کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6933111 | 867592 | 2014 | 20 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Adaptive change of basis in entropy-based moment closures for linear kinetic equations
ترجمه فارسی عنوان
تغییر سازگاری پایه در بستر لحظه ای مبتنی بر آنتروپی برای معادلات سینتیکی خطی
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کلمات کلیدی
بهینه سازی محدب، امکان اجرا، نظریه جنبشی، حمل و نقل، بستن آنتروپی، معادلات لحظه ای،
موضوعات مرتبط
مهندسی و علوم پایه
مهندسی کامپیوتر
نرم افزارهای علوم کامپیوتر
چکیده انگلیسی
Entropy-based (MN) moment closures for kinetic equations are defined by a constrained optimization problem that must be solved at every point in a space-time mesh, making it important to solve these optimization problems accurately and efficiently. We present a complete and practical numerical algorithm for solving the dual problem in one-dimensional, slab geometries. The closure is only well-defined on the set of moments that are realizable from a positive underlying distribution, and as the boundary of the realizable set is approached, the dual problem becomes increasingly difficult to solve due to ill-conditioning of the Hessian matrix. To improve the condition number of the Hessian, we advocate the use of a change of polynomial basis, defined using a Cholesky factorization of the Hessian, that permits solution of problems nearer to the boundary of the realizable set. We also advocate a fixed quadrature scheme, rather than adaptive quadrature, since the latter introduces unnecessary expense and changes the computationally realizable set as the quadrature changes. For very ill-conditioned problems, we use regularization to make the optimization algorithm robust. We design a manufactured solution and demonstrate that the adaptive-basis optimization algorithm reduces the need for regularization. This is important since we also show that regularization slows, and even stalls, convergence of the numerical simulation when refining the space-time mesh. We also simulate two well-known benchmark problems. There we find that our adaptive-basis, fixed-quadrature algorithm uses less regularization than alternatives, although differences in the resulting numerical simulations are more sensitive to the regularization strategy than to the choice of basis.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational Physics - Volume 258, 1 February 2014, Pages 489-508
Journal: Journal of Computational Physics - Volume 258, 1 February 2014, Pages 489-508
نویسندگان
Graham W. Alldredge, Cory D. Hauck, Dianne P. OʼLeary, André L. Tits,