The Pseudo-Direct Numerical Simulation Method considered as a Reduced Order Model

Springer Science and Business Media LLC - Tập 9 Số 1
Sergio Idelsohn1, Juan M. Giménez1, Norberto M. Nigro2
1Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE), Barcelona, Spain
2Centro de Investigación de Métodos Computacionales (CIMEC), Santa Fe, Argentina

Tóm tắt

AbstractThe multiscale method called Pseudo-Direct Numerical Simulation (P-DNS) is presented as a Reduced Order Model (ROM) aiming to solve problems obtaining similar accuracy to a solution with many degrees of freedom (DOF). The theoretical basis of P-DNS is other than any standard ROM. However, from a methodological point of view, P-DNS shares the idea of an offline computation, as ROM does, providing the set of coefficients, as a database or table, needed to solve the main problem. This work highlights the advantages and disadvantages of both methodologies. In particular, the drawback of the standard ROM concerning problems where space and time are not separated variables is discussed. The so-called Idelsohn’s benchmark is possibly the most elemental test that can be proposed to point out this drawback. This one-dimensional heat transfer problem with a moving heat source shows that, unlike ROMs, P-DNS can solve it by reducing the number of degrees of freedom as much as needed.

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Tài liệu tham khảo

Idelsohn SR, Cardona A. Reduction methods and explicit time integration technique in structural dynamics. Advances in Engineering Software. 1984;6(1):36–44.

Idelsohn SR, Cardona A. A load-dependent basis for reduced nonlinear structural dynamics. Computers & Structures. 1985;20(1–3):203–10.

Cardona A, Idelsohn S. Solution of non-linear thermal transient problems by a reduction method. International journal for numerical methods in engineering. 1986;23(6):1023–42.

Baiges J, Codina R, Idelsohn S. Explicit reduced-order models for the stabilized finite element approximation of the incompressible navier-stokes equations. International Journal for Numerical Methods in Fluids. 2013;72(12):1219–43.

Cosimo A, Cardona A, Idelsohn S. General treatment of essential boundary conditions in reduced order models for non-linear problems. Advanced Modeling and Simulation in Engineering Sciences. 2016;3(1):1–14.

Farhat C, Avery P, Chapman T, Cortial J. Dimensional reduction of nonlinear finite element dynamic models with finite rotations and energy-based mesh sampling and weighting for computational efficiency. International Journal for Numerical Methods in Engineering. 2014;98(9):625–62.

Farhat C, Chapman T, Avery P. Structure-preserving, stability, and accuracy properties of the energy-conserving sampling and weighting method for the hyper reduction of nonlinear finite element dynamic models. International journal for numerical methods in engineering. 2015;102(5):1077–110.

Ryckelynck D. A priori hyperreduction method: an adaptive approach. Journal of computational physics. 2005;202(1):346–66.

Ryckelynck D, Chinesta F, Cueto E, Ammar A. On thea priori model reduction: Overview and recent developments. Archives of Computational methods in Engineering. 2006;13(1):91–128.

Nouy A. A priori model reduction through proper generalized decomposition for solving time-dependent partial differential equations. Computer Methods in Applied Mechanics and Engineering. 2010;199(23–24):1603–26.

Chinesta F, Ladeveze P, Cueto E. A short review on model order reduction based on proper generalized decomposition. Archives of Computational Methods in Engineering. 2011;18:395–404. https://doi.org/10.1007/s11831-011-9064-7.

Chinesta F, Cueto E. Pgd-based modeling of materials, structures and processes. Springer 2014.

Chinesta F, Ladevèze P. Separated representations and pgd-based model reduction. Fundamentals and Applications, International Centre for Mechanical Siences, Courses and Lectures. 2014;554:24.

Idelsohn S, Nigro N, Larreteguy A, Gimenez JM, Ryzhakov P. A pseudo-dns method for the simulation of incompressible fluid flows with instabilities at different scales. Computational Particle Mechanics. 2020;7(1):19–40.

Idelsohn SR, Gimenez JM, Nigro NM, Oñate E. The pseudo-direct numerical simulation method for multi-scale problems in mechanics. Computer Methods in Applied Mechanics and Engineering. 2021;380:113774. https://doi.org/10.1016/j.cma.2021.113774.

Gimenez JM, Idelsohn SR, Oñate E, Löhner R. A multiscale approach for the numerical simulation of turbulent flows with droplets. Archives of Computational Methods in Engineering. 2021;28(6):4185–204.

Oliver J, Caicedo M, Huespe AE, Hernández JA, Roubin E. Reduced order modeling strategies for computational multiscale fracture. Computer Methods in Applied Mechanics and Engineering. 2017;313:560–95. https://doi.org/10.1016/j.cma.2016.09.039.

Allier P, Chamoin L, Ladevèze P. Proper generalized decomposition computational methods on a benchmark problem: introducing a new strategy based on constitutive relation error minimization. Adv. Model. and Simul. in Eng. Sci. 2015;2(17). https://doi.org/10.1186/s40323-015-0038-4

Badías A, González D, Alfaro I, Chinesta F, Cueto E. Local proper generalized decomposition. International Journal for Numerical Methods in Engineering. 2017;112(12):1715–32.

Cosimo A, Cardona A, Idelsohn S. Improving the k-compressibility of hyper reduced order models with moving sources: applications to welding and phase change problems. Computer Methods in Applied Mechanics and Engineering. 2014;274:237–63.

Cosimo A, Cardona A, Idelsohn S. Global-local rom for the solution of parabolic problems with highly concentrated moving sources. Computer Methods in Applied Mechanics and Engineering. 2017;326:739–56.

Puigferrat A, de-Pouplana I, Oñate E. FIC-FEM formulation for the multidimensional transient advection-diffusion-absorption equation. Computer Methods in Applied Mechanics and Engineering 2020;365:112984. https://doi.org/10.1016/j.cma.2020.112984

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