Solving PDE with smoothing - Time step Query

[Timeforheroes0]

Hi,
I'm solving an Euler CFD code using the Lax-Wendroff method. It contains a dissipative smoothing term which I'm looking to minimise to optimise the accuracy. The timestep and smoothing terms are uncoupled, however different stable time steps result in different accuracy once the calculation has converged when the smoothing factor is constant.
This doesn't make sense in my mind.. I understand why it would converge slower with a lower stable timestep, but how is the accuracy lower as well (i.e. the effects of smoothing is more pronounced)
Thanks for any help as I can't get my head around it.

 

[gtoguy97]

The dissipative smoothing term in an Euler CFD code is there to help reduce or eliminate numerical oscillations, which can arise from the use of a numerical method that is not perfectly stable. The way it works is by introducing a small amount of numerical dissipation (i.e. "smoothing") to the solution, which reduces the amplitude of the oscillations.However, if the time step is too small then this numerical dissipation can be overly effective and can actually introduce errors to the solution. This is because the numerical dissipation is applied on a larger scale than the physical phenomena being simulated, so it can effectively damp out smaller-scale features in the solution that should be present. As a result, the accuracy of the solution can suffer. So, in summary, the larger the time step, the less pronounced the effect of the numerical dissipation will be, leading to improved accuracy for the solution.