Brief Review of Computational Fluid Dynamics

Abstract

Theoretical hydrodynamics, experimental hydrodynamics, and computational fluid dynamics (CFD) are the three approaches for the study of problems in hydrodynamics. CFD as a flow simulation tool requires physical models described by the governing partial differential equations (PDEs) of fluid dynamics, appropriate, accurate, and stable numerical algorithms for discretization of the governing equations on a mesh generated inside a chosen computational domain, and computer hardware for the solution of the discretized algebraic equations in the computational domain with appropriate boundary conditions. The discretized algebraic equations are coded to generate a computer code in a computer language (such as Fortran, Fortran 90, C, C++, Java, and Python). The computer code is debugged and validated by conducting benchmark simulations; this computer code is run on computer hardware to obtain the numerical solution of the flow field. In this context, CFD can be considered a multidisciplinary field involving fluid dynamics, numerical mathematics, and computer science, as shown in Fig. 3.1, with the ability to solve complex three-dimensional fluid flow problems [1]. In other words, it employs the computer as a tool to solve the discretized linear algebraic equations in an iterative manner (note that the original equations are non-linear, which are linearized and solved iteratively). Generally speaking, theoretical fluid dynamics provides the physical and mathematical models to describe the conservation laws governing fluid motion, experimental fluid mechanics provides measurements and visualization to discover and explore the physical consequences of fluid motion-related phenomena in an application, and CFD builds a bridge between the theoretical models and experiments since it is difficult to obtain the analytical solutions of the complex 3D fluid motions using the theoretical models and it is costly to build the experimental apparatus and conduct experiments for a wide variety of flows of interest. As a result, CFD has become one of the most important technologies for conducting hydrodynamics/fluid dynamics research. In some sense, CFD can be considered similar to the experimental research, since CFD includes the geometry and physical modeling, solution procedure/process, and debugging in writing a computer code to conduct the numerical simulation with the code; thus, numerical simulation is also sometimes called “numerical experiment.” However, in contrast to experiments, CFD can often provide very detailed three-dimensional flow field data for analysis, design, and optimization of industrial products.