Your time integrator is a filter
July 5, 2026
Research project
Your time integrator is a filter
The discretize-first identity extends to time: a forward-Euler step is exactly the derivative of a time-filtered field. At practical CFL numbers the time-integration error is the largest single term in the coarse-simulation residual — larger than the subgrid stress everyone models — and one extra closure term, proportional to the time step, accounts for it.
Paper
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