Mean Mesh Adaptation for Efficient CFD Simulations with Operating Conditions Variability

TL;DR

This paper introduces a novel mesh adaptation method that constructs a single mesh optimized for a range of operating conditions, reducing computational costs in CFD simulations with variable parameters.

Contribution

The work proposes a new approach to build a unique mesh that minimizes average error across multiple operating conditions, improving efficiency in uncertainty quantification tasks.

Findings

Effective in reducing computational cost for variable conditions

Demonstrated on Burgers and Euler flow problems

Achieves comparable accuracy with fewer meshes

Abstract

When numerically solving partial differential equations, for a given problem and operating condition, adaptive mesh refinement (AMR) has proven its efficiency to automatically build a discretization achieving a prescribed accuracy at low cost. However, with continuously varying operating conditions, such as those encountered in uncertainty quantification, adapting a mesh for each evaluated condition becomes complex and computationally expensive. To enable more effective error and cost control, this work introduces a novel approach to mesh adaptation. The method consists in building a unique adapted mesh that aims at minimizing the average error for a continuous set operating conditions. In the proposed implementation, this unique mesh is built iteratively, informed by an estimate of the local average error over a reduced set of sample conditions. The effectiveness and performance of the method are demonstrated on a one-dimensional Burgers equation and a two-dimensional Euler scramjet shocked flow configurations.