An Object-Oriented Programming Approach to Implement Global Spectral Methods: Application to Dynamic Simulation of a Chemical Infiltration Process

Abstract

Boundary-value problems (BVPs) in relatively simple geometriescan be solved using global spectral methods. These discretizationmethods are applicable to a wide range of problems and are suitablefor a "rapid prototyping" approach to simulator development forcomplex systems. Object-Oriented Programming techniques for solvingBVPs are introduced in this work. Object classes are created toencapsulate trial function sequences, discretized differential andquadrature operators, and other data structures used for spectraldiscretization and projection operations. Operator/functionoverloading subsequently is used to numerically implement theGalerkin projection method. Emphasis is placed on developingnumerical methods suitable for discretizing 2- and 3-dimensionalproblems, integrating the resulting ODE/AE systems in time, andreconstructing the solutions in the physical space. A detailed model of anisothermal carbon-carbon chemical vapor infiltration (CVI) systemwas studied as a true test of the ability of the numerical methods.