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05: Pretty Pictures - FEA & CFD Verification and Validation
Verification, validation and engineering judgement in numerical simulation
12 September 2026
The Seduction of a Colourful Plot
Colourful plots derived from numerical simulations are extremely engaging. More importantly, they are a powerful means of communicating complex engineering data. When a simulation is properly constructed, a contour plot can make temperature distributions, stresses, flow fields or vibration behaviour immediately understandable.
Modern engineering software has made producing such results remarkably easy. FEA and CFD solvers are increasingly integrated directly into CAD packages, providing an almost seamless transition from geometry to simulation. Meshing can be highly automated and sophisticated mathematical models can be deployed without requiring the user to understand their theoretical foundations or where different mathematical models should be deployed. This represents a valuable democratisation of technologies that were once the preserve of specialists. But herein lies the danger: Producing a colourful simulation plot is relatively easy. Knowing whether it represents reality is considerably more difficult.
What Exactly Have I Solved?
A numerical solver will generally provide an answer to the problem it has been given. The critical question is whether the engineer has given it the right problem.
A seemingly modest change in a boundary condition can produce a substantially different result. In thermal analysis, estimating heat transfer from a surface may itself require empirical analysis. In vibration analysis, the way a component is mounted can fundamentally alter its predicted response. Material properties, contact conditions, constraints, mesh design and simplifications can all determine whether the resulting simulation is useful or misleading.
CFD can present an even greater challenge. Fluid flows can involve separation, transition, turbulence, compressibility, heat transfer and other interacting phenomena, many of which require particular mathematical models and considerable expertise to simulate appropriately. The extraordinary difficulty of turbulence is captured by a remark commonly attributed to physicist Werner Heisenberg:
"When I meet God, I am going to ask him two questions: Why relativity? And why turbulence? I really believe he will have an answer for the first." Werner Heisenberg.
Modern CFD software can nevertheless allow an engineer to select a generic turbulence model, generate a mesh, press solve and obtain a beautiful flow field. The result may look entirely convincing.
But a convincing simulation and a correct simulation are not the same thing.
Verification and Validation
Two questions sit at the heart of credible numerical simulation.
Verification asks: are we solving the mathematical equations correctly?
· Has the solution converged?
· Is the mesh sufficiently refined?
· Is the time step appropriate?
· Are numerical errors acceptably small?
·Are relevant conservation requirements satisfied?
Useful verification approaches include mesh-independence and time-step-independence studies, monitoring convergence histories and residuals, checking conservation of mass and energy, and comparison with exact or established analytical benchmark solutions.
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Validation asks: does the mathematical model adequately represent the real physical system for the intended application?
Where practicable, numerical predictions should therefore be compared against experimental measurements, physical testing, operational data, published experimental data or other independent physical evidence.
The distinction is important: a simulation can be numerically correct yet still provide the wrong engineering answer.
Sensitivity Analysis
Sensitivity analysis provides another important test of model credibility. What happens if the heat-transfer coefficient is 30% higher or lower? What if friction changes? What if a support is less rigid than assumed? What happens when material properties, turbulence models or operating conditions are varied across credible ranges?
A sensitivity study does more than increase confidence in a result. It can reveal which parameters and assumptions actually control the behaviour of the system. That insight can sometimes be more valuable than the original simulation.
First-Principles Checks
An independent first-principles calculation can provide an especially valuable reference. It will typically involve a greatly simplified model which nevertheless captures the dominant physics of the system. An order-of-magnitude calculation may establish what sort of answer should reasonably be expected, how the result should scale, or what limiting behaviour should occur. If a sophisticated numerical model predicts something radically different, the discrepancy should be understood rather than accepted simply because the numerical result looks convincing.
This is why analytical and numerical methods complement rather than compete with one another. The analytical model helps reveal the underlying physics; the numerical model allows the engineer to investigate complexities that the analytical model cannot readily accommodate.
A numerical model/solver is only a tool and ultimately, it is the engineer’s responsibility to assess the validity of his result. The colourful plot is not the end result – the end result is the engineer’s final assessment.
05: Pretty Pictures - FEA & CFD Verification and Validation
Verification, validation and engineering judgement in numerical simulation
12 September 2026
The Seduction of a Colourful Plot
Colourful plots derived from numerical simulations are extremely engaging. More importantly, they are a powerful means of communicating complex engineering data. When a simulation is properly constructed, a contour plot can make temperature distributions, stresses, flow fields or vibration behaviour immediately understandable.
Modern engineering software has made producing such results remarkably easy. FEA and CFD solvers are increasingly integrated directly into CAD packages, providing an almost seamless transition from geometry to simulation. Meshing can be highly automated and sophisticated mathematical models can be deployed without requiring the user to understand their theoretical foundations or where different mathematical models should be deployed. This represents a valuable democratisation of technologies that were once the preserve of specialists. But herein lies the danger: Producing a colourful simulation plot is relatively easy. Knowing whether it represents reality is considerably more difficult.
What Exactly Have I Solved?
A numerical solver will generally provide an answer to the problem it has been given. The critical question is whether the engineer has given it the right problem.
A seemingly modest change in a boundary condition can produce a substantially different result. In thermal analysis, estimating heat transfer from a surface may itself require empirical analysis. In vibration analysis, the way a component is mounted can fundamentally alter its predicted response. Material properties, contact conditions, constraints, mesh design and simplifications can all determine whether the resulting simulation is useful or misleading.
CFD can present an even greater challenge. Fluid flows can involve separation, transition, turbulence, compressibility, heat transfer and other interacting phenomena, many of which require particular mathematical models and considerable expertise to simulate appropriately. The extraordinary difficulty of turbulence is captured by a remark commonly attributed to physicist Werner Heisenberg:
"When I meet God, I am going to ask him two questions: Why relativity? And why turbulence? I really believe he will have an answer for the first." Werner Heisenberg.
Modern CFD software can nevertheless allow an engineer to select a generic turbulence model, generate a mesh, press solve and obtain a beautiful flow field. The result may look entirely convincing.
But a convincing simulation and a correct simulation are not the same thing.
Verification and Validation
Two questions sit at the heart of credible numerical simulation.
Verification asks: are we solving the mathematical equations correctly?
· Has the solution converged?
· Is the mesh sufficiently refined?
· Is the time step appropriate?
· Are numerical errors acceptably small?
·Are relevant conservation requirements satisfied?
Useful verification approaches include mesh-independence and time-step-independence studies, monitoring convergence histories and residuals, checking conservation of mass and energy, and comparison with exact or established analytical benchmark solutions.
Validation asks: does the mathematical model adequately represent the real physical system for the intended application?
Where practicable, numerical predictions should therefore be compared against experimental measurements, physical testing, operational data, published experimental data or other independent physical evidence.
The distinction is important: a simulation can be numerically correct yet still provide the wrong engineering answer.
Sensitivity Analysis
Sensitivity analysis provides another important test of model credibility. What happens if the heat-transfer coefficient is 30% higher or lower? What if friction changes? What if a support is less rigid than assumed? What happens when material properties, turbulence models or operating conditions are varied across credible ranges?
A sensitivity study does more than increase confidence in a result. It can reveal which parameters and assumptions actually control the behaviour of the system. That insight can sometimes be more valuable than the original simulation.
First-Principles Checks
An independent first-principles calculation can provide an especially valuable reference. It will typically involve a greatly simplified model which nevertheless captures the dominant physics of the system. An order-of-magnitude calculation may establish what sort of answer should reasonably be expected, how the result should scale, or what limiting behaviour should occur. If a sophisticated numerical model predicts something radically different, the discrepancy should be understood rather than accepted simply because the numerical result looks convincing.
This is why analytical and numerical methods complement rather than compete with one another. The analytical model helps reveal the underlying physics; the numerical model allows the engineer to investigate complexities that the analytical model cannot readily accommodate.
A numerical model/solver is only a tool and ultimately, it is the engineer’s responsibility to assess the validity of his result. The colourful plot is not the end result – the end result is the engineer’s final assessment.
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