Introduction and Kinetics of Particles

Abstract

There are two main approaches in simulating the transport equations (heat, mass, and momentum), continuum and discrete. In continuum approach, ordinary or partial differential equations can be achieved by applying conservation of energy, mass, and momentum for an infinitesimal control volume. Since it is difficult to solve the governing differential equations for many reasons (nonlinearity, complex boundary conditions, complex geometry, etc.), therefore finite difference, finite volume, finite element, etc., schemes are used to convert the differential equations with a given boundary and initial conditions into a system of algebraic equations. The algebraic equations can be solved iteratively until convergence is insured. Let us discuss the procedure in more detail, first the governing equations are identified (mainly partial differential equation). The next step is to discretize the domain into volume, girds, or elements depending on the method of solution.