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Old   September 5, 2011, 06:48
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I am running a hydrodyamics simulation that is using a 3rd order TVD Runge-Kutta time stepping method along with appropriate 3rd order reconstruction routines to calculate primitive variables at cell boundaries for use in a variety of Riemann solvers to calculate the fluxes. However, my question is quite simple:

After each completed loop of the three steps in the RK algorithm, is the total amount of time elapsed increased by a single time step, three time steps or a third of the time step?

I have tried to compare my results against test problems in the literature and while I can reproduce the solution it is usually at the wrong time. I am just not sure how to control the time step in the calculation of the overall time elapsed. Everything else is working fine!

Thoughts anyone?
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Old   September 5, 2011, 07:17
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Hello Meerkat, this link might help you:

note that the step (timestep) here is h, and the coefficients are the b's....So in the three step method, your bs are 1/6, 2/3, 1/6 (note they add up to 1!). This means that if you have applied your method correctly, the solution is advanced by h (in space or time).

Might I suggest that you turn to the explicit Euler: du/dt = (u(n+1)-u(n))/delta t... that's the easiest and most simple, I'm quite sure there won't be stability issues with an O(3) method....

So pick the Euler, and try a simple testcase, i.e. a density bubble transported by a constant flow velocity.... thereby, you know the physical speed of the problem and can debug your code!

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