Meshless Computational Fluid Dynamics – Feedback

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In a previous article, Karalit’s Marco Mulas explained the benefits the immersed boundary (IB) approach to Computational Fluid Dynamics (CFD). Vendors Ansys and CD-adapco reply.


Immersed boundaries (IB) is a method which, according to some, does not require the generation of a mesh. However, this is not fully accurate, as the IB method does indeed necessitate a mesh, (albeit rudimentary and simple to generate).

While this particular method proves to be extremely fast, we believe the major disadvantages outweigh its benefits. A viable alternative to the IB method is to combine a body-fitted mesh with a Cartesian mesh approach, taking advantage of mature solver technologies while providing a high quality mesh.

IB “grid” generation method weaknesses:
Inaccuracies in computation of wall-bounded flows, especially for turbulent flows. For example, using the IB method for the computation of heat transfer at walls can lead to large errors.

The actual error depends upon the algorithm used. Solvers using body-fitted methods are known to be much more accurate for computation of wall-bounded flows.

Implementing physics models (for example multiphase or reacting flow models) is challenging as a special treatment has to be done at the boundary cells. This makes the development of a full capability CFD solver even more challenging.


The IB method is not as mature and validated as methods using body-fitted meshes.

Companies who are implementing this approach typically use a body-fitted overset mesh to resolve the walls boundary layer. While this removes some of the limitations highlighted above, it also adds the complexity of the overset method which requires an interpolation to pass information from the overset mesh to the IB mesh.

One can argue that the use of overset mesh simply displaces the errors from the wall region to the area where the overset and IB regions meet. For example, knowing that simulation of multiphase flow or a reacting flame with complex chemistry requires high-quality meshes, how accurate can these simulations be if the region of interest is where the overset mesh meets the IB region?

How easy is it to locate these overlapping regions at a distance from the region where a high quality mesh is needed? Not having any access to validations/examples, makes answering these questions difficult. However, what is sure is that any technique must be fully validated before it is applied to high-end, complex-physics CFD simulations.

As previously mentioned, our experience dictates that a good alternative to the IB method is a technique known as the cut-cell method which combines a body-fitted mesh and Cartesian mesh approach. This method eliminates the disadvantages of using an overset mesh and uses solver technologies, which have been proven for decades, while fully resolving all geometric features of a design and providing a high quality mesh.

We recognise the relevance of IB methods for CFD simulations at the early design stage, when the process (meshing and simulation) must be fast and approximated simulation results are acceptable.

However, once more refined performance predictions are required, we recommend using a more classic approach. It should also be noted that as traditional meshing methods performance increases — and the time it takes to mesh complex geometries with high quality, body-fitted meshes decreases — it is likely that meshing time, a major benefit of IB, will be challenged by these other methods.
Gilles Eggenspieler, Ansys


Sometimes, fashions lose favour for good reasons. There is no doubt that immersed boundary methods were quite fashionable once-upon-a-time, and these methods played an important part in the history of CFD. But the requirement for accurate simulation results have only become more pressing in the decades since finite-difference immersed boundary methods were put aside for more accurate finite volume solutions with body fitted meshes.

What made immersed boundary methods so fashionable was the concept of simple Cartesian meshes. The great hope of these methods was the idea of a fully automated mesh that required literally no manual effort. The eventual conclusion was that, for general applications, the cost in terms of lost accuracy was just too overwhelming to be overcome by the benefits of fully automated meshing.

CD-adapco responded to the needs of the industry and leveraged the best of both approaches to address the needs of engineers with real world simulation requirements. Their solution is known as the “trimmed cell” mesh.

The trimmed cell mesh is an advanced Cartesian style mesh that is highly automated and requires minimal user input. The cells that intersect the CAD geometry are trimmed to fit the body, thus providing the simplicity of a Cartesian mesh AND the accuracy of a boundary fitted mesh. The CD-adapco trimmed cell mesh also simultaneously improves accuracy and ease-of-use with the ability to perform automatic mesh refinement on complex real world geometries.

An inherent weakness of all forms of immersed boundary (IB) methods, shared to some extent by the trimmed mesh approach, is their inability to efficiently resolve thin boundary layers. This is profoundly important in turbulent flows, particularly when the mesh is not aligned with the boundary.

These layers have well-known characteristics: the flow near the wall runs broadly parallel to it, except in local separation or reattachment regions; and gradients normal to the wall are large in comparison to those along it. Good resolution of these gradients is important in many circumstances, and is essential for accurate prediction of drag, heat transfer and flow separation.

These features and requirements favour the use of boundary-fitted meshes, with cells which are long in the flow direction and thin across it. Again, CD-adapco brought a solution to market that provides highly automated prism layer meshing in conjunction with the trimmed cell mesh.

The hybrid approach of the trimmed cell mesh with prism layers is the state-of-the-art in rapid CAD-to-CFD for complex cases that today’s simulation engineers face every day.

Karalit replies

In their response to my article on the immersed boundary (IB) approach to CFD, two traditional vendors provide the same two defenses that inhibited research into this methodology back in the 1990s:

The immersed boundary method is not accurate and not validated by testing and research.

The best approach is to combine a body-fitted mesh with a Cartesian mesh (Ansys), use a body-fitted overset mesh (Ansys, although this supposedly “adds complexity”), or use a prism-layer mesh in conjunction with a trimmed-cell mesh (CD-Adapco).

These vendors would lead us to believe that nothing in CFD has changed in three decades that have brought us widespread access to the Internet, smart phones, HDTV and the cloud, to name just a few innovations.

Addressing the first point, the IB approach has hardly ever been fashionable as one vendor posits. Rather, it has emerged from decades of testing and validations performed by the world’s leading CFD labs for every type of CFD problem.

As for the turbulent problems that are allegedly so troublesome, one has to look no further than studies validating the IB approach from the Center for Turbulence Research (CTR), a research consortium operated jointly by Stanford University and NASA Ames Research Center. The CTR is widely considered one of the leading CFD labs in the world.

Nearly a dozen studies validating the IB approach can be found on the Karalit website.

To address the second point, Karalit offers the immersed mesh approach to augment the standard IB approach. The immersed mesh approach is exactly what the traditional vendors say is the best approach. Furthermore, it is well-designed, fully developed, and completely automated.

The responses of traditional vendors to the IB approach remind me of Aesop’s fox and the grapes fable. When the fox cannot reach the grapes, he automatically pronounces them sour. The vendors with traditional solutions that haven’t changed appreciably since the 1990s cannot reach the grapes because it would take a huge investment of time and money.

Therefore, the grapes are sour.

I think we should let users taste the grapes for themselves and be the ones to judge if they are sour or sweet.
Marco Mulas, founder and chairman, Karalit

Ansys and CD-adapco respond to Marco Mulas

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