FEM is actually used also in the CFD applications...As a general comment, I would say that you can find well suited the field of fluid-solid interaction.

Juris Vencels : Juris, An example is fluid-structure interaction (FSI) in civil engineering, turbine design, biomedical engineering , biomechanics etc., where structural mechanics can be handled by FEM, and fluid mechanics can be computed with FVM. Though either FEM or FVM can be utilized for development of stand-alone softwares for FSI, the user code contributions in different opensource softwares based upon the physics of particular projects, will in principle, render coupling of two different softwares a beneficial task characterized with extended features or capabilities. The linear and non-linear elasticity equations of Elmer can be coupled with CFD equations of OpenFOAM. A code work on FSI coding with Elmer and OpenFOAM can be found at http://illinoisrocstar.github.io/ElmerFoamFSI/index.html.

Another different application, that uses Elmer (FEM software) and OpenFOAM (FVM software) is modeling ofthe thermal response of polymer composite hydrogen cylinder ( Article Modeling thermal response of polymer composite hydrogen cyli...

Following the answers

if I'm not mistaken, the FEM was developed for solid mechanics problems (it is the most accurate in coarse mesh) and the FVM for fluid mechanics problems (it is the most conservative). For your question, the benefit will be if you have a liquid-solid interface problem in a personal code. But apart from that, the FEM-based commercial code makes the task easier and smoother.

This could help you.

Fluid Dynamics simulations are governed by a set of partial differential balance equations, that describe the state of a flow at any given point in space-time. Obtaining the general solution is rarely trivial, and sometimes even impossible. Therefore, we use numerical methods that provide us approximate solutions to these equations. FEM (Finite Element Method) and FVM (Finite Volume Method) are two of the most popular numerical methods that are used to solve the equations, which finally reduce the system of partial differential equations into a system of algebraic equations. However, that’s where the similarities end. Both methods are vastly different when it comes to the modelling approach as described below using simple examples(without the intricacies in each!).

Finite Element Method:

FEM uses “elements” that are used to discretise the flow control volume and these elements mimic the local behaviour of the flow field. These elements create a set of equations, which is the “weak” form equations of the system. This “weak” form has simpler, lower order derivatives than the original “strong” form of the equation. The weak form is usually obtained by multiplying the original governing equation with a so-called “shape function” and integrating it over the domain. In other words:

For a given governing equation:

∂u∂x=0,∂u∂x=0,

∫(∂u∂x∗v)=0∫(∂u∂x∗v)=0

is the integral to obtain a weak form, where u is the variable under study, x is the independent variable, and v is the shape function. After integration, one obtains the weak form and u is the weak solution of the resulting equation.

Now, the domain in consideration is first discretised into smaller elements, each of which have a corresponding weak equation and a shape function that together approximate the original equation. For the entire domain, we would get a system of equations which can be solved by standard matrix methods such as Gauss Elimination, or numerical differential methods such as Runge-Kutta, etc.

Finite Volume Method:

The Finite Volume Method, in total contrast to the Finite Element Method is far more intuitively obvious when it comes to fluid/thermal applications. In FVM, we directly divide the domain into small volumes (cells) of simple shapes and let the fluid physically flow through these cells. The fluid motion through these cells is governed by the governing equations of mass, momentum and energy conservation. These governing equations are integrated across the volume of each cell. The fluxes are approximated by assuming, for example, that the flux at the entry and exit vary linearly, thereby converting the integral equation into an algebraic equation. Successive cells have similar algebraic equations, with the previous exit flux becoming the inlet flux for the next cell. The resulting equations are then simultaneously solved using matrix methods.

In summary the difference primarily exists in the modelling approach. The governing equations are the same and the solution methods of the simultaneous equations are also the same.

https://www.quora.com/What-is-the-major-difference-between-FEM-and-FVM-in-CFD

https://resources.pcb.cadence.com/blog/2020-finite-element-method-fem-vs-finite-volume-method-fvm-in-field-solvers-for-electronics#:~:text=The%20accuracy%20of%20the%20FVM,the%20FVM%20versus%20the%20FEM.

Many scholars use this combined approach for FSI studies i.e. FVM to obtain CFD solutions, which is then imported into FEM to solve the fluid-induced structural deformation.

This is, however, normally a one-way coupling, as one often finds hard to import the FEM structural deformation back to FVM and strongly couple them (semi-perfectly match the dynamic and kinetic conditions).