Pourarian Shokouh, Kearsley Anthony, Wen Jin, Pertzborn Amanda
Shokouh Pourarian is a PhD student in the Department of Civil, Architectural and Environmental Engineering, Drexel University, Philadelphia, Pennsylvania.
Anthony Kearsley is a mathematician in Mathematical and Computational Science Division at the National Institute of Standards and Technology (NIST), Gaithersburg, MD.
Energy Build. 2016 Jun 15;122:53-62. doi: 10.1016/j.enbuild.2016.04.019. Epub 2016 Apr 11.
Efficiently, robustly and accurately solving large sets of structured, non-linear algebraic and differential equations is one of the most computationally expensive steps in the dynamic simulation of building energy systems. Here, the efficiency, robustness and accuracy of two commonly employed solution methods are compared. The comparison is conducted using the HVACSIM+ software package, a component based building system simulation tool. The HVACSIM+ software presently employs Powell's Hybrid method to solve systems of nonlinear algebraic equations that model the dynamics of energy states and interactions within buildings. It is shown here that the Powell's method does not always converge to a solution. Since a myriad of other numerical methods are available, the question arises as to which method is most appropriate for building energy simulation. This paper finds considerable computational benefits result from replacing the Powell's Hybrid method solver in HVACSIM+ with a solver more appropriate for the challenges particular to numerical simulations of buildings. Evidence is provided that a variant of the Levenberg-Marquardt solver has superior accuracy and robustness compared to the Powell's Hybrid method presently used in HVACSIM+.
高效、稳健且准确地求解大量结构化非线性代数方程和微分方程，是建筑能源系统动态模拟中计算成本最高的步骤之一。在此，对两种常用求解方法的效率、稳健性和准确性进行比较。使用HVACSIM+软件包进行比较，它是一种基于组件的建筑系统模拟工具。HVACSIM+软件目前采用鲍威尔混合法来求解对建筑物内能量状态和相互作用动力学进行建模的非线性代数方程组。结果表明，鲍威尔方法并非总能收敛到一个解。由于有大量其他数值方法可供使用，因此出现了哪种方法最适合建筑能源模拟的问题。本文发现，用一种更适合建筑数值模拟特定挑战的求解器替换HVACSIM+中的鲍威尔混合法求解器，会带来可观的计算效益。有证据表明，与HVACSIM+目前使用的鲍威尔混合法相比，Levenberg-Marquardt求解器的一个变体具有更高的准确性和稳健性。
