Basic CFD concepts
An introduction to computational fluid dynamics: the governing equations, the CFD workflow, turbulence modeling and meshing, with short video lessons.
What is computational fluid dynamics?
Computational fluid dynamics (CFD) uses numerical methods to solve problems involving the flow of liquids and gases. In practice it means using a computer to calculate how a fluid moves through or around a geometry, and what happens to pressure, temperature and velocity on the way. CFD is one type of CAE simulation, next to structural, thermal and system analysis.
Instead of building a prototype and testing it in a wind tunnel or a flow rig, you create a digital model of the geometry, define the conditions (which fluid, what speed, what temperature) and let the software solve the physics. The result is a three-dimensional picture of the flow that would be hard or impossible to measure.
CFD rests on the conservation of mass, momentum and energy, written as the Navier–Stokes equations. These are too complex to solve analytically for anything but the simplest cases, so CFD splits the domain into millions of small cells and solves an approximation on each, a process called discretization. Done carefully, the result is accurate enough for engineering decisions: drag predictions within a few percent of wind tunnel data are routine.
Its strength is flexibility as much as accuracy. You can test hundreds of design variants in the time it takes to build one prototype, and see what no sensor can measure: where the flow separates on a wing, the recirculation in a mixing vessel or the temperature field through a battery pack, early in the design when changes are cheap.
The governing equations
Every CFD simulation solves the same set of equations, named after Claude-Louis Navier and George Gabriel Stokes, who derived them independently in the 19th century. They express three conservation laws.
Conservation of mass (continuity)
Mass is neither created nor destroyed: what flows into a region must flow out, adjusted for any change in density. For incompressible flow this means the velocity field is divergence-free. In a simulation, the continuity equation makes sure no mass is invented or lost anywhere in the domain.
∂ρ/∂t + ∇·(ρu) = 0 (1)
Conservation of momentum
This is Newton’s second law for a fluid. A small parcel of fluid is pushed by pressure gradients, slowed by viscous friction between fluid layers and acted on by body forces such as gravity:
ρ(∂u/∂t + u·∇u) = −∇p + ∇·τ + ρg (2)
The difficult part is the nonlinear convective term u·∇u: the velocity appears in its own derivative. This nonlinearity is the mathematical root of turbulence and the reason CFD needs iterative numerical methods rather than closed-form solutions.
Conservation of energy
When temperature matters, in heat transfer, compressible and buoyancy-driven flows, a third equation transports thermal energy: conduction through the fluid, convection with the flow, viscous dissipation and any heat sources. For many isothermal, incompressible problems it can be left out, which makes the simulation much simpler.
Together with an equation of state for compressible flow, these equations describe fluid motion completely. The point of CFD is to solve them numerically over millions of points in space and time.
Fluid dynamics fundamentals in six videos
These six short videos from the YouTube channel The Efficient Engineer explain the physics every simulation rests on. Under each one we sum up the concept and why it matters in CFD. The videos load from YouTube only when you press play.
Bernoulli’s equation
When a fluid speeds up, its static pressure drops, and the other way round. This explains the lift on a wing and the pressure drop in a venturi. Strictly it applies to inviscid, incompressible, steady flow along a streamline, but it remains a quick check: if a simulated nozzle flow does not roughly follow Bernoulli, something in the set-up is probably wrong.
Aerodynamic drag
Drag opposes the motion of a body through a fluid. Pressure drag comes from high pressure in front and a low-pressure wake behind; friction drag from viscous shear along the surface. CFD can split drag into these parts and show where on the geometry the losses occur. The drag coefficients page lists values for common shapes.
Aerodynamic lift
Lift acts perpendicular to the flow and comes from the pressure difference between the upper and lower surfaces, driven by the shape and the angle of attack. It is central to wings, turbine blades and automotive downforce, and predicting it well needs a fine mesh near the surface and a turbulence model that captures the boundary layer.
Viscosity
Viscosity is a fluid’s internal resistance to deformation. In the Navier–Stokes equations it sits in the diffusion term and causes the no-slip condition at walls. It sets the boundary layer thickness, the pressure drop in pipes, heat transfer rates and whether the flow is laminar or turbulent, so define it carefully, constant or temperature-dependent.
Laminar and turbulent flow
Laminar flow moves in smooth layers; turbulent flow is chaotic, with eddies at many scales. The Reynolds number, the ratio of inertial to viscous forces, decides which. Most engineering flows are turbulent, so the choice of turbulence model, the mesh and the expected accuracy all depend on it. The dimensionless numbers page covers the Reynolds number and related quantities.
Conduction and the heat equation
Conduction carries heat through a material without bulk motion, and the heat equation describes how temperature spreads over time. In CFD it matters in solids such as heat sinks and pipe walls, and in slow-moving fluids. Many simulations couple conduction in solids with convection in the fluid, so-called conjugate heat transfer, which Simcenter STAR-CCM+ and Simcenter FLOEFD handle natively.
The CFD workflow
Whatever the software, every CFD simulation has three phases: pre-processing, solving and post-processing.
Pre-processing: define the problem
First you create or import the CAD geometry, clean it up (remove small features, close gaps) and define the fluid domain. Then you generate the mesh, dividing the domain into millions of small cells where the equations are solved; its quality directly sets the accuracy. Finally you define the physics: the equations, the fluid properties, the turbulence model and what happens at each boundary.
Pre-processing often takes 60–80 % of the time in a CFD project, and it matters more than the solver run: a perfectly converged solution on a poor mesh is still a wrong answer.
Solving: run the simulation
The solver starts from an initial guess and refines the solution iteration by iteration until the changes become negligible, which is called convergence. For steady problems you monitor the residuals and integral quantities such as forces or mass flow; transient problems march through time, solving the equations at every time step.
The cost depends on the number of cells, the physics (turbulence, multiphase, reactions) and whether the case is steady or transient: from minutes on a laptop to days on a cluster. Cloud computing such as Volupe X offloads the heavy runs.
Post-processing: understand the results
Contour plots of pressure, velocity and temperature, streamlines, vector fields, iso-surfaces and reports of forces, mass flow and heat transfer turn the solution into information.
This is where engineering judgement meets the data: you validate the simulation against known physics or measurements, find problems in the set-up and extract the design insight the simulation was for.
Turbulence modeling
Most real flows are turbulent, with eddies from the size of the domain down to tiny dissipative scales. Resolving all of them, direct numerical simulation (DNS), needs a mesh and a time step so fine that it is impractical for nearly all engineering work. Turbulence models capture the effect of the eddies without resolving each one.
RANS: Reynolds-averaged Navier–Stokes
The most widely used approach in industry. RANS splits the flow into a time-averaged part and fluctuations, and models the effect of the fluctuations with extra transport equations. Common models are k–ε (robust, general purpose), k–ω SST (better near walls, widely used for external aerodynamics and heat transfer) and Spalart–Allmaras (popular in aerospace). RANS is relatively cheap and good enough for many applications.
LES: large eddy simulation
LES resolves the large, energy-carrying eddies and models only the smallest scales. It is much more accurate than RANS for strongly unsteady flows such as separation, jets and combustion, but also far more expensive, typically 100–1000 times the cost, and it needs a transient run on a fine mesh.
DNS: direct numerical simulation
DNS resolves every scale without a model. It is the most accurate approach but limited to low Reynolds numbers and small domains, so it is mainly a research tool for developing and validating turbulence models.
The right model depends on the flow, the accuracy you need, the computing budget and experience. The turbulence model selector recommends one for your case, and the turbulence boundary conditions calculator gives the inlet values it needs.
Meshing
The mesh is the set of small cells over which the equations are solved, and it often has the largest effect on accuracy, convergence and cost. A coarse mesh misses flow details; an overly fine one wastes computing time. The skill lies in putting the right resolution in the right places.
Mesh types
Structured meshes of hexahedral cells are accurate and efficient but hard to generate for complex geometry. Unstructured tetrahedral meshes are easy to generate but need more cells for the same accuracy. Polyhedral meshes, a strength of Simcenter STAR-CCM+, sit in between: fewer cells than tetrahedra, good numerical properties and robust automatic generation.
Boundary layer meshing and y+
Near walls the velocity rises from zero to the free-stream value over a thin boundary layer, which decides drag, heat transfer and separation. It is resolved with thin, stretched prism layers. The wall distance y+ tells you how well the first cell matches what the turbulence model needs, and the y+ calculator gives the first cell height before you mesh.
Mesh independence
A result is only trustworthy if it barely changes when you refine the mesh. In a mesh independence study you run the same case on progressively finer meshes and check that the key results converge. The GCI calculator quantifies that convergence as a numerical uncertainty.
Where CFD is used
CFD is used wherever fluid flow or heat transfer matters. Some of the areas Volupe’s customers work in:
Automotive: external aerodynamics (drag and downforce), underhood thermal management, cabin HVAC, brake cooling, exhaust design and battery thermal management for electric vehicles.
Aerospace and defence: wing and fuselage aerodynamics, engine intakes and exhausts, cabin air, thermal protection and propulsion. Aerospace was one of the first industries to adopt CFD.
Energy: gas, steam, wind and hydro turbines, combustion, heat exchangers, reactor cooling and solar thermal systems, where CFD helps raise efficiency and cut emissions.
Marine and offshore: hull resistance and propulsion, propeller cavitation, wave loads on structures and offshore platforms, often with multiphase models and moving meshes.
Electronics cooling: PCB thermal analysis, data centre airflow, heat sinks and LED thermal management. Simcenter FLOEFD brings these simulations into the CAD environment.
Process, chemical and pharmaceutical: mixing, reactors, particle transport (with Altair EDEM for granular flows), spray drying, filtration and clean-room airflow, often with multiphase and multi-component flow.
Introduction to CFD: a video course
For a deeper look at the theory and practice, this video course walks through the whole CFD process: discretization, the finite volume method and linear solvers; geometry, meshing and boundary conditions; iteration, convergence and stability; and post-processing and validation.
Knowing what happens inside the solver makes you a better, more critical user of any CFD tool. If you prefer structured training with hands-on exercises, see our training courses for Simcenter and Altair software.
CFD software from Volupe
Volupe is a Siemens Platinum Smart Expert Solutions Partner and an Altair Channel Partner, providing licences, support and training for CFD and multiphysics software across Europe.
Simcenter STAR-CCM+ is a multiphysics CFD solver that covers single-phase flow through combustion, multiphase, fluid–structure interaction and electrochemistry, with automated polyhedral and overset meshing, built-in CAD and design exploration. About Simcenter STAR-CCM+.
Simcenter FLOEFD runs CFD inside your CAD system (Solid Edge, NX, CATIA, Creo) for fast thermal and flow results, especially in electronics cooling and HVAC. About Simcenter FLOEFD.
Simcenter HEEDS is a design exploration platform rather than a solver. It drives Simcenter STAR-CCM+, Simcenter FLOEFD or other tools and uses its SHERPA search to find better designs in fewer runs. About Simcenter HEEDS.
Altair CFD tools include AcuSolve (finite element CFD), nanoFluidX (GPU-accelerated particle-based flow) and ultraFluidX (lattice Boltzmann external aerodynamics). About Altair simulation software.
Volupe X is our cloud computing platform for running large simulations without on-premise hardware. About Volupe X.
Sources and changelog
Video sources
The six fundamentals videos are by The Efficient Engineer on YouTube.
The introduction course is a YouTube playlist.
Review
Reviewed by Christoffer Johansson, M.Sc., Senior Application Specialist at Volupe.
Changelog
October 2026: new layout with a table of contents, the continuity and momentum equations, and videos that load only when you press play.
Next steps in the CFD Handbook
All CFD Handbook tools →k–ω SST · k–ε · S–A
Interactive guide
Turbulence model selector
Pick a turbulence model and wall treatment for your case, with a y+ target and prism layer count.
Open the selector →
y+ = uτy / ν
Calculator
y+ calculator
Size the first cell for a target y+, then the prism layer stack.
Open calculator →
GCI = Fs|ε| / (rp − 1)
Calculator
Grid Convergence Index (GCI) calculator
Check mesh independence with a three-grid refinement study.
Open calculator →
Questions about getting started with CFD
Page reviewed by
Christoffer Johansson
Senior Application Specialist, M.Sc.
New to Simcenter STAR-CCM+? We reply within one day.
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What is CFD used for?
To predict how liquids and gases flow, and how heat moves with them, before anything is built: drag and cooling of vehicles, pressure drop in pipes and ducts, mixing in process equipment, cooling of electronics and much more. It lets you test design variants quickly and see flow details that are hard to measure.
How accurate is CFD?
With a careful set-up, CFD routinely predicts aerodynamic drag within a few percent of wind tunnel measurements. The accuracy depends on the turbulence model, the mesh near walls and the boundary conditions, so check mesh independence and validate against measurements where you can.
What is the difference between RANS, LES and DNS?
How much of the turbulence they resolve. RANS models all of it and is the affordable industrial workhorse; LES resolves the large eddies and models the small ones, at typically 100–1000 times the cost; DNS resolves everything and is mainly a research tool.
How long does a CFD simulation take?
From minutes to days. A small steady case runs in minutes on a laptop; a large transient model with complex physics can take days on a computing cluster. The number of cells, the physics and whether the case is steady or transient decide the cost.
How do I get started with Simcenter STAR-CCM+?
Start with our training courses, the free templates for Simcenter STAR-CCM+ and the calculators in this handbook. Not a user yet? Request a free trial and our application engineers will help you get going.
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