Report
A Particle Method without Remeshing
| العنوان: | A Particle Method without Remeshing |
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| المؤلفون: | Kirchhart, Matthias, Rieger, Christian |
| سنة النشر: | 2019 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis, 65M75, 65D07, 65D32 |
| الوصف: | We propose a simple tweak to a recently developed regularisation scheme for particle methods. This allows us to chose the particle spacing $h$ proportional to the regularisation length $\sigma$ and achieve optimal error bounds of the form $\mathcal{O}(\sigma^n)$, $n\in\mathbb{N}$, without any need of remeshing. We prove this result for the linear advection equation but also carry out high-order experiments on the full Navier--Stokes equations. In our experiments the particle methods proved to be highly accurate, long-term stable, and competitive with discontinuous Galerkin methods. |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1137/19M1299864 |
| URL الوصول: | http://arxiv.org/abs/1909.07449 |
| رقم الانضمام: | edsarx.1909.07449 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1137/19M1299864 |
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