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2 votes

numerical schemes for 1D PDE: for smaller grid size there is an increased roundoff error, larger size more truncation, so sweet spot in between?

I think there are two types of error being conflated here. The first is that if you are using an $n$-th order spatial discretization and an $m$-th order temporal discretization then the total error is ...
whpowell96's user avatar
  • 2,444
2 votes
Accepted

How to quantify the numerical diffusion term in a second-order upwind advection scheme?

The approach I would try here is that of a modified equation. I am not sure if it goes through for you full problem as your transport speed appears to change with $k$ and $t$. But I will outline how ...
Daniel's user avatar
  • 1,273
1 vote

Numerical calculation of the Berry connection

If you want to fix the phase you can refer to the gauge-fixing method adopted by the paper [Journal of the Physical Society of Japan Vol. 74, No. 6, June, 2005, pp. 1674–1677].
Yu-Hsiang Fu's user avatar
2 votes
Accepted

How to calculate the force of solid applied by fluid? Using finite difference method, DNS, staggered grid, SIMPLE algorithm, immersive boundary

The question is solved. I use wrong coefficient formula. I should use 2d formula but actually I use 3d. And my calculation method using momentum conversation may be wrong, but that is fine, I can use ...
CheapMeow's user avatar
3 votes
Accepted

Why does the FDM give a correct solution to a PDE with a discontinuous initial condition?

Looking at the plots of the errors, it seems that there is not much difference between the oscillations that you have in this case with respect to those that you had in your previous post (Can this ...
Rigel's user avatar
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