The nuclear community has coupled several three-dimensional Computational Fluid Dynamics (CFD) solvers with one-dimensional system thermal–hydraulic (STH) codes. This work proposes to replace the CFD solver by a reduced order model (ROM) reduce computational cost. code RELAP5-MOD3.3 and ROM of finite volume OpenFOAM are partitioned domain decomposition coupling algorithm using an implicit schem...

let $g$ be a finite simple graph whose vertices and edges are weighted by two functions. in this paper we shall define and calculate entropy of a dynamical system on weights of the graph $g$, by using the weights of vertices and edges of $g$. we examine the conditions under which entropy of the dynamical system is zero, possitive or $+infty$. at the end it is shown that, for $rin [0,+infty]$, t...

The energy-conserving sampling and weighting (ECSW) method is a hyper-reduction originally developed for accelerating the performance of Galerkin projection-based reduced-order models (PROMs) associated with large-scale finite element models, when underlying projected operators need to be frequently recomputed as in parametric and/or nonlinear problems. In this paper, extended Petrov–Galerkin P...

The problem of deriving a suboptimal LQG controller which is internally stable is considered. In the case where the controller is internally unstable a procedure is given for modifying the optimization parameters, i.e. the state weighting matrix and/or the process noise intensity. Sufficient conditions for controller stability of appropriately modified optimization problems are given for both t...

This paper is concerned with the reduced-order H∞ filtering problem of commensurate fractional-order systems. Our goal is to construct a reduced-order filter in such a way that the filtering error is within a prescribed H∞-norm error bound. Based on the bounded real lemma for commensurate fractional-order systems, a sufficient condition is established in terms of linear matrix inequalities (LMI...

In this article, an improved reduced order modelling approach, based on the proper orthogonal decomposition (POD) method, is presented. After projecting the governing equations of flow dynamics along the POD modes, a dynamical system was obtained. Normally, the classical reduced order models do not predict accurate time variations of flow variables due to some reasons. The response of the dynam...

In this paper we treat the time evolution of unitary elements in the N level system and consider the reduced dynamics from the unitary group U(N) to flag manifolds of the second type (in our terminology). Then we derive a set of differential equations of matrix Riccati types interacting with one another and present an important problem on a nonlinear superposition formula that the Riccati equat...