A discontinuous and adaptive reduced order model for the angular discretization of the Boltzmann transport equation
Published on Aug 5, 2020in International Journal for Numerical Methods in Engineering3.477
路 DOI :10.1002/NME.6516
Abstract
References36
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Abstract We use a novel nonintrusive adaptive Reduced Order Modeling method to build a reduced model for a molten salt reactor system. Our approach is based on Proper Orthogonal Decomposition combined with locally adaptive sparse grids. Our reduced model captures the effect of 27 model parameters on k eff of the system and the spatial distribution of the neutron flux and salt temperature. The reduced model was tested on 1000 random points. The maximum error in multiplication factor was found to ...
Fuel burnup analysis requires a high computational cost for full core calculations, due to the amount of the information processed for the total reaction rates in many burnup regions. Indeed, they reach the order of millions or more by a subdivision into radial and axial regions in a pin-by-pin description. In addition, if multi-physics approaches are adopted to consider the effects of temperature and density fields on fuel consumption, the computational load grows further. In this way, the need...
Abstract This paper describes an angular adaptivity algorithm for Boltzmann transport applications which uses Pn and filtered Pn expansions, allowing for different expansion orders across space/energy. Our spatial discretisation is specifically designed to use less memory than competing DG schemes and also gives us direct access to the amount of stabilisation applied at each node. For filtered Pn expansions, we then use our adaptive process in combination with this net amount of stabilisation to...
Abstract Nonlinear dynamical systems like thermal hydraulic natural circulation systems can show a very complex behavior under specific conditions. Hence an in-depth analysis of the stability landscape of such systems is necessary. In the field of nuclear reactor technology, the application of advanced system codes, which numerically solve the set of nonlinear partial differential equations describing the underlying system dynamics, is common practice. However, this method is cumbersome and requ...
Abstract A parameterised non-intrusive reduced order model (P-NIROM) based on proper orthogonal decomposition (POD) and machine learning methods has been firstly developed for model reduction of pollutant transport equations. Our motivation is to provide rapid response urban air pollution predictions and controls. The varying parameters in the P-NIROM are pollutant sources. The training data sets are obtained from the high fidelity modelling solutions (called snapshots) for selected parameters (...
Abstract This paper deals with the use of Reduced Order Methods for neutronics modelling. This approach is used whether both accuracy and computational efficiency are required. A very popular category of these methods is based on projection approaches which use spatial basis and test functions for the development of the reduced order model. The selection of the spatial basis and test functions used in the projection phase is a crucial issue since it has an impact on the accuracy and the computat...
Accelerated Solution of Discrete Ordinates Approximation to the Boltzmann Transport Equation for a Gray Absorbing鈥揈mitting Medium Via Model Reduction
Discontinuous isogeometric analysis methods for the first-order form of the neutron transport equation with discrete ordinate (SN) angular discretisation
In this paper two discontinuous Galerkin isogeometric analysis methods are developed and applied to the first-order form of the neutron transport equation with a discrete ordinate ( S N ) angular discretisation. The discontinuous Galerkin projection approach was taken on both an element level and the patch level for a given Non-Uniform Rational B-Spline (NURBS) patch. This paper describes the detailed dispersion analysis that has been used to analyse the numerical stability of both of these sche...
Abstract In this work, a Reduced Basis method, with basis functions sampled by a Proper Orthogonal Decomposition technique, has been employed to develop a reduced order model of a multi-physics parametrized Lead-cooled Fast Reactor single-channel. Being the first time that a reduced order model is developed in this context, the work focused on a methodological approach and the coupling between the neutronics and the heat transfer, where the thermal feedbacks on neutronics are explicitly taken in...
A space-angle DGFEM approach for the Boltzmann radiation transport equation with local angular refinement
In this paper a new method for the discretization of the radiation transport equation is presented, based on a discontinuous Galerkin method in space and angle that allows for local refinement in angle where any spatial element can support its own angular discretization. To cope with the discontinuous spatial nature of the solution, a generalized Riemann procedure is required to distinguish between incoming and outgoing contributions of the numerical fluxes. A new consistent framework is introdu...
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The single parabolic band (SPB) model has been widely used to preliminarily elucidate inherent transport behaviors of thermoelectric (TE) materials, such as their band structure and electronic thermal conductivity, etc. However, in the SPB calculation, it is necessary to determine some intermediate variables, such as Fermi level or the complex Fermi-Dirac integrals. In this work, we establish a direct carrier-concentration-dependent restructured SPB model, which eliminates Fermi-Dirac integrals ...
Solving the neutron transport equations is a demanding computational challenge. This paper combines reduced-order modelling with domain decomposition to develop an approach that can tackle such problems. The idea is to decompose the domain of a reactor, form basis functions locally in each sub-domain and construct a reduced-order model from this. Several different ways of constructing the basis functions for local sub-domains are proposed, and a comparison is given with a reduced-order model tha...