A posteriori analysis for dynamic model adaptation in convection dominated problems

TL;DR

This paper introduces an a posteriori error indicator for adaptive approximation of fluid flow models, enabling efficient model and mesh adaptation in convection-dominated problems, exemplified by Navier-Stokes and Euler equations.

Contribution

It develops a novel a posteriori error indicator that guides both mesh and model adaptivity for complex fluid flow simulations.

Findings

Effective identification of regions suitable for model simplification.

Improved computational efficiency in fluid flow simulations.

Validated approach on Navier-Stokes and Euler equations.

Abstract

In this work we present an a posteriori error indicator for approximation schemes of Runge-Kutta-discontinuous-Galerkin type arising in applications of compressible fluid flows. The purpose of this indicator is not only for mesh adaptivity, we also make use of this to drive model adaptivity. This is where a perhaps costly complex model and a cheaper simple model are solved over different parts of the domain. The a posteriori bound we derive indicates the regions where the complex model can be relatively well approximated with the cheaper one. One such example which we choose to highlight is that of the Navier-Stokes-Fourier equations approximated by Euler's equations.