Numerical Error vs Modeling Error
A discrepancy with experiment can come from the numerics or from the model; separating them is what verification makes possible.
Two Sources of Being Wrong
When a simulation disagrees with an experiment, the disagreement has two possible origins. Numerical error is the gap between the computed solution and the exact solution of the model equations, from discretization, iteration, and round-off. Modeling error is the gap between the exact solution of the equations and reality, because the equations are an approximation. Telling them apart is essential, and it is exactly what verification enables.
Why Separation Matters
- If the discrepancy is numerical, refine the mesh; the model may be fine.
- If the discrepancy is modeling error, refining the mesh will not help; the physics must change.
- If the two are confused, effort goes to the wrong fix, and a good model may be discarded or a bad one trusted.
The Cancellation Trap
The most dangerous case is when numerical error and modeling error happen to cancel, producing agreement with experiment for the wrong reasons. Such agreement is fragile: it vanishes when the mesh changes or the regime shifts, because the two errors no longer cancel. A model validated on a coarse mesh through accidental cancellation will fail unpredictably in use. This is the core reason verification must precede validation.
The Correct Order
Verification first bounds the numerical error, ideally driving it well below the discrepancy of interest. Only then can the remaining gap between simulation and experiment be attributed to the model with confidence. A validation comparison reported without the verification evidence that bounds its numerical error is uninterpretable: the reader cannot tell whether a discrepancy indicts the physics or merely the mesh, nor whether an agreement is real or coincidental.
This separation is the organizing principle of the whole discipline. Verification owns the numerical error; validation owns the modeling error; and the error budget keeps the two accounted for separately so that every discrepancy can be diagnosed and every agreement can be trusted for the right reason.