一种用于灵敏度分析的基于体积的瞬态热传导程序的自动微分
Automatic Differentiation of a Finite-Volume-Based Transient Heat Conduction Code for Sensitivity Analysis
摘要：
提出了一种计算解场和其它模拟输出对任意输入量的导数的一般方法。采用自动微分的方法进行微分，并通过模拟代码按链式规则向前传播导数。提出了一种利用C++程序设计语言的运算符重载和模板功能的面向对象方法。验证结果给出了一个平面壁与表面对流，无量纲的温度场的导数相对于Biot数的计算和比较的解析解。进一步的结果给出了不同的导热系数的区域的复合材料中的传导。温度场的导数计算相对于使用所提出的方法的相之一的电导率。
英文摘要：
A general method for computing derivatives of solution fields and other simulation outputs, with respect to arbitrary input quantities, is proposed. The method of automatic differentiation is used to carry out differentiation and propagate derivatives through the simulation code by chain rule, in forward order. An object-oriented approach using the operator overloading and templating features of the C++ programming language is presented. Verification results are given for a plane wall with surface convection, where the derivative of the dimensionless temperature field with respect to the Biot number is computed and compared to an analytical solution. Further results are given for conduction in a composite material with regions of different thermal conductivity. The derivative of the temperature field is computed with respect to the conductivity of one of the phases using the proposed method.
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