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Flow Solver
Contains flow solver related guides, such as the reference and API guides.
Flow solver reference
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Turbulence models
In the flow solver, the flow field can be solved as laminar or as turbulent using governing equations.
Spalart-Allmaras model
The Spalart-Allmaras (SA) model adds one partial differential equation for the modified eddy viscosity. Learn how the flow solver uses it to model turbulent flows.

Flow Solver
Contains flow solver related guides, such as the reference and API guides.
- Flow solver guides
  Maya HTT's flow solver is included and distributed with Simcenter 3D and Simcenter Femap. This page contains links to flow solver guides, which help you understand how the flow solver works.
- Flow solver reference
  Insert short description here
  - Introduction
    The flow solver computes a solution to the non-linear, partial differential equations for the conservation of mass, momentum, energy, and general scalars in general complex 3D geometries. It uses an element-based finite volume method and iterative Krylov methods to discretize and solve the governing equations.
  - Nomenclature
    The nomenclature table offers a description and sample units or constant values of the variables used in the Flow Solver Reference Manual.
  - Governing equations
    A model can be comprised of multiple flow enclosures. Each enclosure is a separate group of three-dimensional elements that form a separate fluid domain from the remaining geometry. The physical scales of each enclosure, such as the length scale, time scale, pressure, and temperature are independent of the other enclosures. The flow solver solves governing equations separately for each flow enclosure.
  - Source term
    The source term can represent body forces or flow resistance forces to model different physical phenomena.
  - Turbulence models
    In the flow solver, the flow field can be solved as laminar or as turbulent using governing equations.
    - Assumptions
      The derivation of the near-wall relations for turbulent flows depends on several assumptions presented in this section. It is assumed that the flow close to the wall is in the x direction.
    - Mixing length turbulence model
      The mixing length turbulence model is based on Prandtl mixing length hypothesis.
    - Standard k-epsilon model
      The standard k-epsilon model, sometimes called just k-epsilon, calculates turbulent viscosity using turbulent kinetic energy and its dissipation rate. Learn how the flow solver uses it to model turbulent flows.
    - RNG k-epsilon model
      The RNG k-epsilon model improves turbulence modeling by adding a term to the dissipation rate equation, capturing different scales of turbulent motion. It retains the turbulent viscosity calculation from the standard k-epsilon model and includes buoyancy effects and strain rate considerations.
    - Realizable k-epsilon model
      The realizable k-epsilon model improves turbulence modeling by using a variable eddy viscosity formulation and a new dissipation rate equation.
    - k-omega model
      The k-omega model describes the turbulent velocity as a function of the kinetic energy, its specific dissipation rate, as well as the density of the fluid. Learn how the flow solver uses it to model turbulent flows.
    - Shear stress transport model
      The shear stress transport (SST) turbulence model combines the k-epsilon and k-omega models, using blending functions to switch between them. It calculates turbulent viscosity based on strain rate magnitude and includes a production limiter to prevent turbulence build-up in stagnation regions.
    - Spalart-Allmaras model
      The Spalart-Allmaras (SA) model adds one partial differential equation for the modified eddy viscosity. Learn how the flow solver uses it to model turbulent flows.
    - Initializing turbulence models
      Depending on the selected turbulence model, the flow solver calculates the appropriate turbulence quantities starting with a pair of quantities provided by the user.
    - Turbulence model tuning coefficients
      You can modify the turbulence model constants using the advanced parameters in the user.prm file.
    - Turbulent structures
      Vortices are regions where the vorticity magnitude exceeds the strain-rate magnitude, and the pressure is lower than the ambient pressure.
  - Boundary conditions
    This section outlines different boundary conditions supported by the flow solver and the associated considerations.
  - Modeling a gas mixture
    The flow solver uses the scalar equation to model a gas mixed in any proportion with the main gas. The software supports up to five gases in the mixture. All gases are assumed to behave as ideal gases using the ideal gas law.
  - Modeling humidity
    The flow solver uses the gas mixture scalar equation to model humidity that is defined as a mixture of water vapor in air.
  - Modeling non-Newtonian fluid
  - Modeling particle tracking
    The following section describes the equations and forces that model particle trajectories, including treatment and effects of boundary conditions
  - Modeling fluid structure interaction
    Fluid structure interaction (FSI) computations account for motion or deformation of the solid structure boundaries that are interacting with the adjacent fluid flow. The flow solver handles both transient and static fluid structure interactions.
  - Discretization
    The following section describes the discretization methods used by the flow solver to discretize the governing equations.
  - Solver numerical methods
    The following section describes numerical methods used by the flow solver such as the linear equation solution, which acts as a preconditioning method to the basic iterative algorithm, and other solver methods, such as Krylov methods.
  - Flow solver files
    The following table describes the flow solver files, which are written in the run directory during the solving process.
  - Flow solver bibliography
    The following bibliography lists all sources used to explain how the flow solver works.
- Flow solver flowcharts
  This section consists of flowcharts that illustrate the methodology of the flow solver when you run a simple steady-state or transient simulation, and does not cover all features and situations. It also highlights how the flow solver is coupled to the thermal solver for a simple steady-state or transient coupled thermal-flow simulation.

Spalart-Allmaras model

The Spalart-Allmaras (SA) model adds one partial differential equation for the modified eddy viscosity. Learn how the flow solver uses it to model turbulent flows.

Identified by , the modified eddy viscosity is related to the turbulent viscosity by an algebraic equation:

The equation above is non-linear. It is solved using Newton's method.

The modified eddy viscosity is governed by the following transport equation [50]:

where:

ν is the molecular kinematic viscosity.
d is the distance to the nearest solid wall.
Ŝ is the modified vorticity term that maintains log-law behavior to the nearest solid wall defined as follows:

where:
- The magnitude of vorticity is computed as follows:
The non-dimensional function, f_w, which accelerates the decay of the destruction term in the outer region of the boundary layer is given by:
The constants in these equations are: