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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.
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.

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.

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.

Full gravity model

For buoyancy calculations, the gravity force is included in the source term S_{U_j} of the momentum conservation equation, as follows:

where g_j is the j^th component of the gravitational acceleration vector g.

However, incorporating the gravity force directly into the source term can lead to round-off errors. Therefore, the flow solver computes the gravity force based on the following equation:

where ρ_r is a reference density.

The momentum conservation equation in presence of buoyancy is re-written as:

where:

In these equations:

P^* is the pressure field with respect to the hydrostatic variation.
P₀ is called the offset pressure. It is the pressure when z = 0.

The flow solver adds the hydrostatic contribution at the openings where a relative pressure is specified and does not add it at the openings where an absolute pressure is specified. For example, you would not want to add the hydrostatic contribution at the opening at the bottom of a tank draining under gravity, but you would want to add it at the opening at the outlet of a channel through which fluid flows horizontally.

Boussinesq Model

The flow solver uses the Boussinesq model for the flows with the density variation due to small temperature changes. The buoyancy force per unit volume term (ρ - ρ_r) g_j is modeled for incompressible liquid as follows:

where:

β is the coefficient of thermal expansion.
T_r is a reference temperature, at the same condition as ρ_r.

Note:

It is assumed that the pressure-density effects are negligible.

Thus, the momentum conservation equation in presence of buoyancy is:

The reference temperature, T_r, differs depending on the boundary conditions applied to the fluid domain.