If you drop the grid spacing down to where it's tiny, you'll get the time marching errors, and if you drop the time step, you'll usually get the error of differencing terms. How do you quantify the effect of errors in the cross terms of the equations, where it depends on both spatial and temporal differencing?
Hello Cale,
i think that you must verify the CFL number. Also, the mesh can induce errors.
Reducing the time step should never induced errors - indeed the error must go to zero as the spacing (in time or space) goes to zero for a numerical method to be convergent. You should always use convergent numerical methods.
If you are using an explicit time stepping scheme, then you need to check that the time step is small enough compared to the flow speed and the grid spacing. Look up the "CFL condition", as Alliche mentioned.
If you are using an implicit time stepping scheme then your time step and grid spacing are less tightly coupled. Instead, the time step is chosen to resolve a certain amount of the unsteady flow. In the paper below, we used RANS to model the flow on a ship in waves, and we set the time step to resolve the wave dynamics, but not the turbulent flow. However, this is modeling the temporal behavior, and therefore introduces modeling errors on top of any numerical errors.
Article RANS Computational Fluid Dynamics Predictions of Pitch and H...
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