TY - JOUR
T1 - Calibration-Based ALE Model Order Reduction for Hyperbolic Problems with Self-Similar Travelling Discontinuities
AU - Nonino, Monica
AU - Torlo, Davide
N1 - Publisher Copyright:
© The Author(s) 2024.
PY - 2024/10/24
Y1 - 2024/10/24
N2 - We propose a novel Model Order Reduction framework that is able to handle solutions of hyperbolic problems characterized by multiple travelling discontinuities. By means of an optimization based approach, we introduce suitable calibration maps that allow us to transform the original solution manifold into a lower dimensional one. The novelty of the methodology is represented by the fact that the optimization process does not require the knowledge of the discontinuities location. The optimization can be carried out simply by choosing some reference control points, thus avoiding the use of some implicit shock tracking techniques, which would translate into an increased computational effort during the offline phase. In the online phase, we rely on a non-intrusive approach, where the coefficients of the projection of the reduced order solution onto the reduced space are recovered by means of an Artificial Neural Network. To validate the methodology, we present numerical results for the 1D Sod shock tube problem, for the 2D double Mach reflection problem, also in the parametric case, and for the triple point problem.
AB - We propose a novel Model Order Reduction framework that is able to handle solutions of hyperbolic problems characterized by multiple travelling discontinuities. By means of an optimization based approach, we introduce suitable calibration maps that allow us to transform the original solution manifold into a lower dimensional one. The novelty of the methodology is represented by the fact that the optimization process does not require the knowledge of the discontinuities location. The optimization can be carried out simply by choosing some reference control points, thus avoiding the use of some implicit shock tracking techniques, which would translate into an increased computational effort during the offline phase. In the online phase, we rely on a non-intrusive approach, where the coefficients of the projection of the reduced order solution onto the reduced space are recovered by means of an Artificial Neural Network. To validate the methodology, we present numerical results for the 1D Sod shock tube problem, for the 2D double Mach reflection problem, also in the parametric case, and for the triple point problem.
KW - Calibration map
KW - 76L05
KW - 35L60
KW - 65M08
KW - Multiple travelling discontinuities
KW - Model order reduction
KW - Neural network
KW - 35L67
KW - Hyperbolic problems
UR - http://www.scopus.com/inward/record.url?scp=85207846471&partnerID=8YFLogxK
U2 - 10.1007/s10915-024-02694-z
DO - 10.1007/s10915-024-02694-z
M3 - Article
SN - 0885-7474
VL - 101
JO - Journal of Scientific Computing
JF - Journal of Scientific Computing
M1 - 60
ER -