Steady Boussinesq convection: Parametric analyticity and computation

IF 2.6 2区 数学 Q1 MATHEMATICS, APPLIED
Jeremiah S. Lane, Benjamin F. Akers
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引用次数: 0

Abstract

Steady solutions to the Navier–Stokes equations with internal temperature forcing are considered. The equations are solved in two dimensions using the Boussinesq approximation to couple temperature and density fluctuations. A perturbative Stokes expansion is used to prove that that steady flow variables are parametrically analytic in the size of the forcing. The Stokes expansion is complemented with analytic continuation, via functional Padé approximation. The zeros of the denominator polynomials in the Padé approximants are observed to agree with a numerical prediction for the location of singularities of the steady flow solutions. The Padé representations not only prove to be good approximations to the true flow solutions for moderate intensity forcing, but are also used to initialize a Newton solver to compute large amplitude solutions. The composite procedure is used to compute steady flow solutions with forcing several orders of magnitude larger than the fixed-point method developed in previous work.

稳定的布辛斯对流:参数解析和计算
研究考虑了具有内部温度强迫的纳维-斯托克斯方程的稳定解法。该方程在两个维度上使用布森斯近似来耦合温度和密度波动。使用扰动斯托克斯展开来证明稳定流变量在强迫大小上是参数解析的。通过函数帕代近似,斯托克斯展开得到了分析延续的补充。帕代近似中分母多项式的零点与稳定流解奇点位置的数值预测一致。事实证明,帕代近似值不仅能很好地近似中等强度强迫下的真实流解,还能用于牛顿求解器的初始化,以计算大振幅解。该复合程序用于计算稳定流解,其强迫比之前工作中开发的定点法大几个数量级。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Studies in Applied Mathematics
Studies in Applied Mathematics 数学-应用数学
CiteScore
4.30
自引率
3.70%
发文量
66
审稿时长
>12 weeks
期刊介绍: Studies in Applied Mathematics explores the interplay between mathematics and the applied disciplines. It publishes papers that advance the understanding of physical processes, or develop new mathematical techniques applicable to physical and real-world problems. Its main themes include (but are not limited to) nonlinear phenomena, mathematical modeling, integrable systems, asymptotic analysis, inverse problems, numerical analysis, dynamical systems, scientific computing and applications to areas such as fluid mechanics, mathematical biology, and optics.
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