Energy preserving reduced-order modeling of the rotating thermal shallow water equation

Date

2022-05-01

Author

Karasözen, Bülent
Ylldlz, S.
Uzunca, M.

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

151
views

0
downloads

© 2022 Author(s).In this paper, reduced-order models (ROMs) are developed for the rotating thermal shallow water equation (RTSWE) in the non-canonical Hamiltonian form with state-dependent Poisson matrix. The high fidelity full solutions are obtained by discretizing the RTSWE in space with skew-symmetric finite-differences, while preserving the Hamiltonian structure. The resulting skew-gradient system is integrated in time by the energy preserving average vector field (AVF) method. The ROM is constructed by applying proper orthogonal decomposition with the Galerkin projection, preserving the reduced skew-gradient structure, and integrating in time with the AVF method. The nonlinear terms of the Poisson matrix and Hamiltonian are approximated with the discrete empirical interpolation method to reduce the computational cost. The solutions of the resulting linear-quadratic reduced system are accelerated by the use of tensor techniques. The accuracy and computational efficiency of the ROMs are demonstrated for a numerical test problem. Preservation of the energy (Hamiltonian) and other conserved quantities, i.e., mass, buoyancy, and total vorticity, show that the reduced-order solutions ensure the long-term stability of the solutions while exhibiting several orders of magnitude computational speedup over the full-order model. Furthermore, we show that the ROMs are able to accurately predict the test and training data and capture the system behavior in the prediction phase.

URI

https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85130714884&origin=inward
https://hdl.handle.net/11511/97508

Journal

Physics of Fluids

DOI

https://doi.org/10.1063/5.0091678

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Numerical heat transfer modelling of a centrifugal solar particle receiver Hiçdurmaz, Serdar; Johnson, Evan F.; Grobbel, Johannes; Amsbeck, Lars; Buck, Reiner; Hoffschmidt, Bernhard (2022-05-12) © 2022 Author(s).Solar particle receivers promise higher operating temperatures compared to molten salt-based receivers. The Discrete Element Method (DEM) tool LIGGGHTS is used to simulate the particle motion in a centrifugal solar particle receiver. A separate thermal model is developed in MATLAB, which uses the particle positions calculated with the DEM simulation. Heat transfer at the particle scale is accounted for with models of particle-particle conduction, particle-fluid- particle conduction, and a n...
Linear and nonlinear optical characteristics of PbMoO4 single crystal for optoelectronic applications Delice, S.; Isik, M.; Hasanlı, Nızamı (2022-10-01) © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.In the present paper, we studied linear and nonlinear optical properties of lead molybdate (PbMoO4) single crystals grown by Czochralski method. Raman measurement was performed in the range of 50–1000 cm−1 and 11 active vibration modes were defined in the spectrum. The nature of the observed modes was discussed in detail. Optical absorption of the material was investigated utilizing room temperatu...
Tensionless strings and Killing(-Yano) tensors Lindström, Ulf; Sarıoğlu, Bahtiyar Özgür (2022-06-10) © 2022 The Author(s)We construct invariants for bosonic and spinning tensionless (null) strings in backgrounds that carry Killing tensors or Killing-Yano tensors of mixed type. This is facilitated by the close relation of these strings to point particles. We apply the construction to the Minkowski and to the Kerr-Newman backgrounds.
Real-time measurement of laser beam characteristics for a waterjet-guided laser machine Subasi, Levent; Gökler, Mustafa İlhan; Yaman, Ulaş (2022-01-01) © 2022, The Author(s), under exclusive licence to Springer-Verlag London Ltd., part of Springer Nature.Waterjet-guided laser machining is a novel process used for precision cutting and drilling of various materials and geometries. There are many noise factors in the process affecting the laser beam characteristics, namely the effective cutting length and laser power in the waterjet. Although these variables are mainly set by the laser and waterjet parameters, uncontrollable factors result in variations. Pre...
Predictive Design and Analysis of Drug Transport by MultiScale Computational Models Under Uncertainty Akalın, Ali Aykut; Dedekargınoğlu, Barış; Choi, Sae Rome; Han, Bumsoo; Özçelikkale, Altuğ (2022-01-01) © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.Computational modeling of drug delivery is becoming an indispensable tool for advancing drug development pipeline, particularly in nanomedicine where a rational design strategy is ultimately sought. While numerous in silico models have been developed that can accurately describe nanoparticle interactions with the bioenvironment within prescribed length and time scales, predictive design of these d...

Citation Formats

B. Karasözen, S. Ylldlz, and M. Uzunca, “Energy preserving reduced-order modeling of the rotating thermal shallow water equation,” Physics of Fluids, vol. 34, no. 5, pp. 0–0, 2022, Accessed: 00, 2022. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85130714884&origin=inward.