Application of Exactly Linearized Error Transport Equations to Sonic Boom Prediction Workshop

Area of Science:

• Aerospace Engineering
• Computational Science
• Acoustics

Background:

• Computational Fluid Dynamics (CFD) workshops highlight challenges in predicting phenomena like sonic booms.
• Discrepancies between simulated and experimental results stem from various errors, necessitating error quantification for reliable decision-making.

Purpose of the Study:

• To quantify errors in CFD simulations, specifically focusing on discretization errors.
• To implement and demonstrate a method for estimating errors in complex multidisciplinary analyses, including sonic boom propagation.

Main Methods:

• Linearized error transport equations (ETE) were combined with truncation error estimation.
• A complex-step method was employed for exact linearization, minimizing modifications to existing CFD and multidisciplinary analysis codes.
• Uniformly refined grids from the 2nd AIAA Sonic Boom Prediction Workshop were utilized.

Main Results:

• The study demonstrates the utility of ETE for error quantification in multidisciplinary analysis.
• A direct link was established between estimated discretization error and flow features (resolved or under-resolved).
• The method proved effective in analyzing the atmospheric propagation of sonic boom signatures.

Conclusions:

• The linearized error transport equations (ETE) provide a valuable tool for quantifying discretization errors in CFD.
• This approach facilitates more reliable predictions in complex scenarios like sonic boom analysis.
• The method's integration with complex-step linearization ensures broad applicability with minimal code changes.