2024/12/02 by Dornier, Hugo, Maître, Olivier P Le, Congedo, Pietro M +3
#Computational Physics (physics.comp-ph) #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn)
paper · doi:10.48550/arxiv.2412.01274
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.