Hi all.
I am solving a linear wave propagation model applying an external impulsive force in soft tissue medium. So in order to reduce the high frequency oscillations, it might be advantageous to use numerical damping besides physical damping. Do I need to choose the "water" and "non solid" option in the material settings of COMSOL for this?
Actually I am trying to validate my model with literature where they used hourglassing to improve the computational efficacy apart from Rayleigh damping using another software. With the same physical and boundary conditions, large deviations in displacement values are coming between my and literature model. Although qualitatively results are matching but not quantitatively.
I am using the physical Rayleigh damping method in my model. Additionally if I use the spring foundation and added mass, will it be beneficial, do they serve the numerical damper role in COMSOL. Do I really need hourglass stabilization to validate my model using COMSOL.
Thank you.
Abhijit
"hourglassing" is an effect caused by the underintegration of finite elements. This leads to zero shear stiffness. Therefore an hourglass control is included. By analysing wave propagation we saw, that the choice of hourglass controll influences the results
Article Comparison of different higher order finite element schemes ...
Hi,
in addition to Christian‘s comment, I would add that it is generally a poor choice to use linear elements for wave propagation analysis. This is also well docim in the article Christian referred to. As was mentioned, you do one crime (under-integratio) and try to remedy it with another heuristic approach that has no theoretical background.
Since you are already using COMSOL, please rely on high-order finite elements. They work much better for transient analysis. They are robust to locking and will give comparable results with much less degrees of freedom. If you use Spectral Elements (not sure what is actually implemented in COMSOL), you can also use a lumped mass matrix and exploit the benefits of explicit time integrators without a loss of accuracy. Please see the following article for details
Article Mass lumping techniques in the spectral element method: On t...
After these general comments, back to your initial question. The goal of adding numerical damping to a time integrator is to damp out the high frequency spurious waves that exist in finite element discretizations. as a rule of thumb, only the first third of the frequency spectrum of a mesh can be assumed as being accurate and representative for the physical modes you want to model. Therefore, numerical damping should be low in the low frequency regime and high in the high frequency regime. However, if you look at the behaviour of Rayleigh damping, the question is whether you need both physical (Rayleigh) and numerical damping. The answer to this is not so straightforward. If you have included Rayleigh damping, the stiffness proportional term will lead to high frequency damping. The damping increases linear with frequency. Depending on the parameter you choose for the damping, it might be sufficient to damp out the spurious waves. But that is something you would need to check for your model. In general, I would say that having physical damping makes numerical damping quite often obsolete.
Spring foundations and added masses are not related to numerical damping. Again, numerical damping is a property of your time integration scheme.
Hourglass control is only important for low order Serendipity elements. But for Spectral Elements it is obsolete. See article mentioned above.
Water and non solid options also have nothing to do with numerical damping.
Hope this helps!
Sascha
I agree with Sascha Eisenträger Sir. Numerical Damping is introduced in the time integration scheme to damp out the spurious high-frequency oscillations present in the system response obtained on time integration. It is usually used when only the first few modes of the system contribute to the response. However, when the contribution of the higher modes is significant as in the case of shock and impact loading, integration schemes with numerical damping are not preferred. The reference below is a good review of time integration techniques.
Article A survey of direct time-integration methods in computational...
Rayleigh Damping, to the best of my knowledge, is used to model the dissipative nature of the system. It is used to model structural damping and not for numerical damping.
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