Home
Flow Solver
Contains flow solver related guides, such as the reference and API guides.
Flow solver reference
Insert short description here
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.
Linear equation solution
The preconditioning method to the basic iterative algorithm is a Incomplete Lower Upper factorization method. As this is not a direct solver, it is used within an iterative refinement loop, in which the exact solution is calculated with iteration.

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.
  - 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.
    - Linear equation solution
      The preconditioning method to the basic iterative algorithm is a Incomplete Lower Upper factorization method. As this is not a direct solver, it is used within an iterative refinement loop, in which the exact solution is calculated with iteration.
    - Solver methods
      The flow solver uses iterative Krylov methods, to solve large set of algebraic equations resulting from the discrete approximation of differential equations.
  - 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.

Linear equation solution

The preconditioning method to the basic iterative algorithm is a Incomplete Lower Upper factorization method. As this is not a direct solver, it is used within an iterative refinement loop, in which the exact solution is calculated with iteration.

The system of equations can be written symbolically as:

A is the coefficient matrix.
x is the solution vector (e.g. the U, V, W. P, H, k, ρ_νΦ).
b is the coefficient vector.

Solving this iteratively, one starts with an approximate solution, xⁿ, that is to be improved by a correction, x' to yield a better solution, xⁿ⁺¹, i.e.,

where

x^' is a solution of the following equation:

r is the the residual given as:

The approximate iterative solver is used to solve the Ax' = rⁿ.