CFD Fundamentals

What Is It?

Computational Fluid Dynamics (CFD) predicts fluid behaviour by solving discretised forms of the governing conservation equations over a defined computational domain. The fluid flow is not measured — it is computed from the equations of mass, momentum and energy conservation, applied to a mesh that represents the geometry and the surrounding fluid space. CFD produces fields of velocity, pressure, temperature and other quantities throughout the domain, from which engineering quantities — forces, flow rates, pressure losses, heat transfer — are derived.

Why It Matters

CFD allows engineers to predict flow behaviour before hardware is built, to understand flow physics that are difficult or impossible to measure experimentally, and to evaluate design alternatives efficiently. External aerodynamics, internal flow through ducts and cooling passages, thermal-fluid behaviour, compressible flow and transient phenomena all benefit from CFD analysis. However, CFD is not a black box that produces truth — it is a numerical approximation of physical equations, and its credibility depends on the quality of the domain, mesh, boundary conditions, turbulence model and verification. Understanding the fundamentals is essential for producing and interpreting CFD results that support engineering decisions.

CFD is a model of the flow — not the flow itself. The predicted velocity and pressure fields are numerical approximations of the governing equations, not measurements. The credibility of the prediction depends on every modelling decision from domain to post-processing.

The CFD Workflow

A CFD analysis follows a structured workflow from geometry to engineering conclusion. Each step builds on the previous one, and errors or poor decisions at any stage can invalidate the entire analysis.

Geometry → Domain definition → Mesh generation → Fluid/material properties → Boundary conditions → Solver setup → Convergence → Result interpretation → Verification & validation

What Is Being Solved

The CFD solver computes fields of physical quantities throughout the domain. The primary variables depend on the flow type and solver formulation, but typically include velocity components, pressure, and — where relevant — temperature, turbulence variables and density.

The Finite Volume Method

The finite volume method is the most widely used discretisation approach in CFD. The domain is divided into small control volumes (cells). The governing equations are integrated over each cell, converting differential equations into algebraic equations relating the cell values to the fluxes across cell faces. The fluxes — mass, momentum and energy crossing each face — are approximated from the cell-centre values using numerical schemes. The solver iterates to find the cell values that satisfy conservation for every cell simultaneously.

Finite volume concept:

Domain divided into cells (control volumes)
Governing equations integrated over each cell
Fluxes computed at cell faces
Cell values updated to satisfy conservation

For each cell: rate of change = flux in − flux out + sources

Cells, Faces and Fluxes

The mesh consists of cells — the control volumes — and faces — the boundaries between adjacent cells. The solver computes fluxes across faces: mass flux (fluid crossing the face), momentum flux (momentum carried by the fluid and viscous stresses) and energy flux (enthalpy, heat conduction). The accuracy of the flux approximation depends on the numerical scheme and the mesh quality. Higher-order schemes provide better accuracy but may introduce oscillations near steep gradients; lower-order schemes are more robust but less accurate. The mesh quality — cell shape, size, orthogonality — directly affects the accuracy of the flux computation.

Steady vs Transient CFD

In steady CFD, the solver seeks a time-independent solution — the flow field that remains constant under the applied boundary conditions. This is appropriate for flows that are physically steady or where the time-averaged behaviour is sufficient. In transient CFD, the solver advances the flow field through time, capturing unsteady phenomena — vortex shedding, pulsed flow, moving boundaries. Steady CFD is cheaper and simpler but may fail to converge for inherently unsteady flows or may converge to a mean-like solution that misses the physics that actually matters. The choice depends on whether the time-dependent behaviour is important to the engineering question.

Incompressible vs Compressible Flow

In incompressible flow, the density is treated as constant — the velocity and pressure fields are solved without coupling to density variation. This is appropriate for low-speed flows where Mach number effects are negligible (typically M < 0.3). In compressible flow, density varies with pressure and temperature, and the energy equation is coupled to the momentum and continuity equations. Compressible CFD is required for transonic, supersonic and hypersonic flows, and for any flow where density variation is significant. The solver formulation differs — incompressible solvers use pressure-based methods; compressible solvers may use density-based methods.

Laminar vs Turbulent Flow

Laminar flow is smooth and ordered — fluid moves in parallel layers with minimal mixing. Turbulent flow is chaotic and fluctuating — eddies of various sizes create intense mixing. The transition between laminar and turbulent depends on the Reynolds number — the ratio of inertial to viscous forces. For low Reynolds number, the flow is laminar and can be solved directly without a turbulence model. For high Reynolds number (most engineering flows), the flow is turbulent and requires a turbulence model to represent the effect of unresolved turbulent fluctuations on the mean flow. The treatment of turbulence is one of the most important and difficult aspects of CFD.

Decision-Driven Fidelity & Model Hierarchy

A strong CFD workflow increases fidelity only when the additional physics can change an engineering decision. Preliminary pressure-drop estimates, inviscid methods, 2D sections, steady RANS, transient RANS and scale-resolving simulation each answer different questions at different cost. The analyst should begin by defining the required output and the failure or performance mechanism it supports, then select the simplest model that can resolve that mechanism. Higher fidelity should be justified by sensitivity, validation evidence or a known limitation of the lower-order model. This hierarchy prevents two common errors: applying expensive CFD to a question that a conservation calculation could answer more transparently, and using an inexpensive model whose assumptions exclude the very physics that govern the design. The analysis plan should make that fidelity argument explicit before mesh generation begins.

Key Takeaways

• CFD solves discretised conservation equations over a computational domain to predict fluid behaviour
• The finite volume method divides the domain into cells and computes fluxes across cell faces
• Steady CFD seeks a time-independent solution; transient CFD captures unsteady behaviour
• Incompressible CFD treats density as constant; compressible CFD couples density, pressure and temperature
• Turbulent flow requires a turbulence model — the choice of model is a critical engineering decision