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What is Accuracy in FEA or CFD Simulation?

This is a common question that haunts most designers – what is the accuracy in FEA or CFD simulation? How accurate are these computer models? With growth in computer power, simulations have started to play a major role in product design and the optimization process.

In the early days of modern technology, simple hand calculations were used, along with data tables and the factor of safety calculations. However, such calculations were insufficient and hence FEA and CFD were originally developed for the design of aerospace and civil engineering structures. Over the last four decades, FEM and CFD have been widely applied to applications beyond these areas. Particularly over the last decade, these numerical techniques are being applied to multiphysics applications such as biomechanics and electromagnetics as well. As the industry has started to use these technologies more extensively, one question that many often ponder about is their reliance.

spark plug

Fig: Simulation technology applied to commonly found spark plug

To summarize, FEM and CFD are just numerical techniques that can solve several partial differential equations. Most physical phenomena are described by partial differential equations: Fluids (Navier-Stokes), Electromagnetics (Maxwell), Solids (Equilibrium), Thermal (Fourier) etc.

We often watch flashy pictures in animations and movies and these are the results of solutions to these PDEs. However, these are specific solutions to a particular boundary condition. Similarly, simulations are also solutions to these PDE’s. However, simulations are generic ones to general boundary conditions. Numerical methods use discretization of the entire region to solve the problem.

Accuracy for the user

Most often this is a question of the user who needs a particular component in mind to be designed.

Firstly, it is necessary to comprehend the application where the component shall be used. Are the conditions static or dynamic? Is it subjected to fatigue or cyclic loading? Considering the correct form of a simulation is the first step in ensuring accuracy.

One of the most common causes of failure is fatigue where the structure weakens with each cycle of loading. Finally, over millions of cycles, the structure suddenly fails. Such failures are catastrophic in nature. Here static or dynamic analysis are only as an order of magnitude approximations.

Modal analysis Truss

Fig: Modal analysis of a truss bridge

Further on, the material properties need accurate calibration and comparison with experiments. Alongside using an appropriate material model (linear, nonlinear – elastic, hyperelastic, plasticity, viscoelasticity etc.), the numbers used for these models need to be appropriately fitted with experiments. Most often, inaccuracies here arise when data is “extrapolated”. Interpolation is acceptable but extrapolation is really dangerous.

Thus, the customer can ensure that the simulations are accurate and within permissible limits by providing the designers with:

  • Exact application of the designed component
  • Typical loading conditions
  • Actual material / material properties / experimental data for the material to be used

Accuracy for the designer

On one end, small scale companies generally prefer to outsource simulations of components to medium scale companies. One the other end of the spectrum are the multinationals. These companies have design departments who specifically use simulations like FEA and CFD. Alternatively, they also outsource to the medium-scale companies. So the designer here refers to the latter.

What do these designers need to concentrate on? What is accuracy and how can it be improved? The aspects from the perspective of the designer includes:

  • Appropriate mesh accuracy
  • Mesh independence
  • Element technology
  • Validation

CAD geometries are stored as B-splines etc. These are curves that are used to represent the exact geometry. Further on, for simulations, these CAD geometries are discretized using FEM meshes. There has been a whole new field, called Isogeometric analysis, that has emerged in the recent decade, where FEM or CFD simulation is done using the actual CAD geometry and eliminating the entire meshing process. However, this is still nascent and is something to look forward to in two decades from now.

One of the prominent questions to ask is if the mesh fits well with the geometry. In general, second-order meshes can replicate curved geometries and thus more suitable than linear elements, for accurate meshing. In addition, the distortion of elements can also reduce the mesh quality substantially and hence the accuracy of the obtained solutions. Some tips for meshing in FEM can be found in the article “How to Mesh your CAD Model for Structural Analysis (FEA)“.

meshrefinements

Fig: Mesh refinements in a CFD model

The second aspect of consideration is regarding mesh independence. Both FEA and CFD simulation require accurate meshing and by default are mesh dependent. However, meshing is an approximation of the actual model into a discretized finite model. Thus, complete mesh independency is never possible. However, it is important to check mesh convergence of the results. This implies, doubling the mesh density and check for changes in the results. It is pertinent to remember here that nodal degrees of freedom (like displacements, temperature etc in FEM and velocities, pressures in CFD) will always have converged. However, the post-processing quantities like strains and stresses that do not converge. This is especially true in the presence of singularities! Check the latest article on SimScale blog, titled “Mesh size influence on the mechanical stress concentration” regarding FEM in the presence of singularities.

Further on, the type of element used again influences the result. This is an aspect where the developer can help the designer to find suitable solutions. For example most linear elements demonstrate volumetric locking effects when used in problems involving compressibility (like rubber materials, plasticity etc). Similarly, using solid elements in thin structures can lead to shear locking. Solutions to these problems are available through the usage of different types of elements and it is necessary for the designer to understand the right usage for improved accuracy.

Boundary conditions that replicate the right loading conditions and material models that represent the actual behavior as provided by the customer is definitely an aspect that is necessary to ensuring realistic simulation results. Understanding the entire workflow and its requirements can go hand-in-glove to creating realistic simulations. A simple sample can be found in the article “CFD workflow quick guide: How to set up a fluid dynamics simulation“.

Finally, validation is the part the most designers forget. Some important questions to ask here include: Is there any data for the application being designed? How well does it compare with the experiments? In that case, what parameters in the model need to be tuned to make it more realistic? Validation plays an important part in ensuring that all the numbers used are realistic and thus ensuring a simulation result as near to reality as possible.

Finally, the developer

Finally, the developer – the person doing the dirty work of developing these algorithms! Most problems representing reality are nonlinear in nature and hence convergence of developed algorithms play a pivotal role.

thermal analysis

Fig:  SimScale: An uncomplicated solution to next-generation CFD simulation and FEA

The developer needs to work on algorithms that are robust in nature and, where necessary, add appropriate error messages that the designer and customer can comprehend. Most commercial software, unlike SimScale, do not allow the designer to meddle with the convergence thresholds. Suitable “caution” boxes need to be added such that the precautions can be exercised by the designer.

What does the future look like for FEA and CFD Simulation?

Further on, as concepts like machine learning are becoming more common, it is not far ahead when the computer programs can guess what the user is trying to do and automatically suggest caution. Another aspect that has recently been kicking dust is automation where the designer tells the program the problem of interest and the computer sets up the simulation environment completely and even on the fly!

Judging the accuracy of the simulation, eventually necessitates that everyone in the chain understands some basic aspects to judge if the results are realistic of just a pretty picture. A recent SimScale article “When is it just a pretty picture?” provides a small glimpse into the post-processing world for FEA.

There exists great potential that is yet to be tapped completely. Caution and judgment are necessary at each step to ensure the accuracy of the results and a realistic FEA or CFD simulation!

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