CFD Analysis Process

The following steps are going to explain the mathematical approach behind a CFD simulation. For you to understand it more easily, they are categorized into 7 steps.

First step:

Problem Statement:

The first step of the simulation is to gather information about the simulation process in general.

  • What is the most convenient way of solving this problem in an economic way:
    • Cheap solution: No high computational costs
    • Fast solution: Fast solution possible without giving up much information of the solution
    • Uncomplicated solution: Simplify the problem as much as possible without restating a new problem
  • Modelling:
    • Laminar or Turbulent - if turbulent \rightarrow +turbulence model + near-wall treatment

    • Combustion

    • Other Physical Models

    • Is the flow steady or unsteady?

    • Are there any problems about the flow simulation that others have dealt with in the past?

    • Will physical phenomena influence the simulation?

    • What is the goal of the CFD simulation?

Second step:

Mathematical Fundamental:
The Initial Boundary Value Problem consists of the Partial Differential Equation the Initial Conditions as well as the Boundary Conditions:

\textbf{IBVP = PDE + IC + BC}
  • Choose flow model that fits your simulation:

    • Spalart-Allmaras
    • k-epsilon
    • k-omega
    • L-VEL & yPlus
  • Identify the forces which cause and influence the motion of the fluid.

  • Define the Computational Domain of the problem.

  • Formulate conservation laws for mass, momentum and energy.
    \rightarrow Governing Equations

  • If possible, simplify the equations:

    • Check for Symmetry
    • Check for dominant flow directions (1D/2D).
    • Terms that have no influence on the solution can be neglected.
    • Incorporate knowledge that you’ve had beforehand (CFD results, measurement data).
  • Add constitutive relations:

    • Shear Stress
    • Viscosity
      • Dynamic Viscosity
      • Kinematic Viscosity
  • Add Boundary Conditions and Initial Conditions.

Third step:

The system of Partial Differential Equations is transformed into algebraic equations. The discretion process is divided into three parts.

1. Mesh generation - Nodes and Cells

  • Structured Mesh / Unstructured Mesh / Hybrid Mesh.
  • Mesh adaption in “critical” regions and set size:
    • r-Refinement
    • h-Refinement
    • p-Refinement

2. Space discretization - Coupled Ordinary Differential Equation/ Differential algebraic equation systems

  • Finite-Difference-Method / Finite-Volume-Method / Finite-Element-Method.
  • High-Order-Approximation / Low-Order-Approximation.

3. Time discretization - Algebraic System (Ax = b).

  • Explicit Schemes / Implicit Schemes

Fourth step:

Iterative solution of the algebraic equation:

  • Solving systems of linear equations:
    • Direct Methods: Gaussian elimination, LU decomposition.
    • Iterative Methods: Strongly Implicit Procedure (SIP) , Alternating Direction Implicit (ADI) , Tridiagonal Matrix Algorithm (TDMA), Runge-Kutta method, Multigrid method.
  • Coupled systems of equations.
  • Nonlinear Equations
  • Methods for transient problems: Linear multistep method etc.

Convergence: Check if the iterations converge.

  • Residuals (Decrease by three orders of magnitude indicate at least qualitative convergence).
  • Mass, Momentum, Energy, and Scalar balances are achieved.

Fifth step:

Simulation Run:
Once the problem is well defined with the boundary conditions, and if necessary with initial conditions, the problem is solved with a software. Open∇FOAM is a popular option for a solver which is used by several companies that provide CFD software. SimScale is among them.

Sixth step:

Looking at the solutions from the the computed flow.

  • Post-Processing of integral parameters (Drag, Lift etc.)
  • Visualization in different dimensions:
    • 1-D: Straight lines
    • 2-D: Contour plots, Streamlines
    • 3-D: Isosurfaces, Isovolumes, Streamtracer
    • Animation of the flow
  • Statistical analysis

Seventh step:

According to AIAA (1998) & Oberkampf and Trucano (2002) the following terminology is widely used and accepted:

Verification (“Are we solving the equations right?”) :

\rightarrow Quantification of errors

  • Compare results with analytical solutions if possible.

If we ignore the fact that there might be coding errors and user errors, we can examine the following:

  • Roundoff Error

  • Iterative Convergence Error

  • Discretization Error

Validation (“Are we solving the right equations?”) :

\rightarrow Quantification of input & physical model uncertainty

  • Input uncertainty

  • Physical uncertainty

General tips

Influencing parameters for computation times in CFD

  • Code used in order to solve the flow (\rightarrow MPI, Vectorization)

  • Hardware (CPU, RAM, etc.)

  • Mesh size / Mesh Quality

  • Algorithms

  • Solvers

Read more about CFD in our related article in the SimWiki.

Also see our ​SimWiki for more about other interesting simulation related questions.

Literature References: