**Why do we use simulation software?**

Simple (often 1-dimensional) problems can usually be solved analytical (with manual calculations). Stress and deformation of solid materials under the influence of forces is a good example as many engineering use classical beam formulae to quickly calculate the deflection of a steel beam.

This approach works fine for a first estimate but engineers often needs a lot more insight into details and a higher accuracy to ready make a good design. Often this insight cannot be obtained following an analytical approach. The formulas (partial differential equations) simply cannot be solved by hand when it comes to a 3D geometry. In addition, it is unfeasible to also include the interaction between different disciplines, such as mechanics and flow theory, when these are linked.

Since the 90s -and thanks to the increased computational power of computers and the use of 3D drawing software- the use of simulation programs has grown tremendously as a tool used to solve complex physical and technical problems. These problems certainly do not only occur in scientific world but also during the design of products and systems. It is precisely the insight gained during the development process through simulations that can save a lot of money in the prototype phase. Moreover, code calculations are often required to demonstrate to a certification body (DNV, BV, Lloyds, ABS) that a design meets the applicable design codes. In addition to the mandatory mechanical code calculations known to many people on hoisting equipment and pressure vessels, this for example also applies to electromagnetic equipment (EMC regulation).

**Under the hood:**

The system of partial equations is solved via numerical solving techniques and a powerful computer when performing simulations. The domain of the problem, for example the geometry of a product, is divided into millions of sub-volumes, also called elements. The elements have common boundary conditions that must be met by the numerical solution. This results into enormous mathematical matrices, which must be solved to obtain insight. This takes time especially if the matrix is ’large’. A fast central server with many processing cores like Demcon Bunova has is very useful. The computer calculates all elements point by point until a sufficiently accurate approximate solution is found.

**Mathematical Equations**

Different sets of mathematical equations are used to describe a range of physical problems:

- In the area of
**fluid dynamics**the physics of liquids and gases are described by the Navier-Stokes equation. In most cases these are made conclusive by adding an appropriate turbulence model. Commonly used models are k-epsilon, k-omega, k-omega SST or the Reynolds stress model. Solving the above equations using a computer is typically called ‘Computational Fluid Dynamics’ (CFD). - In the area of
**heat transfer,**particular attention is paid to conduction, flow (convection) and radiation topics. In the case of solids, the focus is usually on conduction and the physics is described with the help of Fourier’s Law. Applying the right coefficient for thermal conductivity of the materials is of great importance to obtain meaningful results. The ‘Finite Element Method’ (FEM) is often used to solve these type of problems with a computer. - In the area of
**electromagnetism**, Maxwell equations are used to describe the interaction between electric and magnetic fields. This set of equations are a summary of previously separate formulated laws, such as the laws of Gauss, Ampère and Faraday. Simulating electromagnetic fields using a computer is typically called ‘Computational Electro Magnetics’ (CEM). - In the area of
**solid mechanics**, Newton’s laws are applied and combined with material science to determine the deformation of a product or system. It is very important to use the appropriate material model (linear / non-linear) and friction model when solving mechanic problems. Again the ‘Finite Element Method’ (FEM) is used to model these problems.

**Knowledge and experience required to use tools the appropriate way:**

It is important that an engineer has a profound understanding of numerical calculation methods and the physical background of the problem he wants to tackle with simulation software. Depending on the topic, a large number of important choices have to be made when going through the process. All choices will have effect on the outcome of the simulation and the whether it is appropriate representation of the real case.

## Pre-processing:

The geometry must be divided into a large number of elements as indicated earlier. This, together with choosing the right type of elements, is called meshing. The quality of the mesh has influence on the accuracy, convergence and speed of the solution. The elements must be placed in the right way and with the correct resolution through the geometry. In areas where high gradients are expected, more elements must be added. It must be verified that the final mesh does not influence the outcome of the calculation. The solution must independent of the mesh. The meshing procedure starts relative coarse and robust. Refinements are made where required at specific areas. Boundary conditions and material properties have to be added to complete the model. Specific conditions can be pressures, temperatures, forces or for example speeds, all depend on the type of problem. Errors that lead to faulty results are easily introduced in every step. In summary, we can state that the quality of the mesh and the defined boundary conditions have a major influence on the outcome of the simulation.

## Solver:

Once the model has been completed the actual calculations to simulate physics can start. Simulations can be ‘steady state’ or ‘transient’. A steady state calculation means that there is no time-dependency. This for example is often the case with mechanical stress problems as the forces are in equilibrium. Transient problems also have a dependency on time. The temperature rise profile from filling a cold mug with hot coffee is a good example of a time dependent case.

## Post-processing:

The outcome of the simulations are analyzed in a post processing environmental once the solver has completed the calculations. The results of the simulation, or parts of it, are visualized to ease evaluation. The outcome (the numbers) can be inspected up to element level. Contour plots, graphs and tables are created as required. The knowledge and insights which are obtained from the simulation are used by our engineers confirm whether a product works as expected or whether adjustments have to be made. Preferably, a FEM / CFD calculation is made at an early stage in the development process as a good final design often requires a number of iteration. This often saves a lot of time and money.