Adaptive Methods for Non – Linear Empirical Similitude Method

Several problems in engineering realm pose modeling and simulation difficulty due to severe non – linear behavior and debilitating singular or stiff conditions that act as additional impediments. In many such instances advanced numerical schemes are employed to either relax or simplify the PDE that defines the physical process to obtain reasonable output from the simulation. Digressing from this traditional approach, we present an experimental similitude method in this paper to analyze non – linear systems. Combined with the use of original mapping algorithms, we discuss the benefits of empirical similarity techniques and present a heat transfer example for exposition. INTRODUCTION Most technical problems encountered in industrial systems have complex interactions of sub – systems and components unlike conventional problems in the academic world. Analyzing the behavior of a system with a network of components requires multifaceted approximations to reasonably simplify the modeling effort. More often than not, a dominant phenomenon is isolated that captures a major segment of the system response without compromising the integrity of the governing dynamics of the associated physical process. Such a simplification cannot be achieved with considerable ease and requires numerous approximations and assumptions. This feature is more profound in product design, especially in the evolution phase of the product when the geometry is still hypothetical. When a design needs to be qualified parametrically [Otto et al, 2001], the system has to be evaluated mathematically using a procedure that is both accurate and robust. Such a procedure must also encompass uncertainty indicators and error definitions for the designer to take advantage of to maintain rigorous quality and reliability standards. Keeping in mind that most modern designs are intricate in geometry and are manufactured from multi – material composites or involve multiple material effects, any traditional effort like bond