Numerical simulation

Computer simulations that are carried out using numerical methods such as turbulence models are generally referred to as numerical simulation . Well-known examples are weather and climate forecasts , numerical flow simulations or strength and rigidity calculations.

method

Numerical simulations can be divided into the following steps:

Modeling

In the modeling (model structure) the basic properties of a simulation are formulated in the form of mathematical models. The models are usually developed independently of a specific task.

Parameterization

During the parameterization, models are selected, equipped with specific calculated values ​​and linked with one another in such a way that the overall model represents a specific application as well as possible. Inaccurate knowledge of the models or the boundary conditions is the most common source of errors in simulations.

calculation

The numerical methods are special calculation procedures that fall under the sub-area of numerical mathematics . The actual calculation is done by starting a solution program, the so-called solver . This carries out the actual calculation and saves the calculation results. Since a closed solution of the systems is usually not possible, iterative solution methods are used to find an approximate solution. Almost all simulation calculations require very large amounts of data to be processed. Nevertheless, the computing time can vary greatly depending on the simulation method. For this reason, parallel computers , vector computers or PC clusters are often used in this area , with many individual computers working on a result at the same time. However, the speed of such calculations cannot be increased at will, as the number of computing cores involved generally increases the communication effort ( scalability ).

Evaluation and presentation

The results of the calculation are called raw data. These are available as digital result files that now have to be processed in such a way that they are understandable for people. The evaluation required for this is an elementary part of the simulation. On the one hand, statistical methods are used for the evaluation, which summarize or analyze data. An important aspect, however, is also the ability to process data graphically.

Areas of application

The mathematical problems of numerical simulations can often be traced back to the solution of differential equations, the solution of eigenvalue and eigenvector problems, the solution of linear systems of equations or the calculation of integrals. Due to the complexity of the simulation programs and the uncertainty of the applied parameters and boundary conditions, accompanying procedures, such as analytical calculations, are often used in parallel to check the results.

The complexity of different numerical simulations is very different. Therefore, problems such as strength calculations or vibration analyzes of buildings and machine parts have become standard tools for designers - in other processes (weather forecasts, climate calculations), on the other hand, one moves at or beyond the limits of the capabilities of modern computers. There are also fundamental problems such as the chaotic behavior of many dynamic systems.

Numerical simulations can be used in many different ways. Some important or well-known examples are:

Engineering

• Architecture and civil engineering: Static and dynamic strength calculations (buildings, bridges)
• Chemical and process engineering: Combustion processes and chemical reactions (internal combustion engines, yield from chemical syntheses)
• Mechanical engineering: flight simulators, vibration analysis on electrical machines , stresses and deformations (elastic and plastic, e.g. virtual crash tests using finite element methods )
• Technical physics: semiconductor components, heat conduction processes, optical systems (lens systems, lasers, thermal deformations due to absorption), fusion reactors , accelerators and nuclear reactions