Simulate Fluid Flow Applications with the CFD Module

CFD Modeling Software for Single-Phase and Multiphase Flows

Define and solve models for studying systems containing fluid flow and fluid flow coupled to other physical phenomena with the CFD Module, an add-on product to the COMSOL Multiphysics® simulation platform.

The CFD Module provides tools for modeling the cornerstones of fluid flow analysis, including:

  • Incompressible and compressible flows
  • Laminar and turbulent flows
  • Single-phase and multiphase flows
  • Free and porous media flow and flow in open domains
  • Thin film flow

These capabilities are implemented through structured fluid flow interfaces in order to define, solve, and analyze time-dependent (transient) and steady-state flow problems in 2D, 2D axisymmetry, and 3D. In addition to the list above, the CFD Module includes tailored functionality for solving problems that include non-Newtonian fluids, rotating machinery, and high Mach number flow.

The ability to implement multiphysics in a model is important for fluid flow analyses. With the CFD Module, you can model conjugate heat transfer and reacting flows in the same software environment you use to analyze fluid flow problems — simultaneously. Additional multiphysics possibilities, such as fluid-structure interaction, are available when combined with other modules within the COMSOL® product suite.

Lo sapevi? A physics interface is a user interface for a specific physics area that defines equations together with settings for mesh generation, solvers, visualization, and results.

What You Can Simulate with the CFD Module

When you expand COMSOL Multiphysics® with the CFD Module, you have access to features for specialized CFD simulations in addition to the core functionality of the COMSOL Multiphysics® software platform. All of the features listed below are implemented through associated physics interfaces. When defining and solving these problems, the fluid is modeled as incompressible by default but can be interchanged with weakly compressible or fully compressible flow simply by choosing them from a list.

Laminar and Creeping Flow

The Laminar Flow and Creeping Flow interfaces provide you with the functionality for modeling transient and steady flows at relatively low Reynolds numbers. A fluid viscosity may be dependent on the local composition and temperature or any other field that is modeled in combination with fluid flow. For non-Newtonian fluids, you can use the predefined rheology models for viscosity, such as Power Law and Carreau, for easy model setup.

In general, density, viscosity, and momentum sources can be arbitrary functions of temperature, composition, shear rate, and any other dependent variable, as well as derivatives of dependent variables. These settings make it possible to define arbitrary models for viscoelastic flow.

A model of a polystyrene solution injected through a nozzle. Shear-rate-dependent viscosity on the flow of a linear polystyrene solution injected through a nozzle, simulated using the non-Newtonian Carreau model.

Turbulent Flow

A comprehensive set of Reynolds-averaged Navier-Stokes (RANS) turbulence models are available in the corresponding fluid flow interfaces in the CFD Module. The following turbulent flow models are available for transient and steady flows:

Two-Equation Models

  • k-ε model
    The standard k-ε model with realizability constraints
  • Realizable k-ε model
    The k-ε model with modified coefficients satisfying realizability
  • k-ω model
    The revised Wilcox k-ω model (1998) with realizability constraints
  • SST model
    Combination of the k-ε model in the free stream and the k-ω model close to the walls
  • Low-Re k-ε model
    AKN k-ε model, with the possibility to resolve the flow close to walls

Additional Transport-Equation Models

  • Spalart-Allmaras model
    One-equation model with rotational correction, developed for aerodynamic applications
  • v2-f model
    An extension of the k-ε model that accounts for turbulence anisotropy by solving for the wall-normal turbulence velocity fluctuations

Algebraic Turbulence Models

  • Algebraic yPlus model
    • The turbulent viscosity is evaluated by first solving for the wall distance in viscous units using the Reynolds number based on the local speed and dimensional wall distance
    • Robust and computationally efficient, but not as accurate as other more sophisticated models
  • L-VEL model
    • The turbulent viscosity is evaluated by first solving for the wall-parallel velocity in viscous units using the Reynolds number based on the local speed and dimensional wall distance
    • Robust and computationally efficient, but not as accurate as other more sophisticated models

Wall Treatment

You can combine the turbulent flow interfaces with different types of wall treatments, according to the following list:

  • Wall functions
    • Robust and applicable for coarse meshes
    • Limited accuracy
    • Smooth and rough walls
    • Supported by k-ε, Realizable k-ε, and k-ω
  • Low-Reynolds-number treatment
    • Resolves the flow all the way down to the walls
    • Accurate
    • Requires a fine mesh
    • Supported by all turbulence models except the standard k-ε and Realizable k-ε
  • Automatic wall treatment
    • Switches between low-Re treatment and wall functions
    • Accurate according to local mesh resolution
    • Inherits the robustness provided by wall functions
    • Default for all turbulence models except standard k-ε and Realizable k-ε

User-Defined Turbulence Models

Change or extend the model equations directly in the graphical user interface (GUI) to create turbulence models that are not yet included.

A model of turbulent flow in a pipe elbow. The functionality for automatic wall treatment uses a low-Re approach at the well-resolved boundaries in the model (blue) and switches to wall functions (red) at the boundaries where a high resolution is not required (straight sections).

Thin Film Flow

To describe flows in thin domains, such as the thin oil films between moving mechanical parts or fractured structures, the CFD Module provides the Thin Film Flow, Shell interface. This formulation is typically used for modeling lubrication, elastohydrodynamics, or the effects of fluid damping between moving parts due to the presence of gases or liquids (for example, in MEMS).

The Thin Film Flow, Shell interface formulates and solves the Reynolds equation for flow in narrow structures and formulates the mass and momentum balances using a function for the flow averaged across the thickness of the thin structure, which implies that the thickness does not have to be meshed. This functionality helps avoid meshing problems across the gap and thereby saves computation time.

An example of modeling thin film flow in a tilted pad bearing. Pressure and flow in a thin liquid film in a tilted pad bearing. The deformation of the solid structure due to the flow and pressure is shown and multiplied by a factor of around 4000.

Multiphase Flow

In separated multiphase flow systems, you can use surface tracking methods to model and simulate the behavior of bubbles and droplets in detail, as well as free surfaces. For such cases, the shape of the phase boundary can be described in detail, including surface tension effects, using surface tracking techniques for separated multiphase flow.

When bubbles, droplets, or particles are small compared to the computational domain and there is a large number of them, you can use dispersed multiphase flow models. These models keep track of the mass fraction of the different phases and the influence that the dispersed bubbles, droplets, or particles have on the transfer of momentum in the fluid in an averaged sense.

The following separated and dispersed multiphase flow models are available for transient and steady flows:

Separated Multiphase Flow Models

  • Level Set method
    • Used for laminar and turbulent flows
    • Adaptive mesh refinement to resolve the phase boundary between phases
    • Track free liquid surfaces in contact with gases in single-phase flows
  • Phase Field method
    • Used for laminar and turbulent flows
    • Three-phase flow model available for laminar flows
    • Adaptive mesh refinement to resolve the phase boundary between phases
    • Track free liquid surfaces in contact with gases in single-phase flows

Dispersed Multiphase Flow Models

  • Bubbly flow model
    • Used for laminar and turbulent flows
    • Used for a relatively small volume fraction (< 0.1) of dispersed gas bubbles in liquids
    • Assumes that bubbles do not accelerate relative to the continuum liquid (equilibrium)
    • Robust and computationally inexpensive
  • Mixture model
    • Similar to the bubbly flow model, but more generic
    • Accurately describes bubbles in liquids, liquid-liquid emulsions, aerosols, and solid particles suspended in liquids, provided that the acceleration of the dispersed phase relative to the continuum phase can be neglected (equilibrium)
    • More computationally expensive than the bubbly flow model, but still relatively inexpensive
  • Euler-Euler model
    • Used for laminar and turbulent flows
    • Most general dispersed multiphase flow model
    • Can be used to tackle bubbly flows, emulsions, liquid suspensions, aerosols, and solid particles suspended in gases
    • Typical applications range from scrubbing gases with liquids to modeling fluidized beds
    • Most computationally expensive
An example of modeling three-phase flow with COMSOL Multiphysics and the CFD Module.

A separated three-phase flow problem is modeled using the Three-Phase Flow, Phase Field interface.

Porous Media Flow

The CFD Module makes it simple to simulate fluid flow in porous media using three different porous media flow models.

Porous Media Flow Models

  • Darcy's law
    • Robust and computationally inexpensive description of flows in porous structures
    • Available for two-phase flow
  • Brinkman equations
    • An extension of Darcy's law that accounts for the dissipation of kinetic energy by viscous shear
    • Relevant for highly open structures with high porosity
    • More general than the Darcy's Law interface, and therefore more computationally expensive
  • Free and porous media flow
    • Couple flow in porous domains with laminar or turbulent flows in open domains
    • Formulates the Brinkman equations for the porous domain and the laminar or turbulent flow equations for the free flow

High Mach Number Flow

Model transonic and supersonic flows of compressible fluids in both laminar and turbulent regimes. The laminar flow model is typically used for low-pressure systems and automatically defines the equations for the momentum, mass, and energy balances for ideal gases. High Mach number flow is available for the k-ε and Spalart-Allmaras turbulence models.

The COMSOL® software automatically formulates the energy equation coupled to the momentum and mass balance equations for ideal gases. In both cases, when meshing these models, automatic mesh refinement resolves the shock pattern by refining around the regions with very high velocity and pressure gradients.

An example of modeling high Mach number flow using COMSOL Multiphysics and the CFD Module. Shock diamonds in the velocity field of supersonic flow from an ejector are modeled using an interface for turbulent high Mach number flow.

Fluid Flow in Rotating Machinery

Rotating machines, such as mixers and pumps, are common in processes and equipment where fluid flow occurs. The CFD Module provides rotating machinery interfaces that formulate the fluid flow equations in rotating frames and are available for single-phase laminar and turbulent flow. Either define and solve problems using the full time-dependent description of the rotating system or use an averaged approach based on the frozen rotor approximation. This feature is computationally inexpensive and can be used to estimate averaged velocities, pressure changes, mixing levels, averaged temperature and concentration distributions, and more.

Generally speaking, the CFD Module can also solve fluid flow problems on any moving frame, not just rotating frames. You can use moving frames to solve a problem where a structure slides in relation to another structure with fluid flow in between, which is easy to set up and solve by employing a moving mesh.

An example of modeling fluid flow in rotating machinery with the COMSOL software. Flow and pressure field in a centrifugal pump modeled using turbulent flow in rotating machinery.

Creating Real-World Multiphysics Models

In many cases, fluid flow models are coupled to other phenomena, such as heat transfer, structural mechanics, chemical reactions, or electromagnetic fields in electrokinetic flow and magnetohydrodynamics. Modeling multiple physics phenomena in COMSOL Multiphysics® is no different than a single-physics problem, as the CFD Module provides ready-made multiphysics interfaces for the common couplings.

The CFD Module provides a dedicated physics interface for defining models of heat transfer in fluid and solid domains coupled to fluid flow in the fluid domain. These types of models are denoted conjugate heat transfer models, which implies that the fluid flow equations are defined and solved in the fluid domain, while the heat transfer equations are formulated and solved in both the solid and fluid domains.

For laminar flows and turbulence models using the low-Reynolds-number wall treatment, the temperature is continuous across the solid-fluid internal boundary, which is the default setting in the nonisothermal flow interfaces. To simulate turbulent conjugate heat transfer using turbulence models with wall functions, the Nonisothermal Flow interface automatically defines thermal wall functions.

The options of low-Re formulations and thermal wall functions make it very straightforward to define and solve conjugate heat transfer problems in combination with turbulent flow.


With the addition of the Structural Mechanics Module, fluid-structure interaction (FSI) problems can be defined and solved for both laminar and turbulent flow. Two FSI options are available in the CFD Module:

  1. One-way FSI coupling, in which the flow creates a load on a structure, but the deformations are small enough to neglect their influence on the flow
  2. Two-way FSI coupling, in which the flow creates loads on a structure, but the deformations are large and influence the flow by changing the shape of the fluid domain

The two-way coupling defines a moving mesh problem in the fluid domain. The displacements at the solid-fluid surfaces are determined by the balance of forces exerted by the fluid and counterforces exerted by the deforming solid structure. Steady-state and time-dependent studies are available for both one-way and two-way FSI problems for laminar and turbulent flows.


You can use the CFD Module to model reacting systems for both turbulent and laminar flows. This allows for the study and design of reactors, mixers, and any other system where chemical reactions and flow occur. The reacting flow interfaces are able to describe multicomponent transport in diluted and concentrated mixtures. The mixture-average model for multicomponent transport is used for concentrated solutions.

The full Maxwell-Stefan multicomponent transport equations are available in combination with the Chemical Reaction Engineering Module. For turbulent reacting flows, the eddy dissipation model is used to describe turbulence fluctuations in the reaction terms for both diluted and concentrated solutions. To simulate multicomponent transport in concentrated mixtures, the Stefan term is also automatically taken into account; for example, at reacting boundaries.

An example of modeling reacting flow using the COMSOL software.

The isoconcentration surfaces of a reactant in a multijet injection reactor are modeled using the Turbulent Reacting Flow interface.

The Mixer Module expands the capabilities of the CFD Module by adding multiphase flow and free surfaces for rotating machinery. Additionally, you can access a Part Library for impellers and vessels to streamline geometry creation. Both of these features are well suited for modeling processes in the pharmaceutical and food industries.

An example of modeling mixers using the COMSOL software. A mixer equipped with three impellers is modeled to show the flow pattern and shape of the free surface.

The multiphase flow interfaces for dispersed flow in the CFD Module treat the dispersed phase as a field where its volume fraction is a model variable. When combined with the Particle Tracing Module, you can use the CFD Module to model Euler-Lagrange multiphase flow models, where particles or droplets are modeled as rigid particles. With rigid particles modeled separately, the interaction between the fluid and the particles is bidirectional, where the particles affect the fluid flow as well. In addition, the Euler-Lagrange models are computationally inexpensive when studying a relatively small volume fraction of particles.


The Pipe Flow Module defines models for networks of pipes and channels where the fluid flow equations can be solved along lines and curves. By combining this product with the CFD Module, you can create high-fidelity simulations that include pipes and channels connecting to 2D or 3D fluid domains with incompressible, weakly compressible, nonisothermal, and reacting flows.

General Functionality Adapted for Solving CFD Problems

When you build a simulation in COMSOL Multiphysics®, you follow a consistent workflow across all add-on modules. The CFD Module offers specialized functionality for fluid flow simulations to maximize the performance and accuracy you need for a CFD analysis. Here are a few of the CFD-specific features:


Generate flow domains, such as a bounding box, around imported CAD geometries. You can automatically or manually remove details included in a CAD representation that are not relevant for fluid flow.


The CFD Module includes a Material Library with the most common gases and liquids. In combination with the Chemical Reaction Engineering Module, you can also access generic descriptions for physical properties of gases (such as viscosity, density, diffusivities, and thermal conductivity).


The physics-controlled mesh functionality in the CFD Module accounts for boundary conditions in fluid flow problems in order to compute accurate solutions. A boundary layer mesh is automatically generated in order to resolve the gradients in velocity that usually arise at the surfaces where wall conditions are applied.


The fluid flow physics interfaces use a Galerkin least-squares method to discretize the flow equations and generate the numerical model in space (2D, 2D axisymmetry, and 3D). The test function is designed to stabilize the hyperbolic terms and the pressure term in the transport equations. Shock-capturing techniques further reduce spurious oscillations. Additionally, discontinuous Galerkin formulations are used to conserve momentum, mass, and energy over internal and external boundaries.


The flow equations are usually highly nonlinear. In order to solve the numerical model equations, the automatic solver settings select a suitable damped Newton method. For large problems, the linear iterations in the Newton method are accelerated by state-of-the-art algebraic multigrid or geometric multigrid methods specifically designed for transport problems.

For transient problems, time-stepping techniques with automatic time stepping and automatic polynomial orders are used to resolve the velocity and pressure fields with the highest possible accuracy, in combination with the aforementioned nonlinear solvers.


The fluid flow interfaces generate a number of default plots to analyze the velocity and pressure fields. There is an extensive list of derived values and variables that can be easily accessed to extract analytical results.

An example of a CFD model mesh. A benchmark CFD model of an Ahmed body. The boundary layer mesh at the wall surfaces is highlighted in blue.
A model of an inkjet droplet that uses adaptive mesh refinement. Adaptive mesh refinement in time. The phase boundary around an inkjet droplet (gray isosurface) and in the projected immediate path of the droplet are refined with a denser mesh to obtain a sharp phase boundary between the droplet and air.

Build Simulation Apps for Streamlined CFD Simulation

You can build user interfaces on top of any existing model using the Application Builder, included in COMSOL Multiphysics®. This tool enables you to create apps for very specific purposes with well-defined inputs and outputs. Apps can be used for many different purposes:

  • Automate difficult and repetitive tasks that can be linked to a single command by recording GUI operations, which can be complex parameterized sequences that may be difficult to reproduce without errors
  • Create and update reports from a large number of parameterized simulations according to specific routines to grant the best possible reproducibility and quality
  • Provide user-friendly interfaces for specific models to allow nonexperts in modeling and simulation to benefit from the accelerated understanding and optimization capabilities
  • Increase access to models within an organization in order to maximize the return on investment from simulation-driven development and design
  • Get a competitive edge by allowing your customers to get the best possible fit regarding the selection of your products, based on high-fidelity models embedded in user-friendly apps that you provide
An example app for simulating water treatment basin designs. The Water Treatment Basin app demonstrates the use of parameterized geometry sequences; cumulative selection for the automatic definition of boundary conditions; and the building of graphical user interfaces for easy-to-use, tailored apps.

Il prossimo passo?
Richiedi una Dimostrazione
del Software

Ogni esigenza di business e di simulazione è diversa. Per valutare se il software COMSOL Multiphysics® soddisfa o meno le vostre esigenze, non dovete fare altro che contattarci. Parlando con uno dei nostri tecnici commerciali, riceverete consigli personalizzati ed esempi completamente documentati per aiutarvi a ottenere il massimo dalla vostra valutazione e guidarvi a scegliere l'opzione di licenza migliore per soddisfare le vostre esigenze.

Basta cliccare sul pulsante "Contatta COMSOL", inserire i propri contatti ed eventuali commenti o domande specifiche, e inviare la richiesta. Riceverete una risposta entro un giorno lavorativo.