Computational fluid dynamics - Revision history

Emma: Add 3 watermarked SVG illustrations from the Advanced visual plan

2026-11-02T16:11:50Z

Add 3 watermarked SVG illustrations from the Advanced visual plan

← Older revision		Revision as of 17:11, 2 November 2026
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	The governing equations describe changes within small control volumes and exchanges across their boundaries. Flow carries mass, momentum, energy and species between neighbouring locations. Diffusion and source terms represent additional transfers or production. The calculation connects those local balances across the complete domain and advances them according to the chosen solution method.<ref name="CK-196">Cox and Kumar (2002), p. 3-196.</ref>		The governing equations describe changes within small control volumes and exchanges across their boundaries. Flow carries mass, momentum, energy and species between neighbouring locations. Diffusion and source terms represent additional transfers or production. The calculation connects those local balances across the complete domain and advances them according to the chosen solution method.<ref name="CK-196">Cox and Kumar (2002), p. 3-196.</ref>
			[[File:fse-computational-fluid-dynamics-v1.svg\|thumb\|upright=1.5\|alt=Two neighbouring CFD cells exchange transported quantities across a shared face.\|CFD connects local conservation relationships through transport between neighbouring cells. Based on Cox and Kumar (2002), p. 3-196.]]

	Mass conservation offers a useful example. Density can change with time while gas crosses the boundaries of a small region. An additional source can represent material entering the gas phase, such as evaporating droplets. The supplied Fire Dynamics Simulator (FDS) formulation expresses this balance as follows.<ref name="FDS-10">McGrattan et al. (2026), p. 10, equation 2.6.</ref>		Mass conservation offers a useful example. Density can change with time while gas crosses the boundaries of a small region. An additional source can represent material entering the gas phase, such as evaporating droplets. The supplied Fire Dynamics Simulator (FDS) formulation expresses this balance as follows.<ref name="FDS-10">McGrattan et al. (2026), p. 10, equation 2.6.</ref>
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	Reynolds-averaged Navier–Stokes (RANS) approaches solve equations for averaged flow quantities. Additional models represent correlations associated with the unresolved fluctuations. The resulting field can describe the evolution of averages while omitting individual turbulent structures. The averaging procedure is therefore part of the physical meaning of the output, rather than merely a way of displaying it.<ref name="CK-196" />		Reynolds-averaged Navier–Stokes (RANS) approaches solve equations for averaged flow quantities. Additional models represent correlations associated with the unresolved fluctuations. The resulting field can describe the evolution of averages while omitting individual turbulent structures. The averaging procedure is therefore part of the physical meaning of the output, rather than merely a way of displaying it.<ref name="CK-196" />
			[[File:fse-computational-fluid-dynamics-v2.svg\|thumb\|upright=1.5\|alt=Schematic traces distinguish averaged flow from resolved large-scale fluctuations.\|Different turbulence treatments retain different parts of the fluctuating flow. Based on Cox and Kumar (2002), pp. 3-195–3-196, and McGrattan et al. (2026), p. 2.]]

	[[Large eddy simulation\|Large eddy simulation]] (LES) resolves larger turbulent motions and models effects below the effective resolution scale. It can retain more transient spatial detail than an averaged description. Nevertheless, the smaller mixing and reaction processes still require submodels. Resolving visible large eddies does not mean that the chemical reaction zone has been directly calculated.<ref name="CK-195" /><ref name="FDS-2">McGrattan et al. (2026), pp. 2–3.</ref>		[[Large eddy simulation\|Large eddy simulation]] (LES) resolves larger turbulent motions and models effects below the effective resolution scale. It can retain more transient spatial detail than an averaged description. Nevertheless, the smaller mixing and reaction processes still require submodels. Resolving visible large eddies does not mean that the chemical reaction zone has been directly calculated.<ref name="CK-195" /><ref name="FDS-2">McGrattan et al. (2026), pp. 2–3.</ref>
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	Consider two illustrative adjacent gas cells, each initially containing 1.20 kg. Select an external inflow of 0.30 kg/s into the first cell. Let 0.25 kg/s pass from the first cell to the second, while 0.20 kg/s leaves the second cell externally. Assume these rates remain fixed for 10 seconds, with no additional gas mass source.<ref name="CK-196" /><ref name="FDS-10" />		Consider two illustrative adjacent gas cells, each initially containing 1.20 kg. Select an external inflow of 0.30 kg/s into the first cell. Let 0.25 kg/s pass from the first cell to the second, while 0.20 kg/s leaves the second cell externally. Assume these rates remain fixed for 10 seconds, with no additional gas mass source.<ref name="CK-196" /><ref name="FDS-10" />
			[[File:fse-computational-fluid-dynamics-v3.svg\|thumb\|upright=1.5\|alt=Two cell balances both gain half a kilogram, while the combined mass increases by one kilogram.\|Internal exchange cancels when the two cell balances are added. Based on Cox and Kumar (2002), pp. 3-196 and 3-203, and McGrattan et al. (2026), p. 10.]]

	The first cell accumulates 0.05 kg/s, because its inflow exceeds transfer to the second cell by that amount. It therefore gains 0.50 kg and finishes with 1.70 kg. The second cell also accumulates 0.05 kg/s, giving the same final mass. These results follow from the selected flow accounting.<ref name="FDS-10" />		The first cell accumulates 0.05 kg/s, because its inflow exceeds transfer to the second cell by that amount. It therefore gains 0.50 kg and finishes with 1.70 kg. The second cell also accumulates 0.05 kg/s, giving the same final mass. These results follow from the selected flow accounting.<ref name="FDS-10" />

Peter: New FSE wiki article: Computational fluid dynamics (written by GPT-6)

2026-11-01T23:05:53Z

New FSE wiki article: Computational fluid dynamics (written by GPT-6)

New page

'''Computational fluid dynamics''' ('''CFD''') is the numerical solution of equations describing fluid motion and transport. In fire applications, it represents local conservation of mass, momentum, energy and chemical species throughout a computational domain. The domain is divided into many small cells on which the equations are approximated.<ref name="CK-194">Cox and Kumar (2002), pp. 3-194–3-196.</ref> This provides a spatially resolved form of [[Fire modelling|fire modelling]], allowing conditions to vary within rooms and around openings or obstructions.<ref name="VR-11.1">Van Rossum (2027), §§11.1–11.2.</ref>

A [[Zone model|zone model]] instead assigns representative properties to a few prescribed regions. CFD can examine variations that such a representation does not resolve, but it still requires approximations for turbulence, combustion and heat transfer.<ref name="CK-195">Cox and Kumar (2002), pp. 3-195–3-196.</ref> Its credibility depends on the physical model, numerical solution and scenario inputs. A detailed image of smoke or temperature is a presentation of those choices, rather than independent evidence of their accuracy.<ref name="CK-212">Cox and Kumar (2002), p. 3-212.</ref>

== Local conservation and the computational domain ==

The governing equations describe changes within small control volumes and exchanges across their boundaries. Flow carries mass, momentum, energy and species between neighbouring locations. Diffusion and source terms represent additional transfers or production. The calculation connects those local balances across the complete domain and advances them according to the chosen solution method.<ref name="CK-196">Cox and Kumar (2002), p. 3-196.</ref>

Mass conservation offers a useful example. Density can change with time while gas crosses the boundaries of a small region. An additional source can represent material entering the gas phase, such as evaporating droplets. The supplied Fire Dynamics Simulator (FDS) formulation expresses this balance as follows.<ref name="FDS-10">McGrattan et al. (2026), p. 10, equation 2.6.</ref>

<div class="fse-equation">∂ρ/∂t + ∇·(ρu) = ṁ<sub>b</sub>‴</div>

{| class="wikitable"
! Symbol !! Description !! SI unit
|-
| ρ || Gas-mixture density || kg/m³
|-
| t || Time || s
|-
| u || Gas velocity vector || m/s
|-
| ∇·(ρu) || Net outward mass transport per unit volume || kg/(m³·s)
|-
| ṁ<sub>b</sub>‴ || Volumetric gas mass source from represented particles or droplets || kg/(m³·s)
|}

The equation does not determine the velocity by itself. Momentum conservation relates motion to forces and stresses, while energy transport determines thermal changes. The equation of state connects density, temperature, composition and pressure according to the selected approximation. These relations are coupled, so a correct isolated balance is not a complete fire solution.<ref name="CK-196" /><ref name="FDS-11">McGrattan et al. (2026), pp. 10–11.</ref>

Chemical-species equations follow the transport and production of the represented constituents. A combustion model specifies how fuel and oxidiser produce other species and release energy. Thermal radiation and surface heat transfer contribute additional terms. Fire CFD therefore combines fluid equations with models for processes that the numerical grid cannot resolve directly.<ref name="CK-194" /><ref name="FDS-12">McGrattan et al. (2026), pp. 9–12.</ref>

The domain boundary is part of the mathematical problem. It defines where conditions are prescribed and where the model exchanges gas or heat with its surroundings. A computational boundary placed too close to an opening can influence the flow of interest. Cox and Kumar specifically caution against assuming that a fixed-pressure plane at a doorway always represents the surrounding environment adequately.<ref name="CK-boundary">Cox and Kumar (2002), pp. 3-201–3-202 and 3-206.</ref>

== Turbulence and unresolved processes ==

[[Turbulence|Turbulence]] involves motions across a range of scales. Fire plumes contain large structures as well as much smaller mixing processes. A practical building-scale calculation cannot directly resolve all the scales involved in turbulent combustion. The selected turbulence treatment determines which effects are resolved and which require approximation.<ref name="CK-195" />

Reynolds-averaged Navier–Stokes (RANS) approaches solve equations for averaged flow quantities. Additional models represent correlations associated with the unresolved fluctuations. The resulting field can describe the evolution of averages while omitting individual turbulent structures. The averaging procedure is therefore part of the physical meaning of the output, rather than merely a way of displaying it.<ref name="CK-196" />

[[Large eddy simulation|Large eddy simulation]] (LES) resolves larger turbulent motions and models effects below the effective resolution scale. It can retain more transient spatial detail than an averaged description. Nevertheless, the smaller mixing and reaction processes still require submodels. Resolving visible large eddies does not mean that the chemical reaction zone has been directly calculated.<ref name="CK-195" /><ref name="FDS-2">McGrattan et al. (2026), pp. 2–3.</ref>

In the supplied FDS formulation, the LES filter width is associated with local cell size. The represented fields can be interpreted as cell-scale averages. Changing the grid therefore affects both numerical resolution and the division between resolved and modelled turbulence. This is one reason that mesh choice cannot be separated completely from the physical modelling strategy.<ref name="FDS-6">McGrattan et al. (2026), p. 6.</ref>

Combustion and radiation introduce further approximations. The gas temperature available on a practical grid can be lower than the temperature within a thin reacting flame. Radiation treatment must account for the consequences of that limited resolution. The supplied FDS guide explicitly discusses this problem when describing its radiative source term.<ref name="FDS-12" />

The appropriate level of detail depends on the required output. A treatment adequate for overall smoke movement may be inadequate for local surface heat flux. Cox and Kumar discuss this distinction in a validation example where gas predictions and boundary heat-transfer predictions had different quality. Model credibility must therefore be assessed for the quantity being used.<ref name="CK-validationcase">Cox and Kumar (2002), pp. 3-204–3-205.</ref>

== Geometry, boundaries and the fire source ==

The geometry must represent the flow paths relevant to the problem. Openings, obstructions and the fire region influence entrainment and smoke movement. Features smaller than the represented geometry cannot be assumed to exert their real influence automatically. Simplification should therefore be judged against the mechanisms and locations important to the assessment.<ref name="CK-206">Cox and Kumar (2002), p. 3-206.</ref><ref name="VR-11.4">Van Rossum (2027), §11.4.</ref>

Grid shape and geometric capability differ between software implementations. Rectilinear representations simplify some building features, while other approaches allow different treatments of complex surfaces. The relevant limitation is the one documented for the chosen implementation and version. A restriction associated with one grid treatment should not be presented as a universal restriction on CFD.<ref name="VR-11.3">Van Rossum (2027), §11.3.</ref><ref name="FDS-6" />

The fire source requires a justified physical description. Heat release, fuel properties and the area or volume over which the source is imposed influence buoyant motion. Cox and Kumar show that a poorly chosen source size can produce implausible temperatures and distort entrainment. A visually plausible plume is therefore insufficient evidence that the source specification is appropriate.<ref name="CK-206" />

The building surfaces also affect the result. Heat transfer depends on thermal properties and changing surface temperatures, not simply on the existence of a wall. The gas calculation and conduction into the solid must use compatible boundary conditions. An approximation adequate for smoke movement may need refinement when surface heating becomes the principal output.<ref name="CK-boundary" />

Ventilation inputs must describe the intended physical system. Prescribed inlet or outlet conditions can be useful, but do not necessarily reproduce interactions between several branches of a heating, ventilation and air conditioning (HVAC) network. The supplied FDS guide distinguishes such fixed boundaries from a coupled duct-network solver. The assessment must identify which representation is being used and what it assumes.<ref name="FDS-HVAC">McGrattan et al. (2026), p. 111.</ref>

Initial conditions matter when a calculation follows fire development in time. The model starts from a selected thermal and flow state before subsequent changes are applied. Van Rossum places these scenario and material choices within model preparation. The solver then calculates the consequences of that defined problem, rather than selecting an undocumented real fire history.<ref name="VR-11.3" /><ref name="VR-11.4" />

== Mesh, time resolution and numerical error ==

[[Mesh resolution|Mesh resolution]] controls how finely the domain and its changing fields are represented. More cells can describe smaller geometrical and flow features. They also increase computational demand. Van Rossum emphasises that finer cells do not automatically make an entire result more trustworthy, because the other inputs and submodels remain relevant.<ref name="VR-11.3" />

Discretisation replaces continuous derivatives with finite numerical approximations. Cox and Kumar explain how omitted terms create truncation error. Some approximations can act like additional diffusion and smooth the calculated field. A smooth contour can consequently reflect numerical behaviour as well as the physical mixing represented by the model.<ref name="CK-202">Cox and Kumar (2002), pp. 3-202–3-203.</ref>

Refinement studies examine whether the outputs of interest change materially as the grid is altered. They must focus on the locations and quantities relevant to the assessment. Agreement at one monitoring point does not establish that all parts of the solution have comparable resolution. The fire region, openings and vertical buoyant flow deserve particular attention in the cited guidance.<ref name="CK-206" /><ref name="VR-11.3" />

Time resolution is a separate but connected issue. A transient calculation must use time steps appropriate to its grid and numerical scheme. Excessively large steps can lose temporal detail or violate stability conditions. The FDS guide relates advection time stepping to how far fluid can travel across a cell during one update.<ref name="CK-206" /><ref name="FDS-47">McGrattan et al. (2026), pp. 47–49.</ref>

Numerical convergence has several meanings that should remain distinct. An iterative solution can satisfy its discrete equations closely while still changing when the grid is refined. Conversely, a small change between iterations can result from strong underrelaxation rather than an adequately converged solution. Cox and Kumar warn against relying on slowly changing residuals alone.<ref name="CK-202" />

Those iterative observations arise from the RANS solution methods discussed in the handbook chapter. They should not be imposed unchanged on every transient LES algorithm. The applicable checks depend on the solver's documented method. The broader requirement is to demonstrate adequate solution accuracy and stability for the numerical formulation actually used.<ref name="CK-202" /><ref name="FDS-6" /><ref name="FDS-47" />

== Worked conservation check across two cells ==

Consider two illustrative adjacent gas cells, each initially containing 1.20 kg. Select an external inflow of 0.30 kg/s into the first cell. Let 0.25 kg/s pass from the first cell to the second, while 0.20 kg/s leaves the second cell externally. Assume these rates remain fixed for 10 seconds, with no additional gas mass source.<ref name="CK-196" /><ref name="FDS-10" />

The first cell accumulates 0.05 kg/s, because its inflow exceeds transfer to the second cell by that amount. It therefore gains 0.50 kg and finishes with 1.70 kg. The second cell also accumulates 0.05 kg/s, giving the same final mass. These results follow from the selected flow accounting.<ref name="FDS-10" />

Across both cells together, the internal transfer cancels. It is an outflow from one cell and an equal inflow to the other. The external net input is 0.10 kg/s, so total mass rises from 2.40 kg to 3.40 kg over the interval. Summing the individual cell balances gives the same result.<ref name="CK-196" /><ref name="FDS-10" />

This example illustrates a necessary conservation check. If the shared face used inconsistent transfers on its two sides, the combined balance would contain an artificial source or sink. Consistent local accounting is therefore connected to global conservation. The overall balance provides one way to examine the assembled numerical result.<ref name="CK-203">Cox and Kumar (2002), p. 3-203.</ref>

The prescribed rates are not predictions of a complete CFD solver. A physical solution would also require momentum, energy and state relationships to determine compatible flows and thermodynamic conditions. Passing this arithmetic check cannot establish the accuracy of those other processes. It demonstrates why conservation is necessary while remaining insufficient for validation.<ref name="CK-196" /><ref name="CK-203" />

== Verification, validation and application evidence ==

[[Verification and validation|Verification and validation]] address different questions. Verification concerns whether the implementation and numerical solution accurately represent the intended model. Validation concerns how well that model represents the real system for its intended use. A calculation can solve its chosen equations accurately while those equations or submodels remain unsuitable for the application.<ref name="CK-203" />

General fluid-flow benchmarks provide useful evidence about a solver, but do not cover every fire-specific mechanism. Buoyancy, combustion and radiation introduce additional questions. Cox and Kumar specifically distinguish general CFD capability from validity for fire applications. Relevant evidence must address the processes governing the actual prediction.<ref name="CK-203" />

Experimental comparisons should also match the output being used. Gas temperature, species concentration and heat flux are different quantities with different measurement and modelling difficulties. The handbook's discussion of boundary heat transfer illustrates this point. Agreement in one output cannot be transferred automatically to another without examining the responsible submodels.<ref name="CK-validationcase" />

Global mass and energy balances remain valuable diagnostic checks. They can reveal inconsistency even when local images appear plausible. However, a satisfactory global balance can coexist with an inaccurate distribution inside the domain. The cited chapter therefore combines balance checks with convergence, refinement and physical scrutiny of the important flow regions.<ref name="CK-203" /><ref name="CK-206" />

[[Fire Dynamics Simulator|Fire Dynamics Simulator]] is one fire-focused CFD implementation discussed by Van Rossum. Its technical reference documents a particular combination of equations and submodels. Evidence for that combination does not automatically validate a different program, different model options or another version. Software identification belongs alongside the scenario and numerical settings in the assessment.<ref name="VR-11.5">Van Rossum (2027), §11.5.</ref><ref name="FDS-5">McGrattan et al. (2026), pp. 5–6.</ref>

== Interpreting and presenting the result ==

Preprocessing defines geometry, materials, scenarios and inputs; the solver performs the numerical calculation; postprocessing turns its results into plots and other displays. These functions serve different purposes. A postprocessor can reveal patterns that deserve investigation, but cannot independently verify the assumptions that produced them. The underlying numerical quantities remain the evidence being interpreted.<ref name="VR-11.3" />

The reported conclusion should identify the quantities, locations and times actually assessed. It should explain why the chosen resolution and physical treatment are appropriate. Important input assumptions and remaining uncertainties must remain visible. This allows a reader to judge the conclusion against the model's demonstrated capabilities.<ref name="VR-11.3" /><ref name="VR-11.4" />

CFD is particularly useful when the question depends on spatial variation that a simpler representation cannot adequately describe. Its detail nevertheless carries responsibilities for geometry, boundaries, submodels and numerical checks. The final result is a conditional prediction of a defined scenario. Interpretation must retain those conditions instead of treating the visualisation as the event itself.<ref name="CK-195" /><ref name="CK-212" /><ref name="VR-11.4" />

== See also ==
* [[Fire investigation]]
* [[Soot yield]]
* [[Adiabatic surface temperature]]

== Notes ==
<references />

== References ==
* Cox, G., & Kumar, S. (2002). Modeling enclosure fires using CFD. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 3-194–3-218). National Fire Protection Association.
* McGrattan, K., Hostikka, S., Floyd, J., McDermott, R., Vanella, M., Mueller, E., & Paul, C. (2026). ''Fire Dynamics Simulator technical reference guide. Volume 1: Mathematical model'' (NIST Special Publication 1018-1, 6th ed., revision 6.11.1, 10 July 2026). National Institute of Standards and Technology.
* Van Rossum, E. (2027). ''Introduction to Fire Safety Engineering''. Fire Safety Academy.

[[Category:Fire Modelling]]