which satisfy accuracy term. I need a formulation of "delta t" based on wave velocity and element size.
thank you
The step size is normally determined based on the frequency spectrum of the system. In numerical integrators, the step size is adaptively adjusted to capture the high-frequency contribution. First, one needs to decide on the size of the frequency spectrum of the model; that is the number of the significant modes present in the model. Now, in order to avoid numerical stiffness and the possibility that the integrator may search inefficiently for a solution, one needs to adapt the step size to be in the range of one-tenth the time period of the highest significant frequency in your system.
The step size is normally determined based on the frequency spectrum of the system. In numerical integrators, the step size is adaptively adjusted to capture the high-frequency contribution. First, one needs to decide on the size of the frequency spectrum of the model; that is the number of the significant modes present in the model. Now, in order to avoid numerical stiffness and the possibility that the integrator may search inefficiently for a solution, one needs to adapt the step size to be in the range of one-tenth the time period of the highest significant frequency in your system.
I am not sure if it works Professor Khulief ( one-tenth the time period of the highest significant frequency in your system.). Can you share some of the references towards this fact?
Dear Said Elias. The idea is that in order to capture the contribution of the highest frequency in the model, the integrator must assume several steps inside its time period. As to how many steps are sufficient, numerical integration experts found that one needs more than 6 steps (keeping in mind that we have three nodal points in one cycle). Accordingly, as a rule of thumb, 6 to 10 steps is appropriate.
Now, as for your doubt that it may not work; it depends on the integrator you are using. For instance, if you are tackling a system with a wide-spread frequency spectrum, then to capture the highest frequency and at the same time you need a to consider a simulation time span that covers few cycles of the lowest frequency, then you will end up with an enormous number of steps in each single iteration (not to mention the prediction-correction type of algorithms). This is what we call a numerically stiff system, wherein simple integrators often fail to converge to a solution. In this case, you need a numerical integrator that can handle stiff numerical systems. Such integrators use an adaptive scheme to adjust the step size; that is it uses a very small step size for the high frequency sub-system, while using larger step size for the low-frequncy subsystem. This is why parallel numerical integration is developed to handle such situations more efficiently.
You amy wish to read this classical article; https://www.jstor.org/stable/2949581?seq=1#page_scan_tab_contents
But the available literature on this top is extensive and widely accessible on the net.
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