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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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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.
Mass and momentum equations
The flow solver solves conservation equations for mass and momentum for general flow.

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.
    - Mass and momentum equations
      The flow solver solves conservation equations for mass and momentum for general flow.
    - Energy equation
      The instantaneous total energy equation describes the conservation of energy in fluid dynamics, accounting for internal energy, velocity, heat flux, and heat generation.
    - Scalar equation
      The flow solver addresses general scalar equations, defining key variables and terms for transient, convective, and diffusion processes. It includes modeling passive scalars and applications such as gas mixtures and humidity.
    - Equations of state
      An equation of state is a constitutive equation which provides a mathematical relationship between thermodynamic state variables for a given material.
  - 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.
  - 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.

Mass and momentum equations

The flow solver solves conservation equations for mass and momentum for general flow.

These equations can be expressed in Cartesian coordinates and using the tensorial notation [1, 2, 3] are, respectively, the following expressions.

In these equations:

The Einstein convention is used (i, j, k = 1,2,3).
U_j and u_j are the components of the mean and the fluctuating velocity in the x_j direction.
P is the pressure.
ρ is the density of the fluid.
μ is the dynamic viscosity of the fluid.
represents the turbulent (or Reynolds) stresses.
S_{U_j} is the source terms for momentum equation.

These equations are valid for both, incompressible and compressible flows.

The terms of the momentum conservation equation are:

The transient term
The convection term
The pressure gradient term
The stress term
The source term

The source term S_{U_j} can represent body forces or flow resistance forces:

For natural convection flows, S_{U_j} includes the buoyancy force. See Buoyancy force for more information.
For flows through porous blockages, S_{U_j} contains additional resistance terms. See Flow resistance through porous materials for more information.