基于Modelica语言的PDE与DAE问题的一致表示

Consistent Representation of PDE and DAE Problems in Modelica

Modelica语言是为解决复杂物理系统多领域统一建模与仿真问题而提出的一种面向对象基于方程的陈述式建模语言。它对DAE问题的表示已相对成熟,而对PDE问题的表示则相对缺乏。在多领域统一建模框架下,基于面向对象的思想,提出一种PDE与DAE问题一致的表示方法,实现对PDE问题的简单自然描述。然后使用直线法将PDE模型转化为DAE模型,并在Modelica仿真平台MWorks环境中进行求解,初步扩展了Modelica语言以支持三维PDE问题的建模与仿真。最后通过一个热传导PDE问题进行了验证。

Modelica is an object-oriented equation based language for modeling of large, complex, and heterogeneous physical systems. It has been relatively mature for modeling and simulation of differential-algebraic equations （DAEs） systems, while lacks effective modeling of partial differential equations （PDEs） problems. Based on the object-oriented idea, a method of consistent representation of PDE and DAEproblems was proposed, Modelica language was extended to support modeling of three-dimensional PDE problems. Then the PDE model was transferred into DAE model with the method of lines, and was solved in MWorks platform based on Modelica. To illustrate the application of our method, a heat conduction problem was modeled and simulated in Modelica.