تقرير
A fully implicit, asymptotic-preserving, semi-Lagrangian algorithm for the time dependent anisotropic heat transport equation
| العنوان: | A fully implicit, asymptotic-preserving, semi-Lagrangian algorithm for the time dependent anisotropic heat transport equation |
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| المؤلفون: | Koshkarov, O., Chacon, L. |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics Mathematical Physics Physics (Other) |
| مصطلحات موضوعية: | Physics - Plasma Physics, Mathematical Physics |
| الوصف: | In this paper, we extend the operator-split asymptotic-preserving, semi-Lagrangian algorithm for time dependent anisotropic heat transport equation proposed in [Chac\'on et al., JCP, 272, 719-746, 2014] to use a fully implicit time integration with backward differentiation formulas. The proposed implicit method can deal with arbitrary heat-transport anisotropy ratios \chi_{\parallel}/\chi_{\perp}\ggg1 (with \chi_{\parallel}, \chi_{\perp} the parallel and perpendicular heat diffusivities, respectively) in complicated magnetic field topologies in an accurate and efficient manner. The implicit algorithm is second-order accurate temporally, has favorable positivity preservation properties, and demonstrates an accurate treatment at boundary layers (e.g., island separatrices), which was not ensured by the operator-split implementation. The condition number of the resulting algebraic system is independent of the anisotropy ratio, and is inverted with preconditioned GMRES. We propose a simple preconditioner that renders the linear system compact, resulting in mesh-independent convergence rates for topologically simple magnetic fields, and convergence rates scaling as \sim(N\Delta t)^{1/4} (with N the total mesh size and \Delta t the timestep) in topologically complex magnetic-field configurations. We demonstrate the accuracy and performance of the approach with test problems of varying complexity, including an analytically tractable boundary-layer problem in a straight magnetic field, and a topologically complex magnetic field featuring magnetic islands with extreme anisotropy ratios (\chi_{\parallel}/\chi_{\perp}=10^{10}). |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2404.08771 |
| رقم الأكسشن: | edsarx.2404.08771 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |