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Numerical simulation is a set of tools that allow you to obtain a solution to the equations that govern the behavior of real physical phenomena. It is especially useful when applied in the field of engineering. Most physical phenomena (for example, fluid motion or deformations in solids subjected to loads) are modeled mathematically by systems of partial differential equations, which can not be solved analytically. Traditional methods only reach the analytical solution to very simplified versions of the original equations, which limits its scope considerably. Up to the development of computational mathematics the design and optimization of facilities or processes in engineering required the construction of expensive experimental prototypes.

However, thanks to the development of computers and numerical methods, it is possible to predict the state of a system according to the equations that model it: it is possible to predict in detail the field of velocities and pressures in a fluid, or the deformations and strains in each of the points of a solid. The potential of numerical simulation has meant that its use is not limited to analyzing physical or engineering processes, but it is used in the study of economy, biology, etc.

Among the contributions of numerical simulation to the world of engineering, the following stand out:

**Cost and time saving in the conception workflow.** It is no longer necessary to make
expensive prototypes to evaluate how the design will work; it can be achieved through
numerical modeling of the design.

**Optimization of processes and designs.** Through simulations under different operating
conditions and/or geometry it is possible to find the optimum operating parameters of the
designs or processes.

**Detailed knowledge of the process.** Unlike experimental tests, numerical simulation
provides complete information about the problem; the numerical results output the
value of each of the variables involved in each point of the geometry for each moment
of time.

**Detection of malfunctions.** Through numerical simulation it is possible to detect
system malfunctions (for example, excessive load losses, preferential paths in
reactors, areas susceptible to fracture, etc.) The rapid evolution of technology and
sciences allows modeling and numerical simulation of processes from the industrial
and scientific fields. This has allowed the creation and consolidation of tools that
optimize processes, reduce costs, improve the quality of products, create new
technologies, increase safety, reduce environmental pollution, etc. Until recently, the concept of R&D has been linked to the large companies in the sector that
could afford to invest in experimental facilities or prototypes such as wind tunnels or
laboratories. The numerical simulation makes R&D concept accessible to SMEs,
analyzing the phenomena by means of their mathematical behavior equations, instead
of costly trial and error tests.