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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.
Spatial discretization
This section describes the spatial discretization of the governing equations and the terms that compose them.
Convective terms
The discretized convective terms are evaluated using nodal values with first or higher-order schemes. Higher order schemes offer more precision but are less stable.
Second-order CDS scheme
The Central Differencing Scheme (CDS) offers an accurate representation of convecting fluxes and is appropriate for low-speed flows with small Peclet numbers.

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.
      - Governing equations discretization
        Understand how the mass, momentum, and energy equations are discretized and used by the flow solver.
      - Diffusion terms
        The general form of the diffusion term involves evaluating the derivative of a field variable at an integration point using shape functions. For a given node, the flow solver calculates the field variable using shape functions, which are polynomials determined by the flow solver.
      - Pressure term
        Understand how the flow solver computes the pressure term.
      - Convective terms
        The discretized convective terms are evaluated using nodal values with first or higher-order schemes. Higher order schemes offer more precision but are less stable.
        First-order UDS scheme
        The first-order Upwind Differencing Scheme (UDS) offers stable solutions and accurate results for flow fields with no gradients.
        Second-order QUICK scheme
        The second-order Quadratic Upwind Interpolation for Convective Kinematics (QUICK) scheme offers high precision solutions, but has lower stability for regions with strong gradients. This scheme is most appropriate for steady flows.
        Second-order SOU scheme
        The Second-Order Upwind (SOU) scheme offer more precise results than the first-order advection scheme. However, it is less robust than the UDS scheme, but more stable than the QUICK scheme in regions with strong gradients.
        Second-order CDS scheme
        The Central Differencing Scheme (CDS) offers an accurate representation of convecting fluxes and is appropriate for low-speed flows with small Peclet numbers.
        Second-order HI-RES scheme
        The second-order high resolution (HI-RES) scheme does not require a flux limiter, it calculates the limiter at each node to adjust the discretization to prevent unboundedness.
        Second-order MUSCL scheme
        The second-order Monotonic Upstream-centered Scheme for Conservation Laws (MUSCL) scheme offers better precision and convergence for simulation with high aspect ratio grids and meshes.
        Flux limiters
        Flux limiters prevent the development of undesirable artifacts, such as unbounded values or spurious oscillations. Discover the different limiters for SOU, QUICK, CDS and MUSCL schemes.
      - Shape function
        The flow solver computes solution variables, such as velocity components, pressure, and temperature at the mesh nodes. It then approximates the solution variables at arbitrary points in the computational domain with shape functions. The shape functions interpolate solution variables from mesh nodes to the arbitrary point with given nodal solution variables, and the coordinates of an arbitrary point in the computational domain.
    - 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.
  - 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.

Second-order CDS scheme

The Central Differencing Scheme (CDS) offers an accurate representation of convecting fluxes and is appropriate for low-speed flows with small Peclet numbers.

The CDS approximates ϕ_ip as follows, with reference to the geometry depicted in the figure of the Shape function section:

where:

B^e_i is the shape function associated with the node N^e_i.
δ is the local characteristic mesh spacing.
N_B ≥ 2 is the order of accuracy of the shape function.

When the CDS approximation has the generation of spurious oscillations in the solution field, it is implemented in the flow solver as a correction to the implicit UDS scheme, with the imposed flux limiter Ψ_ip ∈ [0, 1], so that at iteration n of the solution the procedure is defined as:

The CDS scheme provides a more accurate representation of the convective fluxes than the UDS scheme and is computationally less time-consuming than the QUICK and SOU second-order schemes.

The CDS advection scheme is appropriate for for low speed flows with small Peclet number.