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Boundary Layer Analysis for One-Dimensional Equations in Radiation Hydrodynamics

Author: HeChunXiang
Tutor: WangYaGuang
School: Shanghai Jiaotong University
Course: Applied Mathematics
Keywords: radiation hydrodynamics equations initial-boundaryvalue problem zero viscosity limit boundary layers analysis multi- scale analysis
CLC: O175.8
Type: Master's thesis
Year: 2012
Downloads: 28
Quote: 0
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Abstract


In this paper we mainly use multi-scale analysis methods, to analyze one-dimensionalisentropic radiation hydrodynamic problem as viscosity goes to zero, especially to de-scribe the boundary layers nearby the boundary. The radiation hydrodynamics is asubject that studies the transmission of thermal radiation in ?uid, and how the radia-tion affects the ?uid. Because the radiation energy density varies as the fourth powerof the temperature, to the ?uids at high temperatures(say, millions of degrees Kelvin),the energy and momentum densities of the radiation field may become dominate thequantities, so it’s of great importance to consider the equations of radiation term. Thetheory of radiation hydrodynamics owns a wide range of application, including in as-trophysics, laser fusion, supernove explosions.The isentropic radiation hydrodynamics system is coupled from the isentropicNavier-Stokes Equation with radiation term and the Boltzmann Equation of radiationtransmission. There is a difference between the solution of these equations and thesolution of inviscid system, hence the boundary layer appears. In this paper we studythe problem with multi-scale method, to derive the equations of inner solutions andboundary solutions, especially we illustrate the coupled relations between the bound-ary conditions of radiation terms in {x = 0} and density-velocity terms, then theinitial-boundary conditions of each order equations can be fixed. With the methods ofcharacteristics and differential equations theories, we eventually obtain the approxi-mate solutions of the original problem, which can be described as the composition ofthe solutions of inviscid radiation hydrodynamics equations and boundary layers.

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations > Boundary Value Problems
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