On the solutions of fluid flow problems with a Chebyshev collocation method using Mathematica

Abstract

AbstractFluid flow problems are important in engineering applications like heat exchangers, renewable energy sources, and electromagnetic processing of materials, among other applications. Some examples related to a computational fluid dynamics (CFD) course are explored in this study. A CFD course provides tools for the numerical solution of fluid flows where an analytical cannot be found. Flows can be described by numerically solving the mass, momentum, and energy conservation equations for incompressible fluids. A Chebyshev collocation spectral method has been used to solve the governing equations. A high‐level functional programming language strategy was implemented in Mathematica including readability and adaptability. The programs are built by applying and composing functions, mappings, iterators, and pattern matching. It was noted that students can achieve a better comprehension of the algorithms using this programming approach.