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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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Discretization
The following section describes the discretization methods used by the flow solver to discretize the governing equations.
Other discretization methods
The following section describes discretization methods such as the disjoint mesh pairing method, the immersed boundary, or various mesh moving methods.
Mesh moving methods
The flow solver uses different methods to compute the mesh movement in fluid structure interaction modeling
Radial basis function method
Understand how the flow solver computes the nodal displacement with the radial basis function method.

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.
  - 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.
    - Control-volume method
      The flow solver uses a finite-element based control-volume method for discretization of the governing equations. With this method, the governing equations are integrated over a control volume and over a time step.
    - Spatial discretization
      This section describes the spatial discretization of the governing equations and the terms that compose them.
    - Temporal discretization
      The flow solver uses the Backward Euler and Crank-Nicolson schemes, and the local time step method as time discretization methods.
    - Other discretization methods
      The following section describes discretization methods such as the disjoint mesh pairing method, the immersed boundary, or various mesh moving methods.
      - Disjoint mesh pairing
        The flow solver needs to control the fluxes across the interface between two disjoint meshes. The interface is a coplanar face pair where the nodes and elements of the associated fluid meshes are not coincident.
      - Immersed boundary method
        The flow solver can use the immersed boundary method based on the ghost-cell method to discretize and solve CFD equations. This method allows you to implement boundary conditions for the immersed boundaries without modifying the overall finite-volume algorithms.
      - Mesh moving methods
        The flow solver uses different methods to compute the mesh movement in fluid structure interaction modeling
        Radial basis function method
        Understand how the flow solver computes the nodal displacement with the radial basis function method.
        Inverse distance weighting method
        Understand how the flow solver computes nodal displacement with the inverse distance weighting method.
        Laplace smoothing equation method
        Understand how the flow solver computes nodal displacement with the Laplace smoothing equation method.
  - 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.

Radial basis function method

Understand how the flow solver computes the nodal displacement with the radial basis function method.

The flow solver applies radial basis function (RBF) interpolation to derive the nodal displacement in the fluid mesh by applying the nodal displacement on the structure boundary for FSI computation [58]. The nodal displacement of the solid structure boundary and fluid internal mesh is computed by:

where:

x_{b_j} is the node position on the boundary and represents the x_{b_j}, y_{b_j} and z_{b_j} coordinate components, respectively.
n_b is the number of nodes on the boundary.
∥x∥ is the Euclidean distance.

The flow solver uses the following RBF:

where:

ε is the smoothing factor.
r is the radius.

The α_j coefficients are computed as follows:

where:

d_b is the displacement of the nodes on the structure boundary.
x_{b_i} is the location of the displaced nodes on the solid structure boundary.

The nodal displacement in the fluid mesh, d_t, is computed by:

where x_{I_i} is the node position in the fluid mesh and represents the x_{I_i}, y_{I_i} and z_{I_i} coordinate components, respectively.