3D CFD

An automated CFD simulation uses standardized workflows for geometry preparation, meshing, boundary conditions, solving and postprocessing. This allows variants to be calculated faster, more consistently and with less manual effort. Automation is especially valuable for parameter studies, design studies, optimization and surrogate models. It reduces user errors and makes CFD easier to integrate into modern development processes.

A boundary condition defines how the computational domain interacts with its surroundings. It specifies, for example, how fluid enters, leaves or behaves at solid walls. Typical boundary conditions include inlet, outlet, wall, symmetry plane or periodic boundary condition. Incorrect boundary conditions can lead to physically wrong results even with a high-quality mesh.

Boundary layer resolution describes how finely the mesh represents the flow close to walls. Within the boundary layer, velocity, turbulence quantities and temperature often change strongly over a very small distance. Good boundary layer resolution is crucial for wall friction, pressure loss, heat transfer, flow separation and aerodynamic forces. Depending on the modelling approach, the boundary layer is either resolved near the wall or approximated using wall functions.

Cell size describes the spatial resolution of the computational mesh in a CFD simulation. Small cells can capture local gradients, boundary layers, vortices, narrow gaps or strong temperature changes more accurately. At the same time, smaller cells increase the cell count, runtime and memory demand. A good cell size distribution is therefore always a compromise between accuracy and computational efficiency.

CFD postprocessing is the evaluation and visualization of calculated simulation results. It includes section planes, streamlines, pressure and temperature fields, force evaluations, mass balances, diagrams and comparison tables. Good postprocessing turns raw data into engineering insight. The key is not just an attractive flow image, but a reliable interpretation of the relevant result quantities.

CFD preprocessing includes all steps before the actual calculation. These include geometry preparation, definition of the computational domain, meshing, material selection, boundary conditions, physical models and solver setup. The quality of preprocessing has a major influence on whether a simulation runs stably and produces technically meaningful results. Many CFD problems do not originate in the solver itself, but in incorrect assumptions during preprocessing.

A CFD simulation calculates the behaviour of fluids such as air, water, oil, coolant or gases using numerical methods. Typical results include velocity, pressure, temperature, pressure loss, mass flow rate, forces and heat transfer. The simulation is based on physical conservation equations that are solved on a computational mesh. In industrial development, CFD is used to evaluate and optimize components and systems before they are built or tested.

The CFL number, also called Courant number, describes how far flow information travels within one time step relative to the cell size. It links time-step size, local velocity and mesh resolution. In transient CFD simulations, it is an important criterion for stability and temporal accuracy. High CFL values may be acceptable depending on the solver and numerical scheme, but they must be assessed deliberately.

The computational domain is the spatial region that is calculated in a CFD simulation. It can be the inside of a pipe, a vehicle engine bay, a cooling air duct or the surroundings of a vehicle. The choice of domain influences boundary conditions, runtime and result quality. A domain that is too small can artificially affect the flow, while an unnecessarily large domain increases computational effort.

Computational fluid dynamics is the field that investigates fluid flows using mathematical models and computer-based numerical methods. It combines fluid mechanics, thermodynamics, mathematics, numerical methods and software engineering. The goal is to make flow fields and thermal processes in technical systems predictable by simulation. In practice, the term is often used synonymously with CFD.

The computational mesh divides the domain of a CFD simulation into many small cells or elements. Within these cells, quantities such as pressure, velocity, temperature or turbulence variables are calculated numerically. The mesh resolution determines how well local gradients, boundary layers, vortices or narrow gaps are captured. A mesh that is too coarse may miss important flow effects, while an overly fine mesh greatly increases runtime and memory demand.

Conjugate heat transfer describes the coupled calculation of fluid flow and heat conduction in solid components. It makes it possible to simulate how a fluid heats or cools a component and how heat spreads through the material. CHT is important when wall temperatures cannot simply be prescribed, but result from the interaction between the fluid and the solid. Typical examples include cooling channels, radiators, battery cold plates, engine components and turbomachinery.

Conservation equations state that physical quantities such as mass, momentum and energy must be balanced within a system. In CFD, these equations are applied to many small cells of the computational mesh. This creates a large system of equations that is solved numerically. The quality of a CFD simulation strongly depends on whether these conservation equations are modelled physically and solved in a numerically stable way.

Conservation of energy describes the balance of internal energy, kinetic energy, heat and work in a system. In CFD, it is required when temperature changes, heat transfer, compressibility, viscous heating or chemical reactions are relevant. For purely isothermal flows, the energy equation may sometimes be omitted. In cooling, combustion, heat exchangers and high-speed flows, however, it is essential.

Conservation of mass means that mass is neither created nor destroyed in a closed system. For fluid flows, this means that mass flow rates at inlets, outlets and within the domain must be balanced consistently. In CFD, conservation of mass is especially important for pressure loss analyses, flow distribution, leakage paths and cooling circuits. Errors in the mass balance are a strong warning sign of numerical or modelling problems.

Conservation of momentum describes how the motion of a fluid changes due to forces. These include pressure forces, viscous forces, inertial forces and, if relevant, external forces such as gravity or rotation. In CFD, momentum conservation is the basis for velocity fields, pressure distributions, shear stresses and flow forces. It explains, for example, why pressure losses occur or why a flow separates from a wall.

The continuity equation is the mathematical form of conservation of mass. It ensures that no non-physical mass is created or lost in the simulation. For incompressible flows, it simplifies to the requirement that the velocity field must be divergence-free. In CFD solvers, the continuity equation is closely linked to pressure-velocity coupling.

Continuum mechanics describes matter as a continuously distributed medium rather than modelling individual molecules. This assumption makes it possible to describe flows using fields such as pressure, temperature, density and velocity. For most technical CFD applications, this approach is highly suitable. Only at very small scales, in highly rarefied gases or in molecular effects does the continuum assumption reach its limits.

Convergence means that the numerical solution changes only slightly with further iterations. In CFD, convergence is often assessed using residuals, stable mass flow rates, constant forces, pressure losses or temperatures. A formally converged simulation is not automatically physically correct. Therefore, numerical convergence, plausibility and, where possible, comparison with test data must always be evaluated together.

Correlation with test data compares simulation results with real measurements. The goal is to check and, if necessary, adjust modelling assumptions, boundary conditions, material data, turbulence models or heat transfer approaches. Good test data correlation increases confidence in the simulation and improves its predictive capability. It is a central step in development, especially for engines, cooling systems, aerodynamics and thermal applications.

A coupled solver solves several equations, such as pressure and velocity, simultaneously within one solution procedure. This can capture the coupling between physical quantities more robustly and quickly. Coupled solvers are often advantageous for strongly coupled flows, difficult convergence behaviour or compressible effects. However, they usually require more memory and can be more computationally expensive per iteration.

Density describes the mass of a fluid per unit volume. It is a central material property for mass flow rate, buoyancy, pressure forces, inertia and compressibility. In liquids, density is often approximately constant, while in gases it depends strongly on pressure and temperature. In CFD simulations, correct density modelling is especially important for compressible flows, natural convection, multiphase flows and heat transfer.

A density-based solver uses density or conservative variables as central solution quantities. It is especially suitable for compressible flows, high Mach numbers, strong pressure waves and shock phenomena. Such solvers are often used in high-speed aerodynamics, nozzle flows, turbomachinery or compressible gas flows. For slow incompressible flows, a pressure-based solver is often more efficient.

A design study investigates different design variants using simulations. The goal is to evaluate geometric or functional changes with respect to flow, pressure loss, heat transfer, forces or packaging space. Unlike a simple parameter study, the focus is usually on comparing concrete design alternatives. Design studies support early development phases by revealing optimization potential before prototypes are built.

Discretization influences accuracy, stability, computational time and possible numerical errors in a simulation.

The drag coefficient is a dimensionless quantity describing the flow resistance of a body or component. In aerodynamics, it is commonly referred to as drag coefficient or Cd. It allows different geometries to be compared independently of velocity, density and reference area. In CFD, the drag coefficient is used to evaluate aerodynamic variants, housings, vehicles or flow bodies objectively.

Dynamic viscosity describes the internal friction resistance of a fluid against shear deformation. The higher the dynamic viscosity, the more strongly the fluid resists relative motion between neighbouring layers. It influences boundary layers, pressure loss, Reynolds number and heat transfer. In CFD, dynamic viscosity must be defined correctly as a material property or temperature-dependent function.

The energy equation describes how energy is transported, stored and converted in a flow. It is used when temperatures, heat transfer, compression, expansion or thermal sources must be considered. In cooling and thermal management simulations, it is indispensable. It couples the flow field with the temperature field and enables the assessment of thermal loads.

The finite difference method replaces derivatives in differential equations with differences between neighbouring grid points. It is mathematically intuitive and historically an important basis of numerical flow simulation. For simple and structured grids, it can be very efficient. For complex industrial geometries, however, the finite volume method is often preferred because it handles unstructured meshes more flexibly.

The finite element method divides a domain into small elements and approximates the unknown quantities using shape functions. It is especially well known from structural mechanics and strength analysis. Flow and heat transfer problems can also be solved using the finite element method. In industrial CFD, however, it is often less dominant than the finite volume method, depending on the software and application.

The finite volume method is a numerical method in which the computational domain is divided into small control volumes. The conservation equations are balanced over each of these volumes. This makes the method particularly suitable for flow problems where conservation of mass, momentum and energy must be maintained accurately. Many industrial CFD codes use the finite volume method as their central discretization approach.

The flow field describes the spatial distribution of flow quantities within a computational domain. It includes velocity, pressure, temperature, turbulence quantities and, where relevant, species concentrations. In CFD, the flow field is calculated for every cell of the computational mesh. Its analysis reveals where acceleration, separation, recirculation, losses or non-uniform flow distributions occur.

Flow resistance describes how strongly a component, duct or system restricts the motion of a fluid. It is caused by friction, shape, deflections, internal obstacles or flow separation. High flow resistance usually leads to higher pressure loss and greater energy demand. In product development, flow resistance is reduced to improve efficiency, throughput, cooling performance or aerodynamic behaviour.

A flow simulation describes how a fluid moves through a geometry or around a component. It can reveal acceleration, dead-water regions, recirculation, flow separation and pressure losses. Depending on the engineering question, the simulation can be steady-state, transient, isothermal or coupled with heat transfer. Flow simulations are used in automotive engineering, motorsport, energy technology, mechanical engineering and plant engineering.

Flow velocity describes how fast and in which direction a fluid moves locally. In CFD, it is calculated as a velocity field throughout the computational domain. It influences pressure loss, heat transfer, mixing behaviour, turbulence and forces on components. Very high or highly non-uniform velocities can indicate restrictions, maldistribution, separation or unfavourable geometries.

Fluid dynamics is the branch of fluid mechanics that deals with fluids in motion. It focuses on flow velocities, accelerations, pressure fields, vortices, turbulence and energy transfer. In CFD, fluid dynamics provides the central physical background for calculating technical flows. The term is mainly used when the motion of the fluid is the primary focus.

Fluid mechanics is the science of the behaviour of liquids and gases. It describes how pressure, velocity, density, viscosity and forces are related in fluids at rest or in motion. It forms the physical basis for CFD simulation, aerodynamics, hydraulics, cooling and many mechanical engineering applications. Without an understanding of fluid mechanics, CFD results are difficult to assess correctly.

A grid convergence study systematically investigates how the simulation result changes as the mesh is refined. It is used to estimate the discretization error and assess the numerical quality of a simulation. Unlike a simple plausibility check, it specifically evaluates the influence of the grid on the solution. For critical development decisions, a grid convergence study is an important proof of simulation robustness.

Heat flow rate describes how much thermal energy is transferred per unit time. It is typically given in watts and therefore represents a power. In thermal simulations, heat flow rate is important for quantifying cooling performance, heat removal and thermal loads. It should not be confused with heat flux, which is related to an area and is usually given in watts per square metre.

The heat transfer coefficient describes how effectively heat is transferred between a wall and a flowing fluid. It depends strongly on flow velocity, turbulence, fluid properties, geometry and near-wall behaviour. In CFD, it is often used to evaluate cooling performance, component temperatures and heat exchanger behaviour. A high heat transfer coefficient does not automatically mean a good overall system, because pressure loss and temperature difference must also be considered.

A heat transfer simulation investigates how heat is transported by conduction, convection or thermal radiation. In technical systems, these mechanisms often occur simultaneously and strongly influence the temperature distribution. Heat transfer simulation is especially important for cooling concepts, heat exchangers, thermally loaded components and fluid-flow components. It helps evaluate cooling performance, component temperatures and thermal safety margins.

An initial condition describes the starting state of a simulation. It defines initial values such as pressure, velocity, temperature, turbulence quantities or concentrations in the computational domain. In steady-state simulations, it mainly affects stability and convergence speed. In transient simulations, it can also significantly influence the calculated time history and transition behaviour.

An inlet boundary condition describes how fluid enters the computational domain. Depending on the engineering question, inputs such as mass flow rate, volume flow rate, velocity, total pressure, static pressure, temperature or turbulence quantities may be specified. The inlet condition should represent the real operating condition as accurately as possible. Inaccurate inlet data can strongly affect pressure losses, flow distribution, cooling performance and flow separation in the results.

An iteration is a single numerical solution step within a CFD calculation. In steady-state simulations, the solution approaches a stable state over many iterations. In transient simulations, additional inner iterations may be required within each time step. The number of iterations affects runtime, convergence and the accuracy of the coupled equation solution.

Kinematic viscosity is the ratio of dynamic viscosity to density. It describes how strongly viscous momentum effects spread within the fluid. Kinematic viscosity is especially important for the Reynolds number and therefore for classifying laminar, turbulent or transitional flow. In gases and liquids, it can differ significantly due to changes in temperature and density.

The Mach number is the ratio of local flow velocity to local speed of sound. It describes whether compressibility effects are relevant in a gas flow. At low Mach numbers, a flow can often be treated as approximately incompressible, while at higher Mach numbers density changes, pressure waves and shock phenomena become important. In CFD, the Mach number influences the choice of solver, boundary conditions and physical models.

The mass flow rate describes how much mass of a fluid passes through a surface, channel or component per unit time. It is typically given in kilograms per second. In CFD, mass flow rate is a central quantity for inlet and outlet boundary conditions, mass balances, cooling circuits and turbomachinery. A consistent mass flow balance is an important plausibility check for the simulation.

Mesh generation is the process of creating the surface and volume mesh for a CFD simulation. The CAD geometry is prepared so that a numerically computable mesh can be generated from it. The goal is a mesh that resolves the relevant flow regions sufficiently well while remaining computationally efficient. Good mesh generation is often more important for result quality than later adjustments of individual solver settings.

A mesh independence study checks whether a CFD result still depends strongly on the chosen mesh resolution. Simulations with different mesh refinements are compared. If key results such as pressure loss, force, mass flow rate or heat transfer change only slightly with further refinement, the result is considered largely mesh-independent. Such studies improve the reliability and traceability of CFD results.

Mesh quality describes how suitable a computational mesh is for a stable and accurate numerical calculation. Important criteria include cell distortion, aspect ratio, orthogonality, smoothness of cell size transitions and boundary layer resolution. Poor mesh quality can lead to convergence problems, non-physical results or increased numerical diffusion. Therefore, checking mesh quality is a fixed part of a reliable CFD workflow.

The momentum equation describes the motion of a fluid under the influence of forces. It accounts for pressure gradients, viscous effects, acceleration and external forces. In its viscous form, it is closely related to the Navier-Stokes equations. In industrial CFD simulations, it is one of the central equations for calculating pressure fields, velocities, forces and losses.

The Navier-Stokes equations describe conservation of momentum in viscous fluids. Together with the continuity equation and, where required, the energy equation, they form the main mathematical basis of CFD. They balance pressure forces, inertial forces, viscous forces and external forces. Since these equations usually cannot be solved analytically for real technical flows, CFD solves them numerically.

Numerical accuracy describes how close the computed solution is to the mathematically and physically expected solution. It is influenced by mesh resolution, time-step size, discretization scheme, convergence and modelling assumptions. High numerical accuracy does not automatically mean high physical accuracy if boundary conditions or models are chosen incorrectly. Therefore, numerical accuracy must always be considered together with validation and plausibility checks.

Numerical diffusion is an artificial smoothing of the solution caused by discretization and numerical schemes. It can weaken gradients, vortices, shear layers or temperature differences. In practice, this may make a flow appear more stable, but physically too smeared. Numerical diffusion must be assessed carefully, especially for convection-dominated flows, unsteady structures and coarse meshes.

Numerical dissipation describes the artificial damping of fluctuations or structures by the numerical method. It can help keep a simulation stable, but it can also damp real unsteady structures too strongly. The term is especially relevant in transient simulations, turbulence, acoustics and vortex structures. A good CFD setup avoids unnecessary numerical dissipation without compromising solution stability.

Numerical stability describes whether a simulation can be computed without uncontrolled growth of errors. It depends on mesh quality, time-step size, solver, discretization, boundary conditions and relaxation parameters. An unstable simulation often shows increasing residuals, non-physical values or solver failure. Numerical stability is a prerequisite for reliable results, but it does not guarantee physical correctness.

An outlet boundary condition describes how fluid leaves the computational domain. Common specifications include static pressure, mass flow rate or a dedicated backflow treatment. The outlet location should be chosen so that it does not artificially influence the flow region of interest. Especially in recirculating, unsteady or multi-outlet flows, the outlet condition is an important factor for stability and result quality.

A parameter study compares multiple simulations in which selected parameters are varied systematically. Examples include different mass flow rates, opening areas, wall temperatures, geometry variants or operating points. It shows how engineering targets such as pressure loss, cooling performance, force or temperature change. Parameter studies are an important tool for understanding relationships and making data-driven development decisions.

A periodic boundary condition couples two corresponding surfaces so that the flow repeats periodically. It is used when a geometry consists of repeating segments, such as blade passages, pipe sections, heat exchanger structures or rotating machinery. This allows only a representative sector to be calculated. The periodic assumption is only meaningful if the geometry and operating conditions are truly repetitive.

A plausibility check assesses whether CFD results are technically reasonable and physically understandable. It includes checking mass balances, pressure levels, flow directions, temperatures, forces and orders of magnitude. It is necessary even if residuals are low and the simulation is formally converged. In industrial practice, plausibility checks are an important safeguard against visually convincing but incorrect simulation results.

The Prandtl number is a dimensionless quantity that compares momentum transport and heat transport in a fluid. It depends on viscosity, thermal conductivity, density and heat capacity. A low Prandtl number means that heat diffuses relatively quickly, while a high Prandtl number indicates stronger momentum transport relative to heat diffusion. In CFD, it is important for heat transfer, boundary layers and thermal similarity considerations.

A pressure-based solver uses pressure as the central coupling variable between the continuity and momentum equations. It is commonly used for incompressible and weakly compressible flows. Typical applications include cooling flows, internal flows, low-Mach aerodynamics and many industrial flow problems. For strongly compressible flows or shock waves, a density-based solver may be more suitable.

Pressure drop describes the pressure difference between two points or surfaces in a flow. In practice, the term is often used similarly to pressure loss. Technically, it is useful to distinguish the two: pressure drop is first of all a measurable difference, while pressure loss refers to the irreversible loss of flow energy. In CFD evaluations, it should be clearly defined whether static pressure, total pressure or an averaged pressure is being compared.

The pressure field describes the spatial distribution of static or total pressure in a flow. It is important for evaluating pressure losses, forces, lift, downforce, flow distribution and component loads. Pressure gradients drive flows and can also cause separation or unfavourable backflow. In technical CFD projects, the pressure field is often a central basis for optimization and design.

Pressure loss describes the irreversible loss of mechanical energy in a flow. It is caused by friction, flow deflection, area changes, internal components, turbulence or separation. In CFD projects, pressure loss is one of the most important target quantities for ducts, radiators, filters, valves, exhaust systems and intake systems. Low pressure loss reduces the power demand of pumps, fans or compressors.

A prism layer is an ordered cell layer directly adjacent to solid walls. It is used to resolve the near-wall flow region more accurately, especially boundary layers, wall friction and heat transfer. Prism layers are important in industrial CFD because many relevant losses and thermal effects occur directly at surfaces. Their height, number and growth rate must match the turbulence model and the intended y+ range.

A residual is a measure of how well the discretized equations are satisfied by the current solution. Decreasing residuals indicate that the numerical error within the equation solution is becoming smaller. However, residuals alone are not sufficient to judge the quality of a CFD simulation. Important engineering quantities such as pressure loss, force, mass flow rate or temperature must also be stable and physically plausible.

The Reynolds number is a dimensionless quantity describing the ratio of inertial forces to viscous forces. It helps assess whether a flow is more likely to be laminar, turbulent or transitional. The Reynolds number depends on velocity, characteristic length, density and viscosity. In CFD, it is important for turbulence modelling, similarity considerations, boundary layers and transferring test results to real systems.

A segregated solver solves the equations sequentially rather than simultaneously. This often reduces memory demand and can be very efficient for many industrial applications. Coupling between the equations is established iteratively, for example between pressure and velocity. For strongly coupled or numerically difficult cases, however, a segregated solver may require more iterations.

A sensitivity analysis investigates how strongly a simulation result reacts to changes in individual input quantities. Typical parameters include boundary conditions, material data, mesh resolution, turbulence model, geometry variants or operating points. This makes it possible to identify which inputs are truly decisive for the result. Sensitivity analyses help develop robust designs and avoid unnecessary optimization of unimportant parameters.

Shear stress is a tangential stress caused by friction and velocity gradients in the fluid. It describes how strongly neighbouring fluid layers or the fluid and a wall act on each other. In fluid mechanics, it is important for friction losses, wall loading, boundary layers and viscous effects. In CFD, shear stress can be evaluated within the fluid or directly at walls.

The solver is the numerical algorithm that computes the equation systems of a CFD simulation. It determines how pressure, velocity, temperature, turbulence quantities and other variables are coupled and solved. The choice of solver strongly depends on flow type, compressibility, Mach number, mesh quality and stability requirements. An unsuitable solver can lead to poor convergence, excessive runtime or unreliable results.

A steady-state simulation calculates a time-independent or time-averaged state. It is suitable when the relevant result quantities are not dominated by time-dependent effects. Typical applications include many pressure loss analyses, average flow distribution, steady cooling cases or initial design comparisons. In strongly pulsating, separating or moving flows, however, a steady-state simulation may miss important effects.

A stopping criterion defines when a simulation or iterative process is terminated. Typical criteria include sufficiently low residuals, stable monitored quantities, reached physical time or a maximum number of iterations. In industrial CFD, stopping criteria should be justified not only mathematically but also from an engineering perspective. The key question is whether the relevant result quantities are stable and reliable enough for the task.

A surface mesh represents the geometry of a component or computational domain using small surface cells. It captures edges, curvatures, openings, wall surfaces and CAD details for the CFD model. A clean surface mesh is the basis for a stable and high-quality volume mesh. Errors in the surface mesh, such as gaps, intersections or highly distorted faces, can compromise the entire simulation.

A symmetry plane uses geometric and physical symmetry so that only part of the system needs to be simulated. This can significantly reduce cell count, runtime and memory demand. A symmetry plane is only valid if the geometry, boundary conditions and expected flow behaviour are truly symmetric. If used incorrectly, it can artificially suppress asymmetric effects such as vortices, separation or cross-flow.

The temperature field describes the spatial distribution of temperature within a computational domain. In CFD simulations, it shows where components, fluids or interfaces are hot or cold. It is especially important for cooling, heat exchangers, batteries, engines, power electronics and thermally loaded components. The temperature field is used to assess hot spots, temperature gradients and the effectiveness of a cooling concept.

A thermal simulation calculates temperatures, heat flows and heat distribution in components or complete systems. It is used to identify hot spots, thermal overload, warm-up behaviour or cooling demand. When coupled with CFD, it can also assess the influence of air or liquid flow on the temperature field. Typical applications include battery cooling, power electronics, engine cooling, heat exchangers and vehicle thermal management.

The time step is the time interval between two calculated states in a transient CFD simulation. It determines how finely time-dependent phenomena such as pressure waves, vortex shedding, pulsations or warm-up processes are resolved. A time step that is too large can smooth out important dynamics or cause numerical instability. A time step that is too small increases runtime without necessarily improving the engineering value of the results.

The time-step size describes the size of a single time step in a time-dependent simulation. It must match the flow velocity, cell size and the relevant physical time scale. Especially for moving geometries, acoustic effects, rapid load changes or unsteady vortices, the choice of time-step size is critical. It is often assessed using the CFL number, convergence within each time step and comparison with test data.

A transient simulation calculates the time-dependent evolution of a flow, temperature distribution or system response. In practice, the term is often used similarly to unsteady simulation, but it particularly emphasizes transitions between states. Examples include warm-up processes, load steps, pressure build-up, start-up behaviour or time-dependent cooling. The time-step size and initial condition have a strong influence on stability and the significance of the results.

The turbulence field describes the spatial distribution of turbulent quantities in a flow. These include turbulent kinetic energy, turbulent viscosity, dissipation rate or specific dissipation rate. In industrial CFD, turbulence is usually not fully resolved but modelled using turbulence models. The turbulence field influences mixing, momentum exchange, heat transfer, pressure loss and flow separation.

Under-relaxation is a numerical damping technique in which changes in the solution per iteration are deliberately limited. It is used to stabilize unstable or strongly oscillating solution behaviour. Especially in steady-state simulations with difficult coupling, under-relaxation can improve convergence. Too much under-relaxation makes the simulation slow, while too little can lead to divergence.

An unsteady simulation describes a flow whose quantities change over time. It is required when vortex shedding, pulsations, pressure waves, moving components, load changes or periodic phenomena influence the result. Compared with a steady-state simulation, it is usually much more computationally expensive. In return, it provides time-dependent information that is essential for many real operating conditions.

Validation checks whether a simulation model represents the real physics with sufficient accuracy. CFD results are compared with measurement data, test bench data, wind tunnel data or known reference cases. Validation answers the question of whether the right model is being used for the real engineering task. It is especially important when simulation results are used for development decisions, design or verification evidence.

The velocity field shows the direction and magnitude of the local flow velocity throughout the computational domain. It reveals how the fluid moves through channels, radiators, openings, engine bay regions or around external surfaces. The velocity field can be used to identify acceleration, dead zones, recirculation and non-uniform flow distribution. It is one of the most important result quantities in any CFD simulation.

Verification checks whether the simulation model has been solved correctly from a numerical point of view. It concerns aspects such as mesh quality, convergence, time step, discretization and possible user or implementation errors. Verification answers the question of whether the equations were solved correctly. It differs from validation, because a numerically correct model may still be physically unsuitable.

The volume flow rate describes how much fluid volume passes through a surface or pipe per unit time. It is commonly given in cubic metres per second or litres per minute. Unlike mass flow rate, volume flow rate in gases depends strongly on pressure, temperature and density. In practice, it is often used for fans, pumps, cooling air paths, pipe systems and test bench conditions.

A volume mesh fills the computational domain with three-dimensional cells. The flow equations are solved numerically within these cells, and the result quantities are computed there. Cell shape and cell distribution must match the geometry and expected flow behaviour. Targeted mesh refinement is especially important in boundary layers, narrow gaps, flow deflections or regions with strong gradients.

A wall boundary condition describes the behaviour of the fluid at solid surfaces. It can define no-slip behaviour, wall motion, roughness, wall temperature, heat flux or thermal coupling. In CFD, the wall boundary condition is especially important because wall friction, pressure loss and heat transfer occur directly at surfaces. For moving walls, rotating components or thermally active walls, it must be defined carefully.

The wall distance y+ is a dimensionless quantity describing the location of the first cell centre relative to the wall. It relates the physical wall distance to local flow velocity, density and viscosity. In CFD, y+ indicates whether the near-wall flow is resolved directly or should be modelled using a wall function. An unsuitable y+ range can significantly distort wall friction, heat transfer and flow separation behaviour.

A wall function is a model for the near-wall region of a turbulent flow. It replaces the very fine direct resolution of the viscous sublayer with an empirical or semi-empirical wall treatment. This can significantly reduce the cell count and make industrial CFD simulations more efficient. Wall functions are only reliable when the mesh, y+ range, turbulence model and flow situation are consistent.

Wall shear stress is the shear stress directly at a solid surface. It is caused by the no-slip condition and the velocity gradient in the near-wall boundary layer. In CFD, it is important for friction drag, pressure loss, heat transfer, erosion, deposits and flow separation. Accurate calculation of wall shear stress requires appropriate boundary layer resolution, y+ values and wall treatment.