Basic CFD Concepts — A Practical Introduction to Computational Fluid Dynamics
New to CFD? Don’t worry. We have carefully selected some easily acessible educational material from around the web to get you familiar with the fundamentals.
Basic CFD Concepts — A Practical Introduction to Computational Fluid Dynamics
Computational fluid dynamics — commonly known as CFD — is one of the most powerful tools available to modern engineers. Whether you are designing a heat exchanger, optimising the aerodynamics of a vehicle, or predicting airflow inside a building, CFD allows you to simulate and understand fluid behaviour before building a single physical prototype.
This guide covers the fundamentals you need to get started: the governing equations behind every simulation, the practical CFD workflow from geometry to results, turbulence modeling, mesh generation, and how CFD is applied across industries. Along the way we have included video resources, links to our CFD Handbook calculators, and pointers to the simulation software we work with every day.
What Is Computational Fluid Dynamics (CFD)?
Computational fluid dynamics, or CFD, is a branch of fluid mechanics that uses numerical methods and algorithms to solve problems involving the flow of liquids and gases. In practical terms, it means using a computer to calculate how a fluid moves through or around a geometry — and what happens to quantities like pressure, temperature, and velocity in the process.
The idea is straightforward: instead of building a physical prototype and testing it in a wind tunnel or a flow rig, you create a digital model of the geometry, define the physical conditions (what fluid, what speed, what temperature), and let the software solve the underlying physics. The result is a detailed three-dimensional picture of the flow field that would be extremely difficult — or outright impossible — to measure experimentally.
CFD is built on the same laws of physics that govern all fluid motion: conservation of mass, conservation of momentum, and conservation of energy. These principles are expressed mathematically by the Navier-Stokes equations, which we discuss in the next section. Because these equations are too complex to solve analytically for anything beyond the simplest geometries, CFD breaks them down into millions of smaller, solvable pieces — a process known as discretisation.
The result is not an exact solution in the mathematical sense. It is a numerical approximation — but one that, when done carefully, is accurate enough to make real engineering decisions. CFD simulations today routinely predict aerodynamic drag within a few percent of wind tunnel measurements, and thermal simulations match experimental data well enough to replace physical testing in many product development workflows.
The power of CFD lies not just in its accuracy, but in its flexibility. You can test hundreds of design variants in the time it takes to build a single physical prototype. You can visualise phenomena that no sensor can measure — the precise location of flow separation on a wing, the recirculation zone inside a mixing vessel, or the thermal gradient through a battery pack. And you can do all of this early in the design process, when changes are cheap.
The Governing Equations of Fluid Flow
Every CFD simulation is ultimately solving the same set of equations — the Navier-Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes who independently derived them in the first half of the 19th century. These equations are the mathematical expression of three fundamental conservation laws.
Conservation of Mass (Continuity Equation)
Mass cannot be created or destroyed. In fluid dynamics terms, this means that the amount of fluid flowing into a region must equal the amount flowing out, adjusted for any change in density. For incompressible flows (like water at moderate conditions), this simplifies to the requirement that the velocity field is divergence-free. In a CFD context, the continuity equation ensures that the simulation does not “invent” or “lose” mass anywhere in the domain.
Conservation of Momentum (Navier-Stokes Momentum Equations)
This is Newton’s second law applied to a fluid: force equals mass times acceleration. For a small parcel of fluid, the forces acting on it include pressure gradients pushing from regions of high pressure to low, viscous forces caused by internal friction between fluid layers, and external body forces such as gravity. The momentum equations describe how these forces combine to accelerate or decelerate the fluid. In vector form, the equation links the rate of change of velocity to the pressure gradient, the viscous stress tensor, and any source terms.
What makes these equations notoriously difficult is the nonlinear convective term — the fact that the velocity appears in its own derivative. This nonlinearity is the mathematical root of turbulence, and it is the reason CFD requires iterative numerical methods rather than neat analytical formulas.
Conservation of Energy
When temperature plays a role — which it does in heat transfer problems, compressible flows, and buoyancy-driven flows — a third equation is added to describe how thermal energy is transported. It accounts for heat conduction through the fluid, convective transport (heat carried by the moving fluid), viscous dissipation (friction generating heat), and any volumetric heat sources. For many isothermal, incompressible problems this equation can be omitted, which simplifies the simulation considerably.
Together, these three sets of equations (plus an equation of state linking pressure, density, and temperature for compressible flows) form a complete mathematical description of fluid motion. The challenge — and the entire point of CFD — is solving them numerically across millions of discrete points in space and time.
Fluid Dynamics Fundamentals — Video Resources
The concepts below form the physical foundation that every CFD simulation rests on. We have selected a series of videos from the educational YouTube channel “The Efficient Engineer” that explain each topic with clear visuals and practical examples. Below each video we provide a brief summary of the concept and why it matters in a CFD context.
Bernoulli’s Equation
Bernoulli’s equation describes the relationship between pressure, velocity, and elevation in a flowing fluid. It tells us that when a fluid speeds up, its static pressure drops — and vice versa. This is the principle behind the lift on an aircraft wing and the pressure drop in a venturi. While Bernoulli’s equation strictly applies to inviscid, incompressible, steady flow along a streamline, it remains one of the most useful quick-check tools in engineering. In CFD, it serves as a sanity check: if your simulation of flow through a nozzle doesn’t roughly follow Bernoulli’s relationship, something is likely wrong with the setup.
Aerodynamic Drag
Drag is the force that opposes the motion of an object through a fluid. It has two main components: pressure drag (caused by the shape of the object creating high-pressure regions in front and low-pressure wakes behind) and friction drag (caused by viscous shear along the surface). Understanding and minimising drag is one of the most common applications of CFD in automotive and aerospace engineering. A well-resolved CFD simulation can decompose drag into its contributing parts and show exactly where on a geometry the losses occur — information that is almost impossible to obtain from a wind tunnel test alone. Volupe’s drag coefficient calculator is a helpful companion tool.
Aerodynamic Lift
Lift is the force that acts perpendicular to the flow direction — most famously, the force that keeps aircraft airborne. It arises from pressure differences between the upper and lower surfaces of a body, driven by the curvature of the geometry and the angle of attack. CFD simulations of lift are central to wing design, turbine blade optimisation, and even automotive downforce development. Accurately predicting lift requires careful attention to mesh resolution near the surface and an appropriate turbulence model to capture boundary layer behaviour.
Viscosity
Viscosity is a fluid’s internal resistance to deformation — informally, its “thickness”. Honey has a high viscosity; air has a low one. In the Navier-Stokes equations, viscosity appears in the diffusion term and is responsible for the no-slip condition at walls (the fact that fluid velocity drops to zero at a solid surface). Getting viscosity right in your simulation is critical: it determines boundary layer thickness, pressure drop in pipes, heat transfer rates, and whether a flow is laminar or turbulent. In CFD, you typically define viscosity as a material property — either constant or temperature-dependent — depending on the problem.
Laminar and Turbulent Flow
Fluid flow can be either laminar (smooth, orderly layers sliding past each other) or turbulent (chaotic, with eddies and vortices at many scales). The transition between them is governed by the Reynolds number — a dimensionless ratio of inertial forces to viscous forces. Most engineering flows are turbulent, which is why turbulence modeling is such a central part of CFD (discussed in detail below). Understanding the difference between laminar and turbulent flow is fundamental: the choice of turbulence model, the required mesh resolution, and the expected accuracy all depend on it. Our dimensionless numbers reference page covers the Reynolds number and other key parameters.
Conduction and the Heat Equation
Heat conduction is the transfer of thermal energy through a material without bulk movement of the material itself. The heat equation — a simplified form of the energy conservation equation — describes how temperature distributes over time. In CFD, conduction is relevant both within solid regions (such as a heat sink or a pipe wall) and within the fluid itself, particularly in low-velocity flows where convection is weak. Many practical simulations involve conjugate heat transfer, where conduction in a solid is coupled with convection in the surrounding fluid — a scenario that tools like Simcenter STAR-CCM+ and Simcenter FLOEFD handle natively.
The CFD Simulation Workflow
Regardless of which software you use, every CFD simulation follows the same three-phase workflow: pre-processing, solving, and post-processing. Understanding this workflow is essential for anyone getting started with CFD.
Pre-processing: Defining the Problem
This is where you set up everything the solver needs. The first step is creating or importing a CAD geometry and cleaning it up — removing small features, closing gaps, and defining the fluid domain (the region where the fluid actually flows, as opposed to the solid parts). Next comes mesh generation: dividing the fluid domain into millions of small cells (also called elements or volumes). The mesh is where the equations will be solved, and its quality directly affects the accuracy of the results. Finally, you define the physics: which equations to solve, what fluid properties to use, which turbulence model to apply, and what happens at each boundary (inlets, outlets, walls, symmetry planes, and so on).
Pre-processing often accounts for 60–80% of the total time spent on a CFD project. Getting the geometry, mesh, and boundary conditions right is far more important than running the solver — a perfectly converged solution on a poor mesh is still a wrong answer.
Solving: Running the Simulation
The solver takes the discretised equations and solves them iteratively — starting from an initial guess and refining the solution step by step until the changes between iterations become negligibly small. This is called convergence. For steady-state problems, you typically monitor residuals (a measure of how well the equations are satisfied at each iteration) and integral quantities like forces or mass flow rates. For transient problems, the solver marches through time, solving the equations at each time step.
The computational cost depends on the problem size (number of cells), the complexity of the physics (turbulence model, multiphase flow, chemical reactions), and whether the simulation is steady or transient. Simple simulations might take minutes on a laptop; large industrial models can require days on a high-performance computing cluster. This is where cloud HPC platforms like Volupe X become valuable — offloading heavy computations so that your local hardware is free for other work.
Post-processing: Understanding the Results
Once the solver has converged, the results need to be visualised and analysed. Post-processing tools let you create contour plots of pressure, velocity, and temperature; streamlines and particle traces showing flow paths; vector fields illustrating flow direction; iso-surfaces highlighting regions of interest (such as zones of recirculation or high turbulent kinetic energy); and quantitative reports of forces, torques, mass flow rates, and heat transfer coefficients.
Post-processing is not just about making pretty pictures. It is where engineering judgement meets simulation data. A good post-processing workflow helps you validate the simulation against known physics or experimental data, identify problems in the setup, and extract the design insights that motivated the simulation in the first place.
Turbulence Modeling in CFD
Turbulence is arguably the biggest challenge in computational fluid dynamics. Most real-world flows — from the air around a car to the cooling flow inside an electronics enclosure — are turbulent. Turbulent flows contain eddies at many different length scales, from the size of the domain down to tiny dissipative structures. Resolving every single eddy numerically is called Direct Numerical Simulation (DNS), and it requires a mesh so fine and a time step so small that it remains impractical for nearly all engineering problems. Instead, engineers use turbulence models — mathematical approximations that capture the effect of turbulence without resolving every detail.
RANS — Reynolds-Averaged Navier-Stokes
The most widely used approach in industrial CFD. RANS models decompose the flow into a time-averaged mean component and fluctuating turbulent components, then model the effect of the fluctuations using additional transport equations. Common RANS models include k-ε (robust and general-purpose), k-ω SST (better near-wall behaviour, widely used for external aerodynamics and heat transfer), and Spalart-Allmaras (popular in aerospace). RANS simulations are steady-state, relatively inexpensive, and give good results for many engineering applications.
LES — Large Eddy Simulation
LES resolves the large, energy-containing eddies directly and only models the smallest scales using a sub-grid-scale model. This makes it significantly more accurate than RANS for flows with large-scale unsteadiness — separated flows, jet mixing, combustion — but also much more expensive (typically 100–1000x the cost of RANS). LES requires a transient simulation and a fine mesh, but the results can capture flow physics that RANS simply cannot represent.
DNS — Direct Numerical Simulation
DNS resolves all scales of turbulence without any modelling. It is the most accurate approach but is limited to low Reynolds number flows and small domains. DNS is primarily a research tool — useful for validating turbulence models and understanding fundamental physics, but not practical for industrial design simulations.
Choosing the right turbulence model is one of the most important decisions in a CFD setup. It depends on the flow regime, the accuracy requirements, the available computational budget, and the engineer’s experience. Our turbulence boundary conditions calculator helps you define the correct inlet conditions for whichever model you choose.
Meshing — The Foundation of Every CFD Simulation
The mesh (or grid) is the spatial discretisation of the fluid domain — the collection of small cells across which the governing equations are solved. Mesh quality has a direct and often dominant impact on simulation accuracy, convergence behaviour, and computational cost. A coarse mesh misses flow details; an overly fine mesh wastes computing time. The art of meshing is finding the right resolution in the right places.
Mesh Types
CFD meshes come in several flavours. Structured meshes (hexahedral cells arranged in a regular pattern) offer excellent numerical accuracy and efficiency but are difficult to generate for complex geometries. Unstructured meshes (typically tetrahedral cells) are easier to generate automatically but require more cells for the same accuracy. Polyhedral meshes — a specialty of Simcenter STAR-CCM+ — offer a compelling middle ground: fewer cells than tetrahedral meshes, better numerical properties, and robust automated generation even for complex industrial geometries.
Boundary Layer Meshing and Y+
Near solid walls, the velocity changes rapidly from zero (the no-slip condition) to the free-stream value. Capturing this boundary layer accurately is critical for predicting drag, heat transfer, and flow separation. This requires thin, stretched cells near the wall — typically called prism layers or inflation layers. The non-dimensional wall distance Y+ describes how finely the mesh resolves the boundary layer relative to the turbulence model’s requirements. Getting Y+ right is one of the most important practical skills in CFD meshing. Our Y+ calculator helps you estimate the required first cell height before generating the mesh.
Mesh Independence
A simulation result is only trustworthy if it does not change significantly when you refine the mesh. This is called a mesh independence study (or grid convergence study): you run the same case on progressively finer meshes and check whether the key results converge to a stable value. Our Grid Convergence Index (GCI) calculator provides a systematic way to quantify this convergence and estimate the numerical uncertainty.
CFD Applications Across Industries
Computational fluid dynamics is used in virtually every industry where fluid flow or heat transfer plays a role. Here are some of the most common application areas — many of which Volupe’s customers work with on a daily basis.
Automotive
External aerodynamics (drag and downforce), underhood thermal management, cabin HVAC, brake cooling, exhaust system design, and battery thermal management for electric vehicles. CFD has become an integral part of the automotive development process, reducing the number of physical prototypes and accelerating time to market.
Aerospace and Defence
Wing and fuselage aerodynamics, engine intake and exhaust flow, cabin pressurisation and air quality, thermal protection of spacecraft, and propulsion system design. The aerospace industry was one of the earliest adopters of CFD and remains at the forefront of pushing simulation fidelity.
Energy and Power Generation
Turbine design (gas, steam, wind, and hydro), combustion optimization, heat exchanger performance, nuclear reactor cooling, and solar thermal systems. CFD helps energy companies improve efficiency, reduce emissions, and meet increasingly strict environmental regulations.
Marine and Offshore
Hull resistance and propulsion, propeller cavitation, wave-structure interaction, ballast water management, and offshore platform wind and wave loading. Simulating these flows often requires multiphase models (air and water) and moving meshes — areas where modern CFD tools excel.
Electronics Cooling
PCB thermal analysis, data centre airflow optimisation, heat sink design, and LED thermal management. As electronic devices become smaller and more powerful, managing heat is a critical design challenge. Tools like Simcenter FLOEFD are specifically designed for electronics thermal simulation within the CAD environment.
Process, Chemical, and Pharmaceutical
Mixing and agitation, reactor design, particle transport (using tools like Altair EDEM for granular flows), spray drying, filtration, and clean room airflow. These industries rely heavily on multiphase and multi-component flow simulations.
Introduction to CFD — Video Course
For a deeper dive into the theory and practice of computational fluid dynamics, the video course below walks through the entire CFD process step by step. It covers the mathematical foundations (discretisation, finite volume method, linear system solvers), the pre-processing stage (geometry handling, mesh generation, boundary condition definition), the solver mechanics (iteration, convergence, stability), and the post-processing phase (data extraction, visualisation, validation).
By the end of the course, you will have a solid understanding of what happens “under the hood” of a CFD solver — which makes you a better, more critical user of any simulation tool. If you prefer structured training with hands-on exercises, take a look at our training programmes for Simcenter and Altair software.
CFD Software and Tools at Volupe
Volupe is a Siemens Platinum Smart Expert Solutions Partner and Altair Channel Partner. We provide licenses, technical support, and training for a comprehensive range of CFD and multiphysics simulation tools across 25 European countries.
Simcenter STAR-CCM+
The industry-leading multiphysics CFD solver. STAR-CCM+ covers everything from basic single-phase flows to complex multiphysics scenarios involving combustion, multiphase flow, fluid-structure interaction, and electrochemistry. Its automated meshing (including polyhedral and overset meshes), built-in CAD tools, and design exploration capabilities make it one of the most complete CFD platforms available. Learn more about Simcenter STAR-CCM+ →
Simcenter FLOEFD
A CFD tool embedded directly inside your CAD environment (Solid Edge, NX, CATIA, Creo). FLOEFD is designed for engineers who want fast, accurate thermal and flow results without leaving their design tool. It is especially popular for electronics cooling and HVAC applications. Learn more about Simcenter FLOEFD →
Simcenter HEEDS
Not a CFD solver itself, but a design exploration platform that automates the search for optimal designs. HEEDS connects to STAR-CCM+, FLOEFD, or any other solver and uses its proprietary SHERPA algorithm to intelligently explore the design space — finding better solutions in fewer iterations than traditional DOE methods. Learn more about Simcenter HEEDS →
Altair CFD Tools
Through the Altair HyperWorks suite, Volupe also provides access to AcuSolve (a general-purpose finite element CFD solver), nanoFluidX (a GPU-accelerated particle-based solver for complex free-surface and multiphase flows), and ultraFluidX (a lattice-Boltzmann solver for fast external aerodynamics). These complement the Simcenter portfolio and give customers flexibility to choose the right tool for each application. Learn more about Altair simulation software →
Volupe X — Cloud HPC
Our cloud computing platform lets you run large-scale CFD simulations without investing in on-premise hardware. Upload your case, select the resources you need, and get results faster. Learn more about Volupe X →
Related Resources in the CFD Handbook
This page is part of Volupe’s CFD Handbook — a growing collection of reference material, calculators, and guides for simulation engineers. Here are some resources you might find useful as a next step:
Y+ Calculator — Estimate the required first cell height for your boundary layer mesh based on flow conditions and desired Y+ value.
Turbulence Boundary Conditions Calculator — Calculate turbulent kinetic energy, dissipation rate, and specific dissipation rate for inlet boundary conditions.
Grid Convergence Index (GCI) Calculator — Quantify numerical uncertainty using Richardson extrapolation across multiple mesh levels.
Nusselt Number Calculator — Look up empirical heat transfer correlations for common geometries.
Dimensionless Numbers Reference — Reynolds, Prandtl, Nusselt, Grashof, and other key dimensionless groups explained.
Drag and Lift Coefficients — Reference data and calculation methods for aerodynamic force coefficients.
Empirical Heat Transfer Correlations — Convective heat transfer coefficient formulas for pipes, plates, and other standard geometries.
Volupe Technical Blog — In-depth articles on simulation tips, best practices, and new software features.
