Fluid flow problems arise in almost all industrial sectors: food processing, water treatment, marine engineering, automotive, aerodynamics, and gas turbine design. FEA facilitates the prediction of fluid flow, heat & mass transfer, and chemical reactions (explosions) and related phenomena.
By solving the fundamental equations governing fluid flow processes, FE analyses provide information on important flow characteristics such as pressure loss, flow distribution, and mixing rates. This results in better designs, lower risk, and faster time to the marketplace for product or processes. Models can be developed for physical phenomena such as turbulence, multiphase flow, chemical reactions, and radiative heat transfer.
Solution Approach
The foundation of fluid dynamics is based on the Navier-Stokes equations, the set
of partial differential equations that describe fluid flow. In FEA, this equation
is rewritten as algebraic equations that relate the velocity, temperature, pressure,
and other variables, such as species concentrations. The resulting equations are
then solved numerically, yielding a complete picture of the flow. The equations are
solved iteratively using the method of weighted residuals. The main method of solution
is achieved via the Galerkin method, but others exist. One such variant is the Petrov-Galerkin
method, which is used to solve instances of viscous, high Reynolds number flows.
During the solution, unsymmetrical solution matrices may exist. Therefore, it is
often necessary to use many relatively small & higher order elements in order to
obtain convergence. Due to this problem, it is not uncommon to implement reduced
integration type elements in an analysis.For transient problems, a special time integration
technique known as the semi-explicit scheme is used in large analyses, as it is more
economical than other methods available.
CFD
Despite the fact that most fluid-flow type problems can be implemented successfully using FEA, it is not the paramount technology. Due to the nature of the fluid formulations for solution via FEM, long solution times & poor convergence can be experienced. As a result, a more convenient solution is obtained by using a method known as CFD. This method is based around finite-difference & finite volume solution techniques.
