Reduced Order Strategy for Transient Problems with High Moving Gradients

SERGIO IDELSOHN; ALEJANDRO COSIMO; ALBERTO CARDONA

Montreal

Congreso; 14th U.S. National Congress on Computational Mechanics; 2017

USACM United States Association of Computational Mechanics

The aim of this presentation is to solve parabolic problems with highly concentrated moving gradients. A naive approach to tackle this kind of problems would be to refine the mesh as much as needed in all the regions of the domain that are in the vicinity of the path of the moving gradient. One alternative is to adaptively refine the mesh following the moving gradient. Despite the fact that previous options are valid, both are very expensive and they are not so friendly to the formulation of Reduced Order Models (ROMs) because they do not help to tackle the space-time coupling of such problems [1]. The alternative proposed in this presentation is to adopt a global/local scheme, in which a moving local fine mesh describes the neighborhood of the moving gradient and a coarse global mesh describes the analysis domain. In order to glue the two meshes a number of Lagrange multipliers are added to the boundary contour of the fine mesh [2]. It should be noted that the boundary of the fine domain does not need to conform to the elements' boundary of the coarse domain. The big advantage of the proposed strategy is the possibility to reduce drastically both: the fine mesh Degrees of Freedom (DOF) and the Lagrange multipliers DOF,avoiding the space-time coupling problem existing in the global solution. Only transient heat conduction with a concentrated moving heat source are treated in this presentation but the strategy may be generalized to more complex problems with vectorial unknowns like the Navier-Stokes equations. In a series of numerical examples, it is shown that POD modes may be obtained training the problem in one part of the domain and then, to use only a fewof these POD modes to solve problems with the gradients in different areas without significant variations of the relative error. References [1] A. Cosimo, A. Cardona, S. Idelsohn, ?Improving the k-Compressibility of HyperReduced Order Models with Moving Sources: Applications to Welding and Phase Change Problems?, CMAME, 274, 237-263, 2014. [2] A. Cosimo, A. Cardona, S. Idelsohn, ?General Treatment of Essential Boundary Conditionsin Reduced Order Models for Non-Linear Problems?, AMSES, 3:7, 2016.