CFD Mathematical and Physical Behavior of Equations Full Lecture

When an engineer is tasked with designing a new product, e.g. a winning race car for the next season, aerodynamics play an important role in the engineering process. However, aerodynamic processes are not easily quantifiable during the concept phase. Usually the only way for the engineer to optimize his designs is to conduct physical tests on product prototypes. With the rise of computers and ever-growing computational power (thanks to Moore’s law!), the field of Computational Fluid Dynamics became a commonly applied tool for generating solutions for fluid flows with or without solid interaction. In a CFD software analysis, the examination of fluid flow in accordance with its physical properties such as velocity, pressure, temperature, density and viscosity is conducted. To virtually generate an accurate solution for a physical phenomenon associated with fluid flow, those properties have to be considered simultaneously.

A mathematical model of the physical case and a numerical method are used in a CFD software tool to analyze the fluid flow. For instance, the Navier-Stokes (N-S) equations are specified as the mathematical model of the physical case. This describes changes in all those physical properties for both fluid flow and heat transfer. A mathematical model varies in accordance with the content of the problem such as heat transfer, mass transfer, phase change, chemical reaction, etc. Moreover, the reliability of a CFD analysis highly depends on the whole structure of the process. The verification of the mathematical model is extremely important to create an accurate case for solving the problem. Besides, the determination of proper numerical methods is the key to generate a reliable solution. The CFD analysis is a key element in generating a sustainable product development process, as the number of physical prototypes can be reduced drastically.