Error-based mesh selection for efficient numerical simulations with variable parameters

Advanced numerical simulations often rely on mesh refinement techniques to control discretization errors while limiting computational cost. In parametric studies, however, repeatedly adapting the mesh for each operating condition can lead to significant overhead. To address this issue, we introduce the Error-based Mesh Selection (EMS) method, and its practical variant approximate EMS (A-EMS), which selects, for any given condition, a mesh from a precomputed library expected to minimize the discretization error. The method relies on Gaussian process models of restriction errors to predict, without additional model evaluations, the error associated with each library mesh. While EMS is formulated in a general setting, A-EMSrequires suitable projection operators and error estimators, which may limit its applicability depending on the discretization framework. The approach is assessed on an analytical oblique shock problem and on a supersonic scramjet configuration. In both cases, A-EMSachieves mesh selections close to the optimal choice, significantly outperforming distance-based strategies. In the scramjet test case, the average computational time per evaluation is reduced by a factor of approximately 6 compared to systematic mesh adaptation, while maintaining comparable accuracy. A library of about 32 meshes is sufficient to achieve the prescribed accuracy. Accounting for the cost of constructing the mesh library, the method becomes advantageous after a few tens to a few hundred evaluations, depending on the library size. These results demonstrate that A-EMSis particularly well suited for large parametric studies, such as uncertainty quantification, where the number of evaluations is high.