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# Numerics Background for CFD and FEA

Once you know how to model a physical phenomenon mathematically, your next step is to use a numerical domain to convert that model to a new numerical model. Ever wondered how the colorful pictures and scenic simulation animations are obtained? If yes, then here is the place to be! This SimWiki article emphasizes the numerics background that the user has to deal with when performing simulations

You can imagine that the generation of results for the simulation of geometries with a high level of complexity, like round shapes with complex undercuts, is difficult. The shear stresses in fluids are analogous to friction forces in solids and can be estimated based on the fluid viscosity. As you can imagine, this is not something that is solved easily. All these effects are impossible to calculate exactly with the models that science provides us until today. However, there are very good numerical models that can give us highly accurate approximations of the results, with errors being well below 1%.

## Numerical Models

Numerical models or methods are mathematical tools that have been designed to deal with such complex problems where analytical solutions cannot be used. When numerical methods are implemented, the discretization of the equations, application of solvers, and the necessity for the convergence of residuals all become very important for a successful and accurate simulation.

These numerical techniques, which are a part of the numerics background domain, are used to capture and solve the mathematical expressions behind a process to a more comprehensible result. This naturally helps one build better products and reduce the time to market significantly. Learn more about the numerical models used in engineering simulation here:

## Numerics Inside SimScale Workbench

Inside the SimScale Workbench, numerics is handled under the simulation tree item Numerics. You can read more about how the numerics settings affect the simulation run and the results accuracy for CFD and FEA simulations in the following documentation:

Last updated: February 17th, 2023

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