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Theory
Simcenter STAR-CCM+ simulations are built on numerical algorithms that solve relevant laws of physics according to the conditions that the simulation defines. So that you can identify the physical laws, and understand the methods by which they are solved, Simcenter STAR-CCM+ comes with a Theory Guide.
Reacting Flow
In reacting flows, chemical species mix with each other and react when conditions allow. To model these flows, Simcenter STAR-CCM+ couples species and energy transport equations with the chemistry solvers that compute the source terms.
Gas Phase Combustion—Flamelet Models
To reduce computational expense in combustion simulations, Simcenter STAR-CCM+ can precompute reactions for representative scenarios and tabulate the relevant quantities. A turbulent flame can be approximated as an ensemble of laminar flamelets.
Progress Variable
Within a combustion system, combustion takes place in a thin layer that divides the whole domain between unburnt and fully burnt mixtures. By defining a quantity that represents this distinction in each computational cell, it is possible to solve a transport equation that tracks the progress of transition from the unburnt to fully burnt states.

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Theory
Simcenter STAR-CCM+ simulations are built on numerical algorithms that solve relevant laws of physics according to the conditions that the simulation defines. So that you can identify the physical laws, and understand the methods by which they are solved, Simcenter STAR-CCM+ comes with a Theory Guide.
- Fundamental Equations
  Simcenter STAR-CCM+ models a range of physics phenomena including fluid mechanics, solid mechanics, heat transfer, electromagnetism, and chemical reactions. On a macroscopic scale, where the typical lengths are much greater than the inter-atomic distances, the discrete structure of matter can be neglected and materials can be modeled as continua. The mathematical models that describe the physics of continua are derived from fundamental laws that express conservation principles.
- Fluid Flow
  Simcenter STAR-CCM+ can simulate internal and external fluid flow across a wide range of flow regimes, and for a variety of fluid types. It solves the conservation equations for mass, momentum, and energy for general incompressible and compressible fluid flows.
- Numerical Flow Solution
  In the finite volume method, the solution domain is subdivided into a finite number of small control volumes, corresponding to the cells of a computational grid.
- Turbulence
- Transition
  The term transition refers to the phenomenon of laminar to turbulence transition in boundary layers. A transition model in combination with a turbulence model predicts the onset of transition in a turbulent boundary layer.
- Wall Treatment
  Walls are a source of vorticity in most flow problems of practical importance. Therefore, an accurate prediction of the flow across the wall boundary layer is essential.
- Wall Distance
  Wall distance is a parameter that represents the distance from a cell centroid to the nearest wall face with a non-slip boundary condition. Various physical models require this parameter to account for near-wall effects.
- Heat Transfer
  Heat transfer is the exchange of thermal energy between media at different temperatures. Heat transfers from locations of high temperature to locations of low temperature in order to reach an equilibrium state. The three main mechanisms of heat transfer are: conduction, convection, and radiation.
- Porous Media
  Porous media are continua that contain both fluid and fine-scale solid structures, for example: packed-bed chemical reactors, filters, radiators, honeycomb structures, or fibrous materials. The solid geometrical structures are too fine to be individually meshed and fully resolved by a computational grid.
- Species and Passive Scalars
  Simcenter STAR-CCM+ models the transport, the mixing, and the chemical reactions of multi-component liquids or multi-component gases by solving conservation equations for scalar variables that represent the mass fraction of each species in the mixture. This conservation equation allows for convection, diffusion, and optional source effects, and is solved in addition to the global mass continuity equation.
- Multiphase—Eulerian Approach
  Multiphase flows, where several fluids flow in the domain of interest, play an important role in variety of industrial applications. In general, we associate phases with gases, liquids or solids and as such some simple examples of multiphase flows are: air bubbles rising in a glass of water, sand particles carried by wind, rain drops in air. The definition of phase can be generalized and applied to other fluid characteristics such as size, shape, density, and temperature.
- Multiphase—Lagrangian Approach
  Multiphase flows are found in a wide variety of industrial processes, some examples of which are internal combustion engines, liquid, or solid fueled combustors, spray driers, cyclone dust separators, and chemical reactors. Multiphase in this context refers to one thermodynamic phase, be it a solid, a liquid, or a gas, interacting with another distinct phase.
- Reacting Flow
  In reacting flows, chemical species mix with each other and react when conditions allow. To model these flows, Simcenter STAR-CCM+ couples species and energy transport equations with the chemistry solvers that compute the source terms.
  - Basic Definitions
    Some of the specific terms that are used throughout the reacting flow theory content are summarized here.
  - Governing Equations for Reacting Flows
  - Chemical Kinetics
    Chemical kinetics is concerned with the mechanisms and rates of reaction of chemical species at the molecular level.
  - Reactions—Species Transport
    Using reacting species transport, all species in the mechanism are convected and diffused through the computational domain, and react using the prescribed chemical mechanism.
  - Gas Phase Combustion—Flamelet Models
    To reduce computational expense in combustion simulations, Simcenter STAR-CCM+ can precompute reactions for representative scenarios and tabulate the relevant quantities. A turbulent flame can be approximated as an ensemble of laminar flamelets.
    - Mixture Fraction
      The mixture fraction is the elemental mass fraction that originated from the fuel stream. Mixture fraction is a conserved scalar that is 1 for the fuel stream and 0 for the oxidizer stream.
    - Progress Variable
      Within a combustion system, combustion takes place in a thin layer that divides the whole domain between unburnt and fully burnt mixtures. By defining a quantity that represents this distinction in each computational cell, it is possible to solve a transport equation that tracks the progress of transition from the unburnt to fully burnt states.
    - Flamelet Tables
      To reduce the time that Simcenter STAR-CCM+ spends in computing reaction outcomes during a simulation, Simcenter STAR-CCM+ generates lookup tables before the simulation starts. These lookup tables provide reaction products and mixture properties for a chosen range of states.
    - Chemical Equilibrium
      In some reacting systems, the reaction occurs almost instantaneously when the necessary species are present in the correct proportions. For these systems, the atomic concentrations and initial temperature at a location determine the instantaneous value of any scalar at that spatial location and time.
    - Steady Laminar Flamelet
      In combustion theory, a turbulent flame can be considered as a composition of many thin laminar flamelet structures that are locally one-dimensional. In the tabulated approach, Simcenter STAR-CCM+ solves for reaction products using the one-dimensional model and stores these in the lookup table.
    - Flamelet Generated Manifold
      The Flamelet Generated Manifold (FGM) model is different from the Chemical Equilibrium (CE) and Steady Laminar Flamelet (SLF) models since a progress variable which represents the reaction progress is included to parameterize the thermo-chemistry. The FGM model is appropriate for modeling premixed and partially-premixed flames.
    - Flame Propagation
      There are two flame propagation models in Simcenter STAR-CCM+ that are used to calculate the flame movement in space, for premixed and partially-premixed systems, through calculation of the turbulent flame speed.
  - Interphase Reactions
  - Surface Chemistry
    In this generalized surface chemistry implementation, the mass fractions of gas or liquid species at the reacting surfaces are assumed to be the same as the mass fractions of gas or liquid species at the center of the cell volume.
  - NOx
    There are three sources of NOx emissions; thermal, prompt, and fuel. The transport equation that is used to solve for NOx is the same for all NOx models, with the addition of reacting source terms to account for each NOx source.
  - Soot
    The formation and emission of carbonaceous particles is a process that is often observed during the combustion of hydrocarbons. These particulates, called soot, are a carbon-based material comprising mainly of polycyclic aromatic hydrocarbons (PAH's) and are identified in flames and fires as a yellow luminescence.
  - Particle Reactions
    Discrete-phase (Lagrangian, DEM) particles, such as multi-component solid particles or coal particles, can react with the surrounding gases to form either gaseous or solid products. Simcenter STAR-CCM+ provides multiple models which allow you to simulate different types of particle reactions.
  - Polymerization
    Polymerization is a chemical process in which small molecules combine to form larger molecules that contain repeating structural units of the original molecules.
  - Reacting Channel Coupling
    The Reacting Channel Coupling feature couples a 3D Simcenter STAR-CCM+ simulation with the 1D Plug Flow Reactor which uses the CVODE solver.
  - Reactor Network
    A reactor network is a collection of 0D chemical reactors connected together to rapidly simulate detailed chemistry in steady combustors.
  - Reacting Flow Nomenclature
  - Reacting Flow Bibliography
- Internal Combustion Engines
  Numerical modeling of internal combustion engines plays an increasingly important role in improving engine design. CFD simulation of such engines can give a comprehensive insight into the wide-ranging physics of the device, such as turbulent mixing between fuel and air, the ignition, and combustion chemistry.
- Electrochemistry
  Electrochemistry is the discipline investigating relationships between electrical currents and chemical composition change in general.
- Plasma
  Plasma is a state of matter similar to a gas that is composed partially or completely of charged particles such as ions and electrons which are not bound to each other.
- Electromagnetism
  Many engineering applications, such as electric motors, electric switches, and transformers, involve electromagnetic phenomena. Electromagnetic phenomena can be modeled based on the classical theory of Electromagnetism, which describes the interaction between electrically charged particles in terms of electric fields, magnetic fields, and their mutual interaction.
- Batteries
- Solid Mechanics
  Solid Mechanics describes the behavior of a solid continuum in response to applied loads. Applied loads include body forces, surface loads, point forces, or thermal loads that result from changes in the solid temperature. Applied loads induce a stress field in the structure and can cause displacement of the structure—from an initial undeformed configuration to a deformed configuration.
- Aeroacoustics
  Computational aeroacoustics (CAA) is a branch of multiphysics modeling and simulation that involves identifying noise sources that are induced by fluid flow and propagation of the sound waves then generated.
- Finite Element Method
  The Finite Element method is a powerful tool for finding approximate solutions to continuous problems. The methodology is similar to other numerical techniques that approximate continuous partial differential equations with discrete algebraic equations.
- Mesh Motion
  In transient simulations, mesh motion is a numerical technique that allows you to update the position of the computational domain while the solvers run.
- 6-DOF Rigid Body Motion
  Simcenter STAR-CCM+ allows you to model the motion of a rigid body in response to applied forces and moments. In a rigid body, the relative distance between internal points does not change. Therefore, it is sufficient to solve the equations of motion for the center of mass of the body.
- Rotating Flow
  Rotating flow usually occurs in rotating machinery such as pumps, propellers, fans, wind turbines, and so on.
- Harmonic Balance
  Harmonic Balance equations describe periodic unsteady flows where the unsteady frequencies are known beforehand. They are suited to modeling periodically repeating flow fields that typically occur in turbomachinery such as compressors, turbines, and fans.
- Adjoint
  The adjoint method is an efficient means to predict the influence of many input parameters on some engineering quantities of interest in a simulation.
- Design Manager
  Design Manager provides an automated approach within Simcenter STAR-CCM+ to run design exploration studies. Design exploration covers both performance assessment and optimization.
- Scalars, Vectors, and Tensors
  Most physical quantities in Simcenter STAR-CCM+ are either scalars, vectors, or 2nd-order tensors.
- Solution Data Interpolation
  Many operations require interpolation of solution data between different sets of mesh points. For example, remeshing operations require interpolation of existing solution data onto a new mesh. Data interpolation also occurs at the interface between regions, where contacting boundaries exchange data. Additionally, configurable data mappers allow you to interpolate field functions and tabular data to specified meshes.
- Idealizations
  In many simulations, it is common practice to reduce the size of the computational domain using planes of symmetry, axes of rotation, periodicity, or by reducing the 3D domain to a 2D domain. However, when you calculate physical quantities using reports you generally want to account for the whole domain. You can obtain report values for the full model using idealizations.

Progress Variable

Within a combustion system, combustion takes place in a thin layer that divides the whole domain between unburnt and fully burnt mixtures. By defining a quantity that represents this distinction in each computational cell, it is possible to solve a transport equation that tracks the progress of transition from the unburnt to fully burnt states.

The progress variable $c$ indicates whether the chemical state within a cell represents the unburnt conditions ( $c = 0$ ), burnt conditions ( $c = 1$ ), or something in-between ( $0 < c < 1$ ).

Source terms are calculated depending on the specific combustion model.