Last updated on Aug 22, 2024
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- Computational Fluid Dynamics (CFD)
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Sources of error
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Error estimation methods
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Error propagation methods
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Best practices and standards
Computational fluid dynamics (CFD) is a powerful tool for simulating complex flows and phenomena, but it also comes with uncertainties and errors that can affect the reliability and accuracy of the results. How can you quantify and reduce these errors and propagate them to the outputs of interest? In this article, you will learn about the best practices and standards for CFD error estimation and propagation, based on the guidelines of the American Institute of Aeronautics and Astronautics (AIAA) and the European Research Community on Flow, Turbulence and Combustion (ERCOFTAC).
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- Hong Yang Lead CFD Methods, Senior Engineering Specialist at BOMBARDIER
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- Frank Kushner Turbomachinery Vibration / Acoustics Consultant at Frank Kushner Consulting, LLC
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1 Sources of error
CFD errors can arise from various sources, such as modeling assumptions, discretization schemes, numerical algorithms, boundary and initial conditions, and code implementation. These errors can be classified into three types: truncation error, round-off error, and iteration error. Truncation error is the difference between the exact solution of the governing equations and the discrete approximation. Round-off error is the loss of precision due to finite computer arithmetic. Iteration error is the difference between the converged solution and the exact discrete solution.
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- Hong Yang Lead CFD Methods, Senior Engineering Specialist at BOMBARDIER
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Physics models such turbulence and laminar-turbulence transition models are also sources of the errors in CFD, which can make a big difference for separated flows.
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- Güven NERGİZ CFD Enthusiast
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The more errors you encounter in CFD, the more experience you gain. Divergence problems can be caused by many things. Many variables such as mesh, method, model, time step, solver settings, turbulence model... can cause divergence. As you solve divergence problems, you will know what to look for first in the next error.
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2 Error estimation methods
To quantify the errors in CFD, you can use different methods, such as analytical, experimental, or numerical. Analytical methods involve deriving error bounds or formulas based on mathematical analysis. Experimental methods involve comparing CFD results with experimental data or other validated solutions. Numerical methods involve performing grid refinement studies, solution verification, or uncertainty quantification. Each method has its advantages and limitations, depending on the availability of data, resources, and assumptions.
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- Güven NERGİZ CFD Enthusiast
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Experimental studies are really important for the simulations. Finding a validated case, re-simulating it and checking the error similarity would be guide you during your own special study.
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- Ashutosh Sharma Mechanical Designer | CAD/CAE Expert | Python | EIT (PEng) | Machine Learning
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Numerical methods involves techniques such as grid refinement studies (assessing how solution changes with finer grids), solution verification (checking the convergence of the numerical method), and uncertainty quantification (quantifying the uncertainties in the input parameters and their effects on the output)
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- Revanth Hamsagurusamy Mechanical Hydraulics Engineer at CNH Industrial
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The usual method is grid convergence. Richardson extrapolation, Error estimation via the residual, Adjoint-based error estimation, Bayesian inference, and Local error estimation can also be used.
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3 Error propagation methods
To propagate the errors in CFD to the outputs of interest, such as forces, moments, or coefficients, you can use different methods, such as sensitivity analysis, adjoint methods, or Monte Carlo methods. Sensitivity analysis involves calculating the partial derivatives of the outputs with respect to the inputs or parameters. Adjoint methods involve solving a linear system of equations that relates the outputs to the inputs or parameters. Monte Carlo methods involve sampling the inputs or parameters from a probability distribution and computing the statistics of the outputs.
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- Güven NERGİZ CFD Enthusiast
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In CFD, error propagation can be analyzed using three main methods:Sensitivity Analysis: Determines how changes in inputs affect outputs by calculating partial derivatives.Adjoint Methods: Solving a set of linear equations to relate outputs to inputs. They are particularly effective in optimization problems, helping to understand how changes in inputs affect outputs like forces or moments.Monte Carlo Methods: Takes random sampling of inputs and multiple simulations to statistically analyze outputs, providing a detailed understanding of input uncertainties.Each method is chosen based on the specific requirements of the CFD analysis, available computational resources, and the nature of uncertainties in the model.
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4 Best practices and standards
To ensure the quality and credibility of CFD results, you should adhere to best practices and standards, such as those recommended by the AIAA and the ERCOFTAC. This includes defining objectives and scope, choosing appropriate models and parameters, performing grid refinement studies and solution verification, comparing CFD results with experimental data or other validated solutions, conducting uncertainty quantification and propagation, and reporting results with clear and consistent terminology and formats. Following these guidelines can boost the confidence in your CFD results and help communicate them effectively to stakeholders.
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- Frank Kushner Turbomachinery Vibration / Acoustics Consultant at Frank Kushner Consulting, LLC
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Boundary conditions at flow entrance and exit are prime. About 10 years or so a billion dollar income consulting company had a serious error with an odd result for calculation of exciting forces for an impeller stage in a centrifugal compressor. When at Elliott Turbomachinery our CFD expert - Jim Hardin (since retired) - for ANSYS CFX reviewed the model & told them to just pinch the exit passage. Problem solved.
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