Ellipticity of normal mode initialization equations

Bourchtein A.

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Ellipticity of normal mode initialization equations

机译：常态初始化方程的椭圆性

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Criterions of ellipticity of nonlinear normal mode initialization systems with various closure conditions are obtained for different atmospheric models. These present the necessary conditions of well-posedness of correspondent differential boundary value problems. It is demonstrated that initialization with fixed geopotential and initialization of internal baroclinic modes are ill-posed problems. In these cases a divergence of iterative process of numerical solution of initialization equations is a practical consequence of ill-posedness of differential problems. (C) 2002 Elsevier Science Inc. All rights reserved. [References: 21]

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《Applied mathematics and computation》 |2002年第1期|共19页
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Bourchtein A.;
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正文语种 eng
中图分类应用数学;
关键词
Atmospheric models; Normal mode initialization; Boundary value problems; Ellipticity criterions;

机译：大气模型;正常模式初始化;边值问题;椭圆率准则;

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1. Ellipticity of normal mode initialization equations [J] . Bourchtein A. Applied mathematics and computation . 2002,第1期

机译：常态初始化方程的椭圆性
2. Rotating black holes in the FI-gauged N = 2, D = 4 ${\overset{ˉ}{? P}}^{n}$ $$ {overline{mathbb{C}mathrm{P}}}^{mathrm{n}} $$ model [J] . Nicoletta Daniele, Federico Faedo, Dietmar Klemm, The journal of high energy physics . 2019,第3期

机译：在文件中旋转黑洞，d = 4 $？pˉn$$ { overline { mathbb {c} mathrm {p}} ^ { mathrm {n}} $$ Model$
3. Large-N $? ?^{N ? 1}$ $$ mathbb{C}{mathrm{mathbb{P}}}^{mathrm{N}-1} $$ sigma model on a finite interval and the renormalized string energy [J] . Alessandro Betti, Stefano Bolognesi, Sven Bjarke Gudnason, The journal of high energy physics . 2018,第1期

机译：light-n < arequationsource格式=“mathml”> $？？< / mi>nα\leq1$$ mathbb {c} { mathrm { mathbb {p}}} ^ { mathrm {n} -1} $$ Sigma模型有限间隔和重整化串能量$
4. Equations of an elliptic boundary layer in shells of revolution under shock normal edge loading [C] . G A Baregamyan, I V Kirillova, L Yu Kossovich International Conference on Topical Problems of Continuum Mechanics . 2017

机译：休克正常边缘加载下革命壳中椭圆边界层的方程
5. Topics in nonlinear elliptic equations: (1) Bifurcation theory of nonlinear elliptic equations; (2) Spike layer solutions of the Cahn-Hilliard equation. [D] . Shi, Junping. 1998

机译：非线性椭圆方程的主题：（1）非线性椭圆方程的分岔理论；（2）Cahn-Hilliard方程的尖峰层解。
6. Colloquium PaperNonlinear partial differential equations and applications: Some nonlinear elliptic equations from geometry [O] . YanYan Li 2007

机译：非线性偏微分方程及其应用：几何学中的一些非线性椭圆方程
7. This article presents a new numerical model describing the behaviour of a thermally thick wood sample exposed to high solar heat flux (above 1 MW/m2). A preliminary study based on dimensionless numbers is used to classify the problem and support model building assumptions. Then, a model based on mass, momentum and energy balance equations is proposed. These equations are coupled with liquid-vapour drying model and pseudo species biomass degradation model. By comparing to a former experimental study, preliminary results have shown that these equations are not enough to accurately predict biomass behaviour under high solar heat flux. Indeed, a char layer acting as radiative shield forms on the sample exposed surface. In addition to this classical set of equations, it is mandatory to take into account radiation penetration into the medium. Furthermore, as biomass contains water, medium deformation consecutively to char steam gasification must also be implemented. Finally, with the addition of these two strategies, the model is able to properly capture the degradation of biomass when exposed to high radiative heat flux over a range of sample initial moisture content. Additional insights of biomass behaviour under high solar heat flux were also derived. Drying, pyrolysis and gasification fronts are present at the same time inside of the sample. The coexistence of these three thermochemical fronts leads to char gasification by the steam produced from drying of the sample, which it is the main phenomenon behind medium ablation. [O] . Pozzobon, Victor, Salvador, Sylvain, Bézian, Jean Jacques 2018

机译：本文提供了一个新的数值模型，该模型描述了暴露于高太阳热通量（高于1 / MW / m2）的热厚木材样品的行为。基于无量纲数的初步研究用于对问题进行分类并支持模型构建假设。然后，提出了一种基于质量，动量和能量平衡方程的模型。这些方程式与液体蒸汽干燥模型和假物种生物质降解模型耦合。通过与以前的实验研究进行比较，初步结果表明，这些方程不足以准确预测高太阳热通量下的生物量行为。的确，在样品暴露的表面上形成了充当辐射屏蔽层的炭层。除了这套经典的方程式之外，还必须考虑到辐射向介质的渗透。此外，由于生物质中含有水，因此还必须在炭蒸气汽化后进行连续的介质变形。最后，通过添加这两种策略，该模型能够在一定范围的样品初始水分含量下暴露于高辐射热通量的情况下，正确捕获生物质的降解。还得出了在高太阳热通量下生物量行为的其他见解。样品内部同时存在干燥，热解和气化前沿。这三个热化学前沿的共存会导致样品干燥产生的蒸汽产生焦炭气化，这是介质烧蚀的主要现象。
8. On a Normal Form for Second Order Elliptic Equations and Constructive Methods for Dirichlet's Problem. [R] . Gilbert, R. P., Hsiao, G. C. 1974

机译：关于二阶椭圆方程的正规形式及Dirichlet问题的构造方法。

Ellipticity of normal mode initialization equations

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