时间域与空间域耦合物理系统多领域统一建模研究

项目名称： 时间域与空间域耦合物理系统多领域统一建模研究

项目编号： No.60874064

项目类型： 面上项目

立项/批准年度： 2009

项目学科： 轻工业、手工业

项目作者： 陈立平

作者单位： 华中科技大学

项目金额： 34万元

中文摘要： 面向复杂工程物理系统的建模与仿真，针对其多领域之间及时间域与空间域问题之间的耦合特性，研究物理系统时间域微分代数方程与空间域偏微分方程的一致表示方法，基于多领域统一建模规范语言Modelica，给出微分代数方程、偏微分方程、规则或非规则区域与边界以及各种边界条件与初值条件的面向对象的陈述式表示，实现时间域与空间域耦合多领域物理系统的统一建模；并对统一建模导致的大规模偏微分代数方程混合系统进行求解策略的研究，给出混合系统初值边界条件相容性判定、大规模规划分解及偏微分代数问题混合求解的关键算法；据此实现原型系统，并以某型雷达导引头的精确建模与仿真为例进行验证。本项目研究将统一多领域物理系统时间域微分代数方程与空间域偏微分方程的表示，大大地延伸传统多领域统一建模方法的应用范围，有利于推进相关国际标准发展，并为新一代更广泛的复杂工程物理系统的建模与仿真工具的研发提供支撑使能技术。

中文关键词： 物理系统；建模与仿真；时间域与空间域耦合；多领域统一建模；偏微分代数方程

英文摘要： For the modeling and simulation of complex engineering physical systems, a uniform and consistent representation approach of differential-algebraic equations (DAE) in time domain and partial differential equations (PDE) on space domain of physical systems is researched according to the multi-domain coupling among various physical fields and the time-space coupling between time and space domain. The project will present the declarative and object-oriented representation of DAEs, PDEs, regular or irregular domain and boundaries as well as various initial and boundary conditions based on the unified modeling language - Modelica to realize the unified modeling of multi-domain physical systems with time-space domain coupling. Such uniform modeling will result in large-scale hybrid system of partial differential-algebraic equations (PDAE). The solving strategies for PDAE will be studied to give the key algorithms of determining the consistency of initial and boundary conditions, reducing the scale of large systems and solving the PDAE. Finally, a prototype system will be implemented to validate the proposed approach and strategies through the accurate modeling and simulation of certain type of radar seeker. The research will unify the representation of DAE in time-domain and PDE on space-domain of multi-domain physical systems, which greatly expands the application scope of traditional unified multi-domain modeling methods. It is helpful to promote the development of relevant international standards, and can provide the supporting technology for the new generation modeling and simulation tools of complex engineering physical systems.

英文关键词： Physical Systems; Modeling and Simulation; Time-Space Domain Coupling; Multi-domain Unified Modeling; PDAE