative to adjoints is presented which uses a sparse approximate inverse of the Jacobian of the residual to obtain approximate adjoint sensitivities for functional-based adaptation indicators. Since the approximate inverse need only be computed once, it can be recycled for any number of functionals making the new approach more efficient than a conventional adjoint method. This new method for functional-based adaptation will be tested using the quasi-1D nozzle problem, and results are presented for functionals of integrated pressure and entropy.