High-resolution solutions of nonlinear, advection-dominated problems using a generalized finite element method
Autor: | Shilt, Troy, O'Hara, Patrick, McNamara, Jack J. |
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Rok vydání: | 2021 |
Předmět: | |
Druh dokumentu: | Working Paper |
Popis: | Traditional finite element approaches are well-known to introduce spurious oscillations when applied to advection-dominated problems. We explore alleviation of this issue from the perspective of a generalized finite element formulation, which enables stabilization through an enrichment process. The presented work uses solution-tailored enrichments for the numerical solution of the one-dimensional, unsteady Burgers equation. Mainly, generalizable exponential and hyperbolic tangent enrichments effectively capture local, steep boundary layer/shock features. Results show natural alleviation of oscillations and return smooth numerical solutions over coarse grids. Additionally, significantly improved error levels are observed compared to Lagrangian finite element methods. Comment: 26 pages, 34 figures |
Databáze: | arXiv |
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