arXiv subjects

Nirav Vasant Shah

Publications and source records attributed to Nirav Vasant Shah.

3 recordsLinked to original sources

arXiv2022

Thermomechanical modelling for industrial applications

In this work we briefly present a thermomechanical model that could serve as starting point for industrial applications. We address the non-linearity due to temperature dependence of material properties and heterogeneity due to presence of different materials. Finally a numerical example related to the simplified geometry of blast furnace hearth walls is shown with the aim of assessing the feasibility of the modelling framework. Keywords: nonlinear thermomechanical model, finite element method, heterogeneous material, blast furnace.

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arXiv2022

Finite element based model order reduction for parametrized one-way coupled steady state linear thermomechanical problems

This contribution focuses on the development of Model Order Reduction (MOR) for one-way coupled steady state linear thermomechanical problems in a finite element setting. We apply Proper Orthogonal Decomposition (POD) for the computation of reduced basis space. On the other hand, for the evaluation of the modal coefficients, we use two different methodologies: the one based on the Galerkin projection (G) and the other one based on Artificial Neural Network (ANN). We aim at comparing POD-G and POD-ANN in terms of relevant features including errors and computational efficiency. In this context, both physical and geometrical parametrization are considered. We also carry out a validation of the Full Order Model (FOM) based on customized benchmarks in order to provide a complete computational pipeline. The framework proposed is applied to a relevant industrial problem related to the investigation of thermomechanical phenomena arising in blast furnace hearth walls. Keywords: Thermomechanical problems, Finite element method, Proper orthogonal decomposition, Galerkin projection, Artificial neural network, Geometric and physical parametrization, Blast furnace.

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arXiv2020

Discontinuous Galerkin Model Order Reduction of Geometrically Parametrized Stokes Equation

The present work focuses on the geometric parametrization and the reduced order modeling of the Stokes equation. We discuss the concept of a parametrized geometry and its application within a reduced order modeling technique. The full order model is based on the discontinuous Galerkin method with an interior penalty formulation. We introduce the broken Sobolev spaces as well as the weak formulation required for an affine parameter dependency. The operators are transformed from a fixed domain to a parameter dependent domain using the affine parameter dependency. The proper orthogonal decomposition is used to obtain the basis of functions of the reduced order model. By using the Galerkin projection the linear system is projected onto the reduced space. During this process, the offline-online decomposition is used to separate parameter dependent operations from parameter independent operations. Finally this technique is applied to an obstacle test problem.The numerical outcomes presented include experimental error analysis, eigenvalue decay and measurement of online simulation time. Keywords: Discontinuous Galerkin method, Stokes flow, Geometric parametrization, Proper orthogonal decomposition

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