تقرير
A gradient-robust well-balanced scheme for the compressible isothermal Stokes problem
| العنوان: | A gradient-robust well-balanced scheme for the compressible isothermal Stokes problem |
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| المؤلفون: | Akbas, Mine, Gallouet, Thierry, Gassmann, Almut, Linke, Alexander, Merdon, Christian |
| سنة النشر: | 2019 |
| المجموعة: | Computer Science Mathematics Physics (Other) |
| مصطلحات موضوعية: | Mathematics - Numerical Analysis, Physics - Computational Physics, 76D07, 65N30, 65N12 |
| الوصف: | A novel notion for constructing a well-balanced scheme - a gradient-robust scheme - is introduced and a showcase application for a steady compressible, isothermal Stokes equations is presented. Gradient-robustness means that arbitrary gradient fields in the momentum balance are well-balanced by the discrete pressure gradient - if there is enough mass in the system to compensate the force. The scheme is asymptotic-preserving in the sense that it degenerates for low Mach numbers to a recent inf-sup stable and pressure-robust discretization for the incompressible Stokes equations. The convergence of the coupled FEM-FVM scheme for the nonlinear, isothermal Stokes equations is proved by compactness arguments. Numerical examples illustrate the numerical analysis, and show that the novel approach can lead to a dramatically increased accuracy in nearly-hydrostatic low Mach number flows. Numerical examples also suggest that a straight-forward extension to barotropic situations with nonlinear equations of state is feasible. |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1016/j.cma.2020.113069 |
| URL الوصول: | http://arxiv.org/abs/1911.01295 |
| رقم الأكسشن: | edsarx.1911.01295 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1016/j.cma.2020.113069 |
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