تقرير
Generalized upwind summation-by-parts operators and their application to nodal discontinuous Galerkin methods
| العنوان: | Generalized upwind summation-by-parts operators and their application to nodal discontinuous Galerkin methods |
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| المؤلفون: | Glaubitz, Jan, Ranocha, Hendrik, Winters, Andrew R., Schlottke-Lakemper, Michael, Öffner, Philipp, Gassner, Gregor |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis, 65M12, 65M60, 65M70, 65D25 |
| الوصف: | There is a pressing demand for robust, high-order baseline schemes for conservation laws that minimize reliance on supplementary stabilization. In this work, we respond to this demand by developing new baseline schemes within a nodal discontinuous Galerkin (DG) framework, utilizing upwind summation-by-parts (USBP) operators and flux vector splittings. To this end, we demonstrate the existence of USBP operators on arbitrary grid points and provide a straightforward procedure for their construction. Our method encompasses a broader class of USBP operators, not limited to equidistant grid points. This approach facilitates the development of novel USBP operators on Legendre--Gauss--Lobatto (LGL) points, which are suited for nodal discontinuous Galerkin (DG) methods. The resulting DG-USBP operators combine the strengths of traditional summation-by-parts (SBP) schemes with the benefits of upwind discretizations, including inherent dissipation mechanisms. Through numerical experiments, ranging from one-dimensional convergence tests to multi-dimensional curvilinear and under-resolved flow simulations, we find that DG-USBP operators, when integrated with flux vector splitting methods, foster more robust baseline schemes without excessive artificial dissipation. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2406.14557 |
| رقم الأكسشن: | edsarx.2406.14557 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |