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Physics Simulation
Simcenter STAR-CCM+ can model a wide range of physics phenomena including fluid mechanics, solid mechanics, heat transfer, electromagnetism, and chemical reactions. Scenarios with multiple time scales can be solved within the same simulation.
Multiphase Flow
Multiphase flow is a term which refers to the flow and interaction of several phases within the same system where distinct interfaces exist between the phases. Simcenter STAR-CCM+ considers flow options where phases coexist as: gas bubbles in liquid, liquid droplets in gas, and/or solid particles in gas or liquid, and/or (large scale) free surface flows.
Discrete Element Method (DEM)
The Discrete Element Method (DEM) is an engineering numerical method to simulate motion of many interacting discrete objects that are typically solid particles. Although DEM modeling demands significant computing power, it provides detailed resolution that other methods cannot achieve. In Simcenter STAR-CCM+, DEM can be applied to regions with or without a volume mesh.
DEM Phase Interaction Model Reference
The DEM Phase Interaction model provides access to other models that define particle interaction behavior.
Hertz Mindlin Model Reference
The Hertz Mindlin no-slip contact model is the standard model that is used for modeling contact between particles.

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Physics Simulation
Simcenter STAR-CCM+ can model a wide range of physics phenomena including fluid mechanics, solid mechanics, heat transfer, electromagnetism, and chemical reactions. Scenarios with multiple time scales can be solved within the same simulation.
- Defining Physics Workflow
  Simcenter STAR-CCM+ contains a wide range of physics models and methods for the simulation of single- and multi-phase fluid flow, heat transfer, turbulence, solid stress, dynamic fluid body interaction, aeroacoustics, and related phenomena. These physics models are all selected using a physics continuum.
- Setting Up Physics
  This section provides information on how to set up physics models in STAR-CCM+.
- Running Physics Simulations
  This part of the documentation describes preparation and procedures for running a Simcenter STAR-CCM+ simulation.
- Motion
  In general, motion can be defined as the change in position of a body with respect to a certain reference frame.
- Space
  The primary function of the Space models in Simcenter STAR-CCM+ is to provide methods for computing and accessing mesh metrics. Examples of mesh metrics include cell volume and centroid, face area and centroid, cell and face indexes, and skewness angle.
- Time
  The primary function of the time models in Simcenter STAR-CCM+ is to provide solvers that control the iteration and/or unsteady time-stepping.
- Mesh Motion and Adaption
  Many simulations that involve motion or geometry change require you to move or deform the mesh. Other simulations require localized mesh adaption in order to achieve an accurate solution.
- Materials
  Material models simulate substances, including various mixtures.
- Fluid Flow
  Many engineering design projects require you to predict the effect of flowing fluids on containing structures or immersed objects. While you can analyse simple scenarios with hand calculations, complex scenarios require you to apply numerical methods for accurate solutions.
- Viscous Flow
  Viscous Flow is a finite element approach for use with viscoelastic materials and other highly viscous non-Newtonian fluids, such as liquid plastics and rubber, dough and similar foodstuffs, molten glass, and mud. Viscoelastic materials resemble elastic materials, but also exhibit viscous effects, rebounding slowly from deformations.
- Passive Scalars
  Passive scalars are user-defined variables of arbitrary value, assigned to fluid phases or individual particles. They are passive because they do not affect the physical properties of the simulation. An intuitive way to think of passive scalars is as tracer dye in a fluid, but with numerical values instead of colors, and with no appreciable mass or volume.
- Heat Transfer
  Heat transfer is the study of energy in transit due to a temperature difference in a medium or between media. Heat transfer extends thermodynamic analysis through the study of the modes of energy transfer and through development of relations to calculate energy transfer rates.
- Species
  This chapter provides information about the chemical species models in Simcenter STAR-CCM+. A species model is activated whenever a multi-component liquid or multi-component gas is chosen from the Material model section of the Physics Model Selection dialog.
- Porous Media
  Simcenter STAR-CCM+ allows you to simulate the transport of a fluid or energy (e.g. heat, electrical charge) through porous materials using the concept that the action of the porous media can be represented using appropriate loss (or 'diffusion') coefficients.
- Adjoint
  The adjoint method is an efficient means to predict the influence of many design parameters and physical inputs on some engineering quantity of interest, that is, on the engineering objective of the simulation. In other words, it provides the sensitivity of the objective (output) with respect to the design variables (input).
- Fans and Blowers
  Simcenter STAR-CCM+ provides models for axial and radial fans where classical fan laws apply.
- Virtual Disk Model
  The virtual disk model is based upon the principle of representing propellers, turbines, rotors, fans, and so on, as an actuator disk. The actuator disk treatment is practical when you are concerned about the influence of the rotor/propeller behavior on the flow rather than knowing about the detailed interactions between the flow and the blades of the rotating device.
- Turbulence
  Most fluid flows of engineering interest are characterized by irregularly fluctuating flow quantities.
- 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 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.
- Radiation
  The Radiation Model is the gateway, or entry point to all of the radiation modeling capabilities of Simcenter STAR-CCM+. This section describes Simcenter STAR-CCM+’s radiation modeling.
- Aeroacoustics
  Aeroacoustics investigates the aerodynamic generation of sound.
- Reacting Flow
  Simcenter STAR-CCM+ provides a selection of models that you can use to simulate a wide range of reacting flow applications.
- Internal Combustion Engines
  In an internal combustion engine (ICE), for example a gasoline engine, the process of combustion takes place in a cylinder (or cylinders) within the engine. The working fluid is a fuel and oxidizer mixture (usually air), which reacts to form combustion products.
- Multiphase Flow
  Multiphase flow is a term which refers to the flow and interaction of several phases within the same system where distinct interfaces exist between the phases. Simcenter STAR-CCM+ considers flow options where phases coexist as: gas bubbles in liquid, liquid droplets in gas, and/or solid particles in gas or liquid, and/or (large scale) free surface flows.
  - Multiphase Framework
    In mathematical terms, there are two main frameworks in the formulation of the multiphase models in Simcenter STAR-CCM+, the Eulerian and Lagrangian modeling strategies.
  - Multiphase Simulation Concepts
    This section presents the key concepts you come across when using the Simcenter STAR-CCM+ multiphase models.
  - Modeling Multiphase Flows
    Simcenter STAR-CCM+ supports several types of multiphase models, each with their own workflow. Use this section to help identify the choice of models that are appropriate for the type of multiphase analysis that you intend to simulate.
  - Defining Eulerian Phases
    A Eulerian phase in Simcenter STAR-CCM+ represents a distinct physical substance – the phase material – that is modeled in a Eulerian framework. Two materials constitute two different Eulerian phases. The definition of a Eulerian phase includes the set of models that apply to the phase material and the relevant material properties.
  - Defining Phase Interactions
    A phase interaction is an object that defines the choice of models that are used to predict the influence of one phase upon another phase within a multiphase flow simulation. Define a phase interaction for every possible significant coupling.
  - Discrete Element Method (DEM)
    The Discrete Element Method (DEM) is an engineering numerical method to simulate motion of many interacting discrete objects that are typically solid particles. Although DEM modeling demands significant computing power, it provides detailed resolution that other methods cannot achieve. In Simcenter STAR-CCM+, DEM can be applied to regions with or without a volume mesh.
    - Discrete Element Model Reference
      The Discrete Element Model is the prerequisite for any work using the DEM solid particle models.
    - DEM Workflow
      Set up a DEM simulation as you would other Lagrangian simulations, including DEM particles of suitable shape and source.
    - Meshfree DEM Workflow
      Set up a meshfree DEM simulation as you would other DEM simulations. Meshfree DEM simulations have no volume mesh of interiors. In other regards, this workflow has many of the same steps as the mesh-based workflow, although the mesh-based workflow also includes steps related to continuous-phase physics.
    - Meshfree DEM Model Reference
      The Meshfree DEM model allows you to use DEM in simulations that have no volume meshes of interiors. Meshfree DEM simulations do not solve for the flow of the fluid phase. This approach allows you to set up simulations quickly when they are for large DEM particles that are not significantly affected by the fluid phase, such as large particles in air. The essential requirement is that DEM-CFD coupling is not necessary for achieving a valid result.
    - Discrete Element Method Particles
      The Discrete Element Method (DEM) models the particle behavior within the simulation.
    - Setting Phase Boundary Conditions
      The Lagrangian phase boundary conditions specify how the particles interact with wall boundaries.
    - Drag Force Model Reference
      The drag force model calculates the force acting on a particle due to viscosity-induced fluid resistance.
    - Drag Torque Model Reference
      The Drag Torque model calculates the rotational drag exerted on a particle as it spins in a viscous fluid.
    - Modeling Lift Force in the Discrete Element Method
      Simcenter STAR-CCM+ DEM provides two lift force models, one for spin lift force, and another for shear lift force.
    - Modeling Erosion in the Discrete Element Method
      Erosion models are provided in both the Lagrangian and DEM frameworks. For DEM, STAR-CCM+ can model abrasive erosion in addition to impact erosion.
    - DEM Phase Interaction Model Reference
      The DEM Phase Interaction model provides access to other models that define particle interaction behavior.
      - Hertz Mindlin Model Reference
        The Hertz Mindlin no-slip contact model is the standard model that is used for modeling contact between particles.
      - Walton Braun Model Reference
        The Walton Braun model is an elastic-plastic contact model, which is useful in situations where a collision between two bodies includes plastic deformation.
      - Linear Spring Model Reference
        The Linear Spring model calculates contact between particles or between particles and a wall. The relationship between particle compression and contact forces is based on the relationship found in linear springs.
      - User-Defined Contact Force Model Reference
        The User-Defined Contact Force model is an advanced model that allows you to use a contact force you have defined in a field function.
      - Conduction Heat Transfer Model Reference
        The Conduction Heat Transfer model calculates conduction heat transfer between two particles or a particle and a wall.
      - Rolling Resistance Model Reference
        With the DEM model active in a physics continuum, rolling resistance is an optional model in a phase interaction.
      - Linear Cohesion Model Reference
        Cohesion modeling facilitates simulation of inter-molecular attraction forces (Van der Waals forces) between particle surfaces. For some classes of simulations, such as dry powders, these forces significantly affect the outcome and cannot be ignored.
      - Particle Agglomeration Model Reference
        The Particle Agglomeration model introduces attractive inter-particle forces to the particle system. When the bond formation criteron is met, the Particle Agglomeration model acts to form clusters from particles that collide.
      - Bonded Particles Model Reference
        The bonded particle model is a combination of the Hertz Mindlin and Parallel Bonds model, and is activated by default with the Particle Clumps model. When the particles are attached, the Parallel Bonds model determines the connection and inter-particle forces.
      - Simple Failure Model Reference
        The Simple Failure model emulates bonds that fail instantaneously under load.
      - Constant Rate Damage Model Reference
        The Constant Rate Damage model emulates the breaking of bonds in brittle fracture growth. It can also be used to predict bond strengths.
      - Impact Cutting Model Reference
        Like the Simple Failure model and the Constant Rate Damage model, the Impact Cutting model is a damage model for bonded particles. It applies only to fiber-shaped bonded particles modeled with either Particle Clumps or Flexible Fibers. The model breaks a bonded particle into two parts when the user-specified breakage criterion is met. The two resulting bonded particles can then be broken again after the user-specified Breakage Time Interval.
      - Impact Heat Model Reference
        The Impact Heat Model simulates the heating of DEM particles from friction and viscous damping.
      - Particle-Wall Link Model Reference
        DEM particles using this model stick to walls when they come into contact, then move with the wall if necessary.
      - Passive Scalar Transfer Model Reference
        The Passive Scalar Transfer model transfers conserved quantities of passive scalar from one particle to another when the particles are in contact.
      - Visualizing and Reporting Contact
        In general, collisions involving DEM particles are not the same as those involving Lagrangian parcels. With DEM particles, there can be more than one collision between particles or between a particle and a wall, if particles are modeled as spherical composites.
    - Artificial Viscosity Model Reference
      When two particles collide, or when a particle collides with a wall, the DEM module uses the impact velocity to predict the outcome. Impact velocities can increase to the same order of magnitude as the speed of sound in the particle material, which can cause the numerical models to over-predict the overlap between the colliding objects. The large overlap results in inaccurate results or unphysical ones, such as particles passing through walls. You can avoid or reduce these problems by applying the artificial viscosity model.
    - Defining Injectors in the Discrete Element Method
      An injector setup for DEM particles follows the Lagrangian methodology. The main difference between Lagrangian and DEM particles with respect to the injector is the concept of a particle as opposed to a parcel. For a Lagrangian phase (Material and Massless particle types) the parcel can represent many particles at once or a fraction of a particle. For DEM particles, the parcel always represents a single particle, except in the case of the Coarse Grain Particle model.
    - Guidelines for DEM
      DEM gives high resolution, but at a high cost in computational power. Guidelines for DEM mostly consist of finding ways to reduce the computational cost.
    - Discrete Element Method Bibliography
    - Discrete Element Method Field Functions Reference
      This section describes the primitive field functions that are available in the simulation when using the DEM model.
    - Migrating from EDEM
      This section provides information to help you convert an EDEM simulation to run under Simcenter STAR-CCM+.
    - Post-Processing DEM Data
      Simcenter STAR-CCM+ allows you to analyze the flow of DEM phases over boundaries.
  - Dispersed Multiphase (DMP)
    The Dispersed Multiphase (DMP) model simulates dispersed phases in a Eulerian manner. The Dispersed Multiphase model combines aspects of both the Lagrangian Multiphase (LMP) model and the Eulerian Multiphase (EMP) models.
  - Eulerian Multiphase (EMP)
    The Eulerian Multiphase (EMP) model in Simcenter STAR-CCM+ is based on an Eulerian-Eulerian formulation where each distinct phase has its own set of conservation equations.
  - Fluid Film
    Problems where a thin film of fluid exists on solid boundaries are common in engineering practice. Examples include fluid film on the internal surfaces of automotive engines, gas turbines, spray-cooling systems and ink-jet printers.
  - Lagrangian Multiphase (LMP)
    A wide variety of flow processes involve the transport of solid particles, liquid droplets, or gas bubbles—known as dispersed phases—by a gaseous or liquid continuous phase.
  - Mixture Multiphase (MMP)
    In the Mixture Multiphase (MMP) model, mass, momentum, and energy are treated as mixture quantities rather than phase quantities. Simcenter STAR-CCM+ solves transport equations for the mixture as a whole, and not for each phase separately. The model is computationally more efficient than models that simulate each phase separately.
  - Resolved Transition
    Simcenter STAR-CCM+ provides the Resolved Transition model as a phase interaction model, which lets you capture the breakup of pools of liquid to form droplets emerging/stripping from a free surface or small bubbles stripped from a large bubble. This model is meant to be used as part of a hybrid multiphase approach where the Volume of Fluid (VOF) model or Mixture Multiphase (MMP) model is used alongside the Lagrangian Multiphase (LMP) model.
  - Smoothed-Particle Hydrodynamics (SPH)
    Smoothed-Particle Hydrodynamics (SPH) is a numerical method that overcomes the volume meshing-related constraints occurring with mesh-based models. SPH represents the fluid as a collection of particles with material properties that move with the fluid, making it well-suited for applications with highly dynamic free-surface flows.
  - Two-Phase Thermodynamic Equilibrium
    The Two-Phase Thermodynamic Equilibrium is a multiphase mixture approach that is restricted to modeling two phases. With this model Simcenter STAR-CCM+ solves the mass, momentum, and energy as mixture quantities rather than phase quantities. Therefore, the computational efforts are reduced by assuming the suspension to be a homogeneous single-phase system.
  - Volume Of Fluid (VOF) Multiphase
    The Volume Of Fluid (VOF) Multiphase model is a simple multiphase model. It is suited to simulating flows of several immiscible fluids on numerical grids capable of resolving the interface between the phases of the mixture.
  - Modeling VOF Waves
    The VOF Waves model is used to simulate surface gravity waves on the interface between a light fluid and a heavy fluid. This model is typically used with the 6-DOF Motion model for marine applications.
- Dynamic Fluid Body Interaction
  Dynamic Fluid Body Interaction (DFBI) in Simcenter STAR-CCM+ allows you to simulate the motion of a 6-DOF body with the displacement and rotation resulting from the defined mechanical and multiphysics interaction (flow, DEM, solid stress, EMAG).
- Harmonic Balance
  Some unsteady flows have a regularly repeating flow pattern, that is, they are time-periodic. Consider the flow from a fan blade passing across the entrance to a duct. Measurements of the instantaneous flow just within the duct would show a regularly repeating pattern. If the flow disturbances are sufficiently large, and propagate to the end of the duct, measurements of the unsteady flow at any point within the duct show repeating patterns. Such time-periodic patterns can be expressed using Fourier series.
- Solid Stress
  Simcenter STAR-CCM+ allows you to model the response of a solid continuum to applied loads, including mechanical loads and thermal loads that result from changes in the solid temperature.
- Electromagnetism
  Simcenter STAR-CCM+ allows you to model engineering applications involving electromagnetic phenomena. Example applications are electric motors, electric switches, and transformers, which can be modeled based on the classical theory of Electromagnetism.
- Electrochemistry
  Electrochemistry is the study of chemical reactions which occur due to an imposed electrical charge, or a difference in electrical potential at a boundary between a conductor–such as a metal–and an electrolyte. Simcenter STAR-CCM+ provides models that allow you to simulate batteries, corrosion, etching, and other electrochemical reactions.
- Electric Circuits
  Electrical circuits are conducting loops of interconnected electrical components, such as batteries, power sources, resistors, and inductors.
- 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.
- Batteries
  You can simulate batteries in Simcenter STAR-CCM+ using battery cells and battery cycling procedures that are defined either directly in Simcenter STAR-CCM+, or in the external software package Simcenter Battery Design Studio.
- Casting
  Casting simulations are performed using transient multiphase simulations using the VOF model with solidification. Conjugate heat transfer is applied between the solidifying melt and the solid mold.
- Region Sources
  This section provides some guidelines on how to use region sources for some common problems.
- Cell Quality Remediation
  The Cell Quality Remediation model helps you get solutions on a poor-quality mesh. This model identifies poor-quality cells, using a set of predefined criteria, such as Skewness Angle exceeding a certain threshold. Once these cells and their neighbors have been marked, the computed gradients in these cells are modified in such a way as to improve the robustness of the solution.
- Guidelines for Applying Simcenter STAR-CCM+
  This part of the documentation provides guidelines on applying Simcenter STAR-CCM+ models to your applications.
- Common Solvers Reference
  In Simcenter STAR-CCM+, solvers compute the solution during the simulation run.

Hertz Mindlin Model Reference

The Hertz Mindlin no-slip contact model is the standard model that is used for modeling contact between particles.


Theory	See the Hertz-Mindlin No-Slip Contact Model.
Provided By	[physics continuum] > Models > Multiphase Interaction > Phase Interactions > Phase Interaction [n] > Models > DEM Contact Model
Example Node Path	Continua > Physics 1 > Models > Multiphase Interaction > Phase Interactions > Phase Interaction 1 > Models > > Hertz Mindlin
Requires	Optional Models: Lagrangian Multiphase Optional Models: Discrete Element Method (DEM) Multi-Phase Interactions: Multiphase Interaction selected automatically Under Multiphase Interaction, select Phase Interaction Topology: DEM Phase Interaction if it has not been automatically selected.
Properties	Key properties are: Static Friction Coefficient, Rolling Friction Coefficient, Normal Restitution Coefficient, Tangential Restitution Coefficient. See Hertz Mindlin Properties.
Activates	Physics Models	Optional Models and specifically the Rolling Resistance model

Hertz Mindlin Properties

Static Friction Coefficient: $C_{f s}$ (see Eqn. (3254)).
Rolling Friction Coefficient: $μ_{r}$ (see Eqn. (3276)).
Normal Restitution Coefficient: See Eqn. (3257).
Tangential Restitution Coefficient: See Eqn. (3254).