Sánchez Pérez J F, Conesa M, Alhama I, Alhama F, Cánovas M
Network Simulation Research Group, Universidad Politécnica de Cartagena, Cartagena, Spain.
Metallurgical and Mining Engineering Department, Universidad Católica del Norte, Antofagasta, Chile.
PLoS One. 2017 Oct 3;12(10):e0185477. doi: 10.1371/journal.pone.0185477. eCollection 2017.
Classical dimensional analysis and nondimensionalization are assumed to be two similar approaches in the search for dimensionless groups. Both techniques, simplify the study of many problems. The first approach does not need to know the mathematical model, being sufficient a deep understanding of the physical phenomenon involved, while the second one begins with the governing equations and reduces them to their dimensionless form by simple mathematical manipulations. In this work, a formal protocol is proposed for applying the nondimensionalization process to ordinary differential equations, linear or not, leading to dimensionless normalized equations from which the resulting dimensionless groups have two inherent properties: In one hand, they are physically interpreted as balances between counteracting quantities in the problem, and on the other hand, they are of the order of magnitude unity. The solutions provided by nondimensionalization are more precise in every case than those from dimensional analysis, as it is illustrated by the applications studied in this work.
经典量纲分析和无量纲化被认为是寻找无量纲组的两种相似方法。这两种技术都简化了许多问题的研究。第一种方法不需要知道数学模型，对所涉及的物理现象有深入理解就足够了，而第二种方法从控制方程开始，通过简单的数学操作将其简化为无量纲形式。在这项工作中，提出了一种正式的协议，用于将无量纲化过程应用于常微分方程（线性或非线性），从而得到无量纲归一化方程，由此产生的无量纲组具有两个固有属性：一方面，它们在物理上被解释为问题中相互抵消的量之间的平衡，另一方面，它们的量级为1。无量纲化提供的解在每种情况下都比量纲分析提供的解更精确，正如本工作中所研究的应用所示。
