FEA is one method that can be used to solve a limited group of fluid mechanics problems.
Due to instabilities in standard FEA, it cannot be used to solve every CFD problem easily without modification.
Many commercial CFD applications use FVM, but other methods like FEA or FEM can be used to solve fluid dynamics problems as well.
Fluid dynamics problems can rely on specialized numerical techniques to generate practical results. Anyone familiar with numerical methods for solving differential equations might be tempted to apply these to fundamental CFD equations, only to find that certain problems are unsolvable or have very inefficient computation. Selecting the right solution algorithm is important in any complex numerical problem, including CFD problems.
One numerical procedure that is sometimes compared with CFD is finite element analysis (FEA). While it is true that FEA can be used to solve some fluid problems, it is not necessarily a standard method for solving nonlinear partial differential equations, such as the Navier-Stokes equations. In this article, we will compare the uses of FEA vs. CFD methods for solving fluid dynamics problems as well as the possible ways the results from an FEA can be interpreted for systems design.
Choosing FEA vs. CFD Methods for Fluids Problems
Before comparing FEA vs. CFD methods, it’s important to clear up some terminology. FEA is not strictly comparable with CFD; FEA is a method for constructing a numerical scheme to solve a problem, while CFD refers to an application area of computational methods. CFD is overarching, including models and methods used to solve these problems. Within the field of numerical simulations, FEA is most commonly associated with structural analysis. This is understandable; the simulation software industry tends to implement FEA as a standard method for many problems, including structural problems.
Although FEA is not universally applicable to every CFD problem, the finite volume method (FVM) is a standard discretization technique that can be used to solve general CFD problems. According to some CFD simulation package vendors, FVM is sometimes used interchangeably with CFD, as it is a useful starting point for attacking many problems. FVM is the volumetric analogue of 1D or 2D finite difference methods; it is generally used with flow or flux problems, such as advection, or diffusion problems in 3D. In addition, open-source codes like OpenFOAM use FVM as the standard method for solving CFD problems.
When Is FEA Applicable?
The problem with the application of FEA is one of convergence and stability. In a non-self-adjoint 3D nonlinear system of partial differential equations, the FEA solution can become unstable and will diverge from the true solution. This arises due to certain nonlinear terms in the governing equations. In the realm of CFD, the Navier-Stokes equations include nonlinear convection terms that make the problem non-self-adjoint, thus FEA is not applicable in the realm of strong convection.
The convection term in the general Navier-Stokes equations causes this problem to be non-self-adjoint
In the above equation, we have a nonlinear term proportional to the flow rate and its derivatives in each dimension. In order to apply FEA to solve the above equation, a stabilization term must be added. The physical interpretation of “stabilization” is to add a small amount of artificial diffusion to the system, which is known to increase computational efficiency. However, the exact value or form of any stabilization term is debatable and depends on the problem to be solved, so it is difficult to generalize a stabilization method to every possible CFD problem.
There are some methods in the research literature that can be used to solve non-self-adjoint problems using FEA. The classic publication detailing these methods is:
If the system is constructed such that the nonlinearity is removed and the cross terms have a constant gradient, then it is much easier to solve the above problem using standard FEA. If this can’t be accomplished, some stabilization method must be used, or an alternative method that can handle the convection term in the Navier-Stokes equations should be used. FVM is a preferable alternative for general viscous, compressible flows found in real systems.
FVM in a CFD Solver
Using the FVM method for the spatial portion of a CFD problem is preferred due to its stability. In terms of computational effort, FVM and FEA are similar, but the algebraic solution equations in FVM are naturally derived using volume integrals. When applied to a conservation law, such as the mass transport and momentum conservation equations in the Navier-Stokes equations, the divergence term in the equations reduces to a surface integral or from the dimensionality of 3 to 2. This simplifies the calculations and illustrates why FVM is the preferred choice for CFD problems.
Non-adaptive mesh for a simplified model of a front wing and tire of a race car
Systems designers that need to choose between FEA vs. CFD calculations for complex systems should use a CFD solver application. The CFD simulation tools available in Omnis 3D Solver and Pointwise from Cadence are ideal for building and solving CFD problems in complex systems with industry-standard numerical techniques.