You are conflating two different things:
- Proof that your mathematical model is an accurate enough description of physical reality
- Proof that your numerical model is an accurate enough description of the mathematical model
For the first, you run physical validation experiments (using a design of experiments to cover a large enough range of possibilities) and compare the collected data with numerical simulation results. These numerical simulations can be as complex as needed and may include physics + chemistry.
For the second, you find analytical solutions or numerical solutions that are of high degree of accuracy and compare your numerical results. Ideally, your numerical method must be an accurate representation of the mathematical model and that is what most commercial codes do to get certified (for nuclear plant design, for example).
Whether the mathematical model is good enough is a different ball game and is typically determined via both new theory and experiment developments.