کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
519473 867667 2011 21 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A discontinuous Galerkin finite-element method for a 1D prototype of the Boltzmann equation
موضوعات مرتبط
مهندسی و علوم پایه مهندسی کامپیوتر نرم افزارهای علوم کامپیوتر
پیش نمایش صفحه اول مقاله
A discontinuous Galerkin finite-element method for a 1D prototype of the Boltzmann equation
چکیده انگلیسی

To develop and analyze new computational techniques for the Boltzmann equation based on model or approximation adaptivity, it is imperative to have disposal of a compliant model problem that displays the essential characteristics of the Boltzmann equation and that admits the extraction of highly accurate reference solutions. For standard collision processes, the Boltzmann equation itself fails to meet the second requirement for d = 2, 3 spatial dimensions, on account of its setting in 2d, while for d = 1 the first requirement is violated because the Boltzmann equation then lacks the convergence-to-equilibrium property that forms the substructure of simplified models. In this article we present a numerical investigation of a new one-dimensional prototype of the Boltzmann equation. The underlying molecular model is endowed with random collisions, which have been fabricated such that the corresponding Boltzmann equation exhibits convergence to Maxwell–Boltzmann equilibrium solutions. The new Boltzmann model is approximated by means of a discontinuous Galerkin (DG) finite-element method. To validate the one-dimensional Boltzmann model, we conduct numerical experiments and compare the results with Monte-Carlo simulations of equivalent molecular-dynamics models.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Computational Physics - Volume 230, Issue 15, 1 July 2011, Pages 6115–6135
نویسندگان
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