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.

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.

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.

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.