Calibration-Based ALE Model Order Reduction for Hyperbolic Problems with Self-Similar Travelling Discontinuities.

Area of Science:

• Computational Fluid Dynamics
• Numerical Analysis
• Scientific Computing

Background:

• Hyperbolic partial differential equations often feature discontinuities like shock waves.
• Traditional model order reduction (MOR) methods struggle with these discontinuities, requiring complex tracking.
• Existing techniques can be computationally expensive, especially in the offline phase.

Purpose of the Study:

• To develop a novel MOR framework for hyperbolic problems with multiple traveling discontinuities.
• To enable dimensionality reduction without prior knowledge of discontinuity locations.
• To enhance computational efficiency in both offline and online phases of MOR.

Main Methods:

• An optimization-based approach is used to create calibration maps for transforming the solution manifold.
• The optimization process avoids explicit shock tracking by using reference control points.
• An Artificial Neural Network (ANN) is employed in the online phase to recover reduced-order solution coefficients non-intrusively.

Main Results:

• The proposed framework successfully handles hyperbolic problems with multiple traveling discontinuities.
• Numerical validation is demonstrated on the 1D Sod shock tube, 2D double Mach reflection (including parametric cases), and triple point problems.
• The method shows efficiency by avoiding computationally intensive shock tracking techniques.

Conclusions:

• The novel MOR framework offers an efficient and robust solution for hyperbolic problems with traveling discontinuities.
• The non-intrusive online phase using ANNs significantly reduces computational cost.
• This approach provides a valuable tool for simulating complex fluid dynamics phenomena.