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What's your process for analyzing uncertainty in Computational Fluid Dynamics?

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Computational Fluid Dynamics (CFD) is a powerful tool for simulating complex fluid flows and aerodynamic phenomena in aerospace engineering. However, CFD models are not perfect and always involve some degree of uncertainty. Uncertainty can arise from various sources, such as input data, numerical methods, physical models, boundary conditions, and solver settings. Ignoring or underestimating uncertainty can lead to inaccurate or misleading results, which can compromise the design, performance, and safety of aerospace systems. Therefore, it is essential to have a systematic and rigorous process for analyzing uncertainty in CFD. In this article, we will discuss some key steps and methods for doing so.

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Francesco Ambrogi, PhD

Adjunct Assistant Professor at Queen's University
Arthur Cunha Soares

Mechanical Engineer

1 Define the problem

When analyzing uncertainty in CFD, the first step is to define the problem clearly and identify the objectives and constraints. This includes specifying the geometry and domain of the fluid system, fluid properties, flow conditions, quantities of interest (QoIs), sources and types of uncertainty, and acceptable level of uncertainty or error for the QoIs. Doing so will enable you to select the best CFD model, numerical scheme, and uncertainty quantification (UQ) method for your analysis.

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2 Perform sensitivity analysis

The next step is to perform sensitivity analysis, which is the process of assessing how the QoIs vary with respect to the uncertain input parameters. This can help you identify the most influential input parameters that contribute to output uncertainty, reduce the dimensionality of the problem, determine the optimal range and resolution of the input parameters for UQ, and evaluate the linearity or nonlinearity of the input-output relationship. There are various methods for performing sensitivity analysis, such as local, global, or regional methods; among them are finite difference, Sobol indices, Morris screening, and polynomial chaos expansion (PCE).

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3 Quantify uncertainty

The third step is to quantify uncertainty, which is the process of estimating the distribution and propagation of the input uncertainty to the output uncertainty. UQ can help you characterize the uncertainty in the input parameters, propagate the input uncertainty to the output uncertainty, estimate the uncertainty in the QoIs, and visualize and interpret the uncertainty. This can be done through Monte Carlo simulation (MCS), PCE, stochastic collocation, Bayesian inference, and evidence theory. Each method has its own advantages and disadvantages which should be taken into consideration when selecting a method.

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Francesco Ambrogi, PhD

Adjunct Assistant Professor at Queen's University
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I believe the most important question we should ask ourselves when performing CFD is: can I trust my results? To answer this question TWO very important steps must be followed. 1. Grid convergence study: this is an INTERNAL test, and it has nothing to do with reference data. This test is to show that you can trust your numerical model. Keep in mind that grid sensitivity study must be carried out for every important quantity you will be presenting in your research. 2. Validation check: this is an EXTERNAL test. Before analyzing complex cases you should always validate your model by running canonical flows (fully developed channel flow, boundary layers) and comparing your results with existing high fidelity DNS or LES simulations.

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Arthur Cunha Soares

Mechanical Engineer
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In my experience, it's essential to grasp the expected fluid behavior before running simulations. Comparing obtained results with anticipated outcomes is crucial. Different models excel in capturing specific phenomena, so understanding your goal is vital when choosing a turbulence model, for instance. Furthermore, conducting validation tests is crucial to ensure the reliability of the model being used. Also, employing grid convergence tests is essential for identifying an optimal mesh size, otherwise you might end up using too much computational power for not so much better results.

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4 Validate and verify

The final step is to validate and verify your CFD model and UQ results. Validation involves comparing your CFD results with experimental or analytical data to assess the accuracy and reliability of your model, while verification is the process of checking your CFD code and UQ method for numerical errors and convergence. To do this effectively, you should choose relevant and reliable data sources for comparison, apply appropriate error and uncertainty metrics for comparison, conduct grid and time refinement studies for convergence, and perform code and method verification tests for correctness. Ultimately, validation and verification will help you evaluate the quality and credibility of your CFD model and UQ results, as well as identify the sources and magnitude of uncertainty and error.

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5 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?

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What's your process for analyzing uncertainty in Computational Fluid Dynamics?

1

2

3

4

5

1 Define the problem

2 Perform sensitivity analysis

3 Quantify uncertainty

4 Validate and verify

5 Here’s what else to consider

Aerospace Engineering

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What's your process for analyzing uncertainty in Computational Fluid Dynamics?

1

2

3

4

5

1 Define the problem

2 Perform sensitivity analysis

3 Quantify uncertainty

4 Validate and verify

5 Here’s what else to consider

Aerospace Engineering

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