Best Practices for Minimizing Errors in CFD — Lesson 1

Introduction

This tutorial focuses on best practices for minimizing errors in Computational Fluid Dynamics (CFD) simulations. Understanding the various sources of numerical errors and how to address them is crucial for obtaining accurate results in CFD applications, which can range from design optimization to safety analyses.

Step 1: Understand Different Types of Errors

Familiarize yourself with the four main types of errors that can impact the accuracy of CFD simulations:

1. Roundoff Errors

   • Caused by the limitations of machine arithmetic.
   • Particularly significant in cases with high aspect ratio cells or large value ranges.
   • Mitigation: Use double precision calculations. Check the precision setting when launching the simulation.

2. Iteration Errors

   • The difference between the solution at a specific iteration and the converged solution.
   • Mitigation: Define target variables (e.g., lift coefficient) and set a convergence criterion for residuals. Monitor the target variables as iterations progress.

3. Discretization Errors

   • The difference between the CFD solution on a given grid and the theoretical solution on an infinitely fine grid.
   • Mitigation: Conduct a mesh resolution study using increasingly finer grids to assess discretization error.

4. Modeling Errors

   • Discrepancies between the physical reality and the model's predictions.
   • Mitigation: Choose appropriate models and validate them against experimental data.

Step 2: Minimize Roundoff Errors

To ensure calculations are not affected by roundoff errors:

• Check Precision Settings

  • When starting Fluent, confirm it is set to double precision.
  • If uncertain, look for 'dp' in the title bar of Fluent.

• Define Target Variables

  • Identify key quantities relevant to your simulation.
  • Compare results from single precision and double precision calculations. If they differ, use double precision going forward.

Step 3: Reduce Iteration Errors

To control iteration errors in your simulations:

• Define Target Variables

  • Choose relevant indicators for your simulation's performance (e.g., efficiency, mass flow rate).

• Set a Convergence Criterion

  • Plot the target variables during iterations and select a tight convergence criterion for residuals.
  • Aim for a steady decrease in residuals and ensure that the target variables stabilize after a certain number of iterations, which indicates convergence.

Step 4: Conduct a Mesh Resolution Study

To address discretization errors:

• Perform Mesh Refinement

  • Run simulations on a series of grids with increasing refinement.
  • Compare results between first-order and second-order discretization to identify the most accurate solution.

• Use Extrapolation Techniques

  • When practical, use results from finer meshes to estimate the error and convergence.

Step 5: Identify and Mitigate Modeling Errors

To tackle modeling errors effectively:

• Select Appropriate Models

  • Understand the physics of the problem and choose models accordingly. For turbulent flows, consider various turbulence models.

• Validate with Experimental Data

  • Compare CFD results with experimental measurements to assess the accuracy of your models.

• Document Assumptions

  • Keep track of all assumptions made during the modeling process, including geometry simplifications and boundary conditions.

Step 6: Address Systematic Errors

To minimize systematic errors:

• Understand the Application

  • Gain a clear understanding of the physical system to know what details are necessary in your model.

• Perform Uncertainty Analysis

  • Analyze the impact of uncertainties in boundary conditions and material properties to evaluate their effects on simulation outcomes.

Conclusion

By following these best practices, you can significantly improve the accuracy of your CFD simulations. Understanding and addressing roundoff, iteration, discretization, modeling, and systematic errors will lead to more reliable results. As you advance, continue to document your assumptions and seek validation against real-world data to ensure the integrity of your simulations. Consider exploring additional resources and courses to deepen your knowledge in CFD practices.