I am looking for more information about numerical damping.
While I was working for nonlinear wave propagation, I observed high frequency oscillations due to different frequencies propagating at different speeds. High frequency oscillations also occurs in shock wave propagation problems.
Numerical damping is generally applied to damp out these high frequency oscillations. The numerical damping is fictitious damping. Therefore, the energy damped should be as minimum as possible to achieve correct response in the system.
Bulk viscosity is one of the method used to damp out the high frequencies due to shock wave propagation. There are other methods like Hulbert Chung scheme and Tchamwa-Wielgosz scheme works on filtering the high frequencies from the solution. Sometimes, fictitious stiffness proportional damping can be added to damp high frequencies.
these links may help you
https://www.researchgate.net/publication/230816108_Numerical_damping_of_spurious_oscillations_a_comparison_between_the_Bulk-Viscosity_method_and_the_Tchamwa-Wielgosz_dissipative_explicit_scheme
http://derecho.math.uwm.edu/classes/NWP/XX-DampingVsDispersion.pdf
Formerly called Amplitude Decay error, numerical damping, nowadays, is rarely considered as an error. As well described by Mr. Ravi shankar Badry, numerical damping is one of the characteristics of the method we are using to solve the dynamic problem. Some of these methods can control the amount of numerical damping induced to the solution. This feature sometimes helps the method to yield stable solutions, specially in problems involving high flexibility which means the problem has a very stiff part along with a loose one at the same time.
Article Approximation of structural damping and input excitation force
Ravi, Jumaa, Saeed, Mohammad,
Thanks for your valuable inputs. Still I have some questions.
1) What is the historical background of numerical damping (ND) and who has first made the use of this term?
2) As per my understanding, ND is the additional damping supplied during numerical solution to damp out spurious oscillations in the numerical solution and it is not the inherent property of any integration algorithm then why it is called numerical damping?
3) what is the source of spurious oscillations in the numerical solution?
4) whether the ND is required only for undamped systems with external excitation? OR Damped systems do not require ND in their numerical solution?
I am interested too see the response from the other researchers. Here are the answers to some of your questions.
2). Numerical damping terms seems widely applied in the literature. For example, some of the time integration schemes inherently damp out the energy through so called numerical damping. Below paper may be helpful.
http://web.mit.edu/kjb/www/Principal_Publications/On_a_Composite_Implicit_Time_Integration_Procedure_for_Nonlinear_Dynamics.pdf
http://web.mit.edu/kjb/www/Principal_Publications/Insight_into_an_implicit_time_integration_scheme_for_structural_dynamics.pdf
3). One of the source of Spurious oscillations in the numerical solution is the inability of the traditional FEM techniques to deal with very high frequencies. High frequency content is also generated is shock wave propagation problems.
Please refer my question where in simple elastic nonlinear material is used without damping. As waves are propagating at different speed at different stress levels, at some point very high frequency content is appears. Reducing element size wont help much in such scenarios, as the element size reduces, higher frequency appears.
https://www.researchgate.net/post/Is_it_possible_to_analyse_nonlinear_elastic_wave_propation_using_finite_element_method
4). ND is not only required for undamped systems, it is also required for damped systems as well, if the damping is not enough to suppress the high frequency content.
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