Implementing state-space methods for multizone contaminant transport
Implementing state-space methods for multizone contaminant transport
复制标题
实施多区域污染物传输的状态空间方法
DOI：
10.1016/j.buildenv.2013.09.021
复制
发表时间：
2014
影响因子：
7.4
通讯作者：
M. Sohn
中科院分区：
文献类型：
--
作者：
S. T. Parker;D. Lorenzetti;M. Sohn
“充分混合区”近似是模拟建筑物中污染物迁移的一种有用模型。多区域软件工具，如CONTAM [1]和COMIS [2]使用时间推进数值方法来求解所得的常微分方程。相比之下，状态空间方法解析地求解相同的方程[3]。使用矩阵指数的直接解析解在计算上对于某些应用是有吸引力的，例如，当气流在相对长的时间段内不改变时。然而，对于大型系统，即使是矩阵指数也需要数值估计。本文评价了两种求矩阵指数的方法：特征值分解和Padé算法。此外，它认为一个变化优化稀疏矩阵，并与参考向后欧拉时间推进scheme.State空间的解决方案可以运行几个数量级的速度比参考方法，更显着的加速为更多的区域。这使得它们对于需要在恒定气流条件下快速计算浓度和暴露的应用特别有价值，例如实时预测或监测室内污染物。对于大多数模型，这三种方法都具有较低的误差（中位数分数偏差<3·10−5，归一化均方误差<3·10−7，缩放绝对误差<4·10−4）。然而，对于最大的模型考虑（1701区）特征值分解显示出显着增加的错误。
The “well-mixed zone” approximation is a useful model for simulating contaminant transport in buildings. Multizone software tools such as CONTAM [1] and COMIS [2] use time-marching numerical methods to solve the resulting ordinary differential equations. By contrast, the state-space approach solves the same equations analytically [3]. A direct analytical solution, using the matrix exponential, is computationally attractive for certain applications, for example, when the airflows do not change for relatively long periods. However, for large systems, even the matrix exponential requires numerical estimation. This paper evaluates two methods for finding the matrix exponential: eigenvalue decomposition, and the Padé algorithm. In addition, it considers a variation optimised for sparse matrices, and compares against a reference backward Euler time-marching scheme.The state-space solutions can run several orders of magnitude faster than the reference method, with more significant speedups for a greater number of zones. This makes them especially valuable for applications where rapid calculation of concentration and exposure under constant air flow conditions are needed, such as real-time forecasting or monitoring of indoor contaminants. For most models, all three methods have low errors (magnitude of median fractional bias <3·10−5, normalised mean square error <3·10−7, and scaled absolute error <4·10−4). However, for the largest model considered (1701 zones) eigenvalue decomposition showed a dramatic increase in error.
影响因子：
3.1
作者：
Al-Mohy, Awad H.;Higham, Nicholas J.
通讯作者：
Higham, Nicholas J.