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Flow Solver
Contains flow solver related guides, such as the reference and API guides.
Flow solver reference
Insert short description here
Source term
The source term can represent body forces or flow resistance forces to model different physical phenomena.
Flow resistance through porous materials
Learn how the flow solver models flow resistance through isotropic and orthotropic porous materials.

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.
    - Buoyancy force
      For buoyancy-driven flows, the flow solver uses the full gravity model for multiphase and multicomponent flows or flows with density differences from non-temperature sources, and the Boussinesq model for flows with small temperature-induced density variations.
    - Cavities
      Understand how the flow solver computes reference temperatures differently for enclosed cavities and cavities with openings.
    - Flow resistance through porous materials
      Learn how the flow solver models flow resistance through isotropic and orthotropic porous materials.
  - 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.

Flow resistance through porous materials

Learn how the flow solver models flow resistance through isotropic and orthotropic porous materials.

The pore structure resists the flow of the fluid passing through the porous material.

An isotropic porous material has the same loss coefficient in all directions.
An orthotropic porous material has three different loss coefficients that correspond to the three orthogonal principal axes.

The resistance to flow is included in the source term S_{U_j} of the momentum conservation equation as described by the Darcy-Forchheimer law [26]

Isotropic resistance

For an isotropic porous material, the source term accounts for the resistance to flow as follows:

where

K is the permeability of the porous material that you specify.
R is the inertial loss coefficient of the porous material that you specify, and represents the fraction of the dynamic head lost per unit distance and has a dimension of inverse length.
is the magnitude of the velocity. The velocity is expressed in unit vectors of the global coordinates as .

Orthotropic resistance

An orthotropic material has three orthogonal principal axes X₁, X₂, X₃. Each axis has a different loss coefficient.

The components of the resultant resistance force per unit volume along the principal axes X₁, X₂, X₃ are defined as follows:

where

R₁₁, R₂₂, and R₃₃ are the specified inertial loss coefficients of the porous material in the directions of X₁, X₂, and X₃ respectively.
K₁₁, K₂₂, and K₃₃ are the specified permeabilities of the porous material in the directions of X₁, X₂, and X₃ respectively.
U₁, U₂, and U₃ are the velocity components in the directions of X₁, X₂, and X₃ respectively.

The equation above is written in matrix form as follows:

The resistance force in the global Cartesian coordinates is:

where [T] is the transformation matrix between the coordinates along the principal axes and the global Cartesian system. The components of the velocity along the principal axes are expressed in the global Cartesian velocity components as follows:

where superscript ^T represents the transpose of the matrix.

Combining equations, the source term for the momentum conservation equation in the global Cartesian coordinate system is written as:

The resistance force is nonlinear and is re-computed at each iteration.