Introduction: Brief Review of Finite Volume Method (FVM) in Computational Fluid Dynamics

Abstract

Computational fluid dynamics (CFD) is sometimes regarded as a mature technology. In the author’s opinion, this is only partly correct. The fundamental ideas of CFD such as the finite volume method (FVM) are indeed well established, whereas some classes of problems such as hypersonic heating or real fluid simulations are still challenging, as will be discussed in the subsequent chapters. Thus, we begin this book by reviewing those basics in this chapter, specifically by describing the governing equations (i.e., the Navier–Stokes equations, or equations of mass, momentum, and energy conservation) for compressible flows. They are discretized, for computational purposes, by the FVM, which is the conventional procedure. Through this approximation, the equations are closed along with the equation of state and are valid for every computational element (=cell). In this chapter, only a brief explanation is given of how those equations are numerically solved in the framework of the FVM, using methods such as space reconstruction, slope limiting, flux computation, and time integration. Interested readers, including who have just entered the CFD world, are encouraged to refer to the standard books mentioned in the Preface.