New development of convective reaction-diffusion systems and validation of numerical computation

对流反应扩散系统新进展及数值计算验证

基本信息

批准号：
16340042
负责人：
OHARU Shinnosuke
金额：
$ 6.66万
依托单位：
Chuo University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (B)
财政年份：
2004
资助国家：
日本
起止时间：
2004 至 2006
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-16340042/
关键词：
Evolution operator Convective reaction-diffusion system Computational fluid dynamics Nonlinear pertuebation of analytic semigroup Multicomponent multiphase fluid phenomena Mathematical modeling of nonlinear Numerical simulation Validation of

项目摘要

1. Researches on environmental fluids which are typical examples of multicomponent multiphase fluids. The continuous models have been obtained as coupled systems of Navier-Stokes systems and convective reaction-diffusion systems. Numerical models which are consistent with the continuous models were formulated as high precision, upwind and TVD schemes, and numerical simulations based on those models have been performed.2. Fluid flow analysis around structures in environmental fluids. Numerical models for convective reaction-diffusion phenomena in environmental fluids have been developed. In particular, numerical analysis of air flows and motion of environmental pollutants in the over complex geographical topographies have been made.3. Studies in time-dependent nonlinear perturbations of integrated semigroups. Time-dependent semilinear evolution equations are treated from the point of view of nonlinear evolution operator theory and have been applied to various mathematical models formulated as large-scale semilinear systems of partial differential equations.4. The mathematical approach to HIV infection process and HAART therapies. Mathematical models of HIV disease progressions are formulated from the point of microbiology and physiology of HIV infection process in the immune system of an individual infected patient. The results of computer simulations based an the model agree with clinical data.5. Researches on time-dependent nonlinear perturbations of analytic semigroups. A general theory for time-dependents nonlinear perturbation of analytic semigroups have been advanced and a characterization of the existence of nonlinear evolution operators has been obtained in terms of their semilinear generators. As a particular application of this theory, a bone remodeling model was completely solved.

1、多组分多相流体典型代表环境流体的研究。连续模型是作为纳维-斯托克斯系统和对流反应扩散系统的耦合系统获得的。建立了与连续模型一致的数值模型，包括高精度、迎风式和TVD方案，并基于这些模型进行了数值模拟。 2．环境流体中结构周围的流体流动分析。环境流体中对流反应扩散现象的数值模型已经开发出来。特别是对过于复杂的地理地形中的气流和环境污染物的运动进行了数值分析。 3．积分半群的瞬态非线性扰动研究。含时半线性演化方程是从非线性演化算子理论的角度来处理的，并已应用于各种大规模半线性偏微分方程组的数学模型中。 4． HIV 感染过程和 HAART 疗法的数学方法。 HIV疾病进展的数学模型是从个体感染患者免疫系统中HIV感染过程的微生物学和生理学角度制定的。基于该模型的计算机模拟结果与临床数据相符。 5．解析半群的瞬态非线性扰动研究。提出了解析半群的瞬态非线性扰动的一般理论，并根据非线性演化算子的半线性生成器获得了非线性演化算子存在性的表征。作为该理论的具体应用，骨重塑模型得到了彻底解决。