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Daniel Fuster (∂'Alembert)

Séminaire mécanique des fluides
Date: 08/04/2025 11:00

Regularization versus discretization errors in the presence of discontinuities
Understanding the sources of regularization and discretization errors in the presence of discontinuities is a challenging and important problem for several reasons. First, regularization methods allow the representation of solutions using functions with finite wavelengths. Also understanding the origin of these errors also paves the way for developing new methods capable of representing solutions with arbitrary accuracy, even when the gradients or the flux of the variable itself are discontinuous. Finally, in the context of Adaptive Mesh Refinement strategies, the ability to construct optimal grids that minimize numerical errors depends on the effectiveness of error estimation techniques in capturing errors introduced by both the mathematical model and the numerical method.

In this talk, we will demonstrate that errors can arise not only from the discretization of continuum operators but also from the modeling choices made to obtain a solution. This is particularly relevant in solvers relying on the one-fluid approach, continuum surface tension models, or the projection of singular forces onto a grid. By introducing an additional length scale in the model—larger than the grid size—we will analyze the relative contributions of these errors in various problems involving the solution of elliptic equations. We will show that regularization errors can be suppressed to arbitrary order, enabling the accurate representation of discontinuous solutions using relatively large band filters. Additionally, I will present preliminary results on the potential of the proposed methods to enhance the accuracy of numerical simulations for multicomponent systems.

 

 

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  • 08/04/2025 11:00