Memorias de investigación
Ponencias en congresos:
Fast time integration of PDEs combining POD and Galerkin projection based on a limited set of mesh points
Año:2015
Áreas de investigación
  • Ingeniería aeronaútica
Datos
Descripción
Recently, an adaptive method to accelerate time dependent numerical solvers of systems of PDEs that require a high cost in computational time and memory has been proposed [3] (see also [1, 2]). The method combines on the fly such numerical solver with a proper orthogonal decomposition, from which we identify modes, a Galerkin projection (that provides a reduced system of equations), and the integration of the reduced system. The strategy is based on a truncation error estimate and a residual estimate, designed to control the truncation error and the mode truncation instability, respectively. These estimates support the selection of the appropiate time intervals in which the numerical solver is run to first construct and then update, on demand, the POD modes. Moreover, to reduce the computational effort needed at the outset to generate the initial POD subspace, information from former simulations or generic libraries (e.g. trigonometric functions or orthogonal polynomials) were also used. To improve the computational efficiency of the method presented in [3] a crucial step is to use a limited number of points (instead of the whole computational mesh used in the spatial discretization) to both perform POD and to Galerkin?project the equations. In this work we will discuss and compare several alternatives in representative examples illustrating that a suitable point selection can make the cost of the reduced order model (associated with POD, Galerkin projection and the integration of the resulting Galerkin system) negligible compared to that of the reference numerical solver.
Internacional
Si
Nombre congreso
Bifurcations and instabilities in fluid dynamics (BIFD 2015)
Tipo de participación
960
Lugar del congreso
Paris, Francia
Revisores
Si
ISBN o ISSN
00000000
DOI
Fecha inicio congreso
15/07/2015
Fecha fin congreso
17/07/2015
Desde la página
1
Hasta la página
1
Título de las actas
Proceedings of BIFD 2015
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Participantes
Grupos de investigación, Departamentos, Centros e Institutos de I+D+i relacionados
  • Creador: Grupo de Investigación: Dinámica y estabilidad no lineal en ingeniería aeroespacial
  • Departamento: Matemática Aplicada a la Ingeniería Aeroespacial