Last. Harbir Antil(GMU: George Mason University)H-Index: 17
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Least-squares Petrov-Galerkin (LSPG) model-reduction techniques such as the Gauss-Newton with Approximated Tensors (GNAT) method have shown promise, as they have generated stable, accurate solutions for large-scale turbulent, compressible flow problems where standard Galerkin techniques have failed. However, there has been limited comparative analysis of the two approaches. This is due in part to difficulties arising from the fact that Galerkin techniques perform optimal projection associated wi...
#1John Tencer(SNL: Sandia National Laboratories)H-Index: 6
Two of the most popular deterministic radiation transport methods for treating the angular dependence of the radiative intensity for heat transfer: the discrete ordinates and simplified spherical harmonics approximations are compared. A problem with discontinuous boundary conditions is included to evaluate ray effects for discrete ordinates solutions. Mesh resolution studies are included to ensure adequate convergence and evaluate the effects of the contribution of false scattering. All solution...
Last. Karen Willcox(MIT: Massachusetts Institute of Technology)H-Index: 48
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Numerical simulation of large-scale dynamical systems plays a fundamental role in studying a wide range of complex physical phenomena; however, the inherent large-scale nature of the models often leads to unmanageable demands on computational resources. Model reduction aims to reduce this computational burden by generating reduced models that are faster and cheaper to simulate, yet accurately represent the original large-scale system behavior. Model reduction of linear, nonparametric dynamical s...
Last. I. M. Navon(FSU: Florida State University)H-Index: 49
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This article presents the first Reduced Order Model (ROM) that efficiently resolves the angular dimension of the time independent, mono-energetic Boltzmann Transport Equation (BTE). It is based on Proper Orthogonal Decomposition (POD) and uses the method of snapshots to form optimal basis functions for resolving the direction of particle travel in neutron/photon transport problems. A unique element of this work is that the snapshots are formed from the vector of angular coefficients relating to ...
Summary This report presents a numerical study of reduced-order representations for simulating incompressible Navier–Stokes flows over a range of physical parameters. The reduced-order representations combine ideas of approximation for nonlinear terms, of local bases, and of least-squares residual minimization. To construct the local bases, temporal snapshots for different physical configurations are collected automatically until an error indicator is reduced below a user-specified tolerance. An...
This work presents a technique for statistically modeling errors introduced by reduced-order models. The method employs Gaussian-process regression to construct a mapping from a small number of computationally inexpensive “error indicators” to a distribution over the true error. The variance of this distribution can be interpreted as the (epistemic) uncertainty introduced by the reduced-order model. To model normed errors, the method employs existing rigorous error bounds and residual norms as i...
#1A. K. Gaonkar(IITB: Indian Institute of Technology Bombay)H-Index: 2
#2Salil S. Kulkarni(IITB: Indian Institute of Technology Bombay)H-Index: 11
In the present paper, a method to reduce the computational cost associated with solving a nonlinear transient heat conduction problem is presented. The proposed method combines the ideas of two level discretization and the multilevel time integration schemes with the proper orthogonal decomposition model order reduction technique. The accuracy and the computational efficiency of the proposed methods is discussed. Several numerical examples are presented for validation of the approach. Compared t...
A nonlinear, low-order physics-based model for the dynamics of forced convection wall heat transfer in pulsating flow is formulated, based on the proper orthogonal decomposition technique. In a multivariate approach, proper orthogonal decomposition modes are constructed from computational fluid dynamics data for laminar flow and heat transfer over a flat plate in pulsating flow, spanning a range of pulsation frequencies and amplitudes. Then, the conservation equations for mass, momentum, and ene...
This work aims to advance computational methods for projection-based reduced order models (ROMs) of linear time-invariant (LTI) dynamical systems. For such systems, current practice relies on ROM formulations expressing the state as a rank-1 tensor (i.e., a vector), leading to computational kernels that are memory bandwidth bound and, therefore, ill-suited for scalable performance on modern many-core and hybrid computing nodes. This weakness can be particularly limiting when tackling many-query ...
Abstract This paper investigates a reduced order model for the angular discretisation of the radiative transfer equation (RTE) when considering non grey participating gases. The key idea is to use a global model for the gas radiative properties and to derive an angular reduced order model, based on the Proper Orthogonal Decomposition (POD) method, for each absorption coefficient class independently. Angular POD basis functions are extracted from high order SN reference solutions. A finite elemen...
