# 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
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• Modelling:
• Laminar or Turbulent - if turbulent \rightarrow +turbulence model + near-wall treatment

• Combustion

• Other Physical Models

• 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
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• 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
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• 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 youâve had beforehand (CFD results, measurement data).
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• Shear Stress
• Viscosity
• Dynamic Viscosity
• Kinematic Viscosity
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• Add Boundary Conditions and Initial Conditions.

### Third step:

Discretization:
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 âcriticalâ 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. OpenâFOAM is a popular option for a solver which is used by several companies that provide CFD software. SimScale is among them.

### Sixth step:

Post-Processing:
Looking at the solutions from the the computed flow.

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

### Seventh step:

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

#### Verification (âAre we solving the equations right?â) :

\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 (âAre we solving the right equations?â) :

\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