Lucia Parussini

Fictitious Domain approach with hp-finite element approximation for incompressible fluid flow

We consider the application of Fictitious Domain approach combined with least squares spectral elements for the numerical solution of fluid dynamic incompressible equations. Fictitious Domain methods allow problems formulated on a complicated shaped domain ? to be solved on a simpler domain ? containing ? . Least Squares Spectral Element Method has been used to develop the discrete model, as this scheme combines the generality of finite element methods with the accuracy of spectral methods. Moreover the least squares methods have theoretical and computational advantages in the algorithmic design and implementation. This paper presents the formulation and validation of the Fictitious Domain Least Squares Spectral Element approach for the steady incompressible Navier-Stokes equations. The convergence of the approximated solution is verified solving two-dimensional benchmark problems, demonstrating the predictive capability of the proposed formulation.

Fictitious Domain Approach Via Lagrange Multipliers with Least Squares Spectral Element Method

We consider the application of Fictitious Domain approach combined with Least Squares Spectral Elements for the numerical solution of partial differential equations. Fictitious Domain methods allow problems formulated on a complicated shaped domain Ω to be solved on a simpler domain Π containing Ω. Least Squares Spectral Element Method has been used to develop the discrete model, as this scheme combines the generality of finite element methods with the accuracy of spectral methods. Moreover the least squares methods have theoretical and computational advantages in the algorithmic design and implementation. This paper presents the formulation and validation of the Fictitious Domain/Least Squares Spectral Element approach. The convergence of the relative energy norm η is verified computing smooth solutions to two-dimensional first and second-order differential equations, demonstrating the predictive capability of the proposed formulation.

Sensitivity analysis of dense gas flow simulations to thermodynamic uncertainties

The paper investigates the sensitivity of numerically computed flow fields to uncertainties in thermodynamic models for complex organic fluids. Precisely, the focus is on the propagation of uncertainties introduced by some popular thermodynamic models to the numerical results of a computational fluid dynamics solver for flows of molecularly complex gases close to saturation conditions (dense gas flows). A tensorial-expanded chaos collocation method is used to perform both a priori and a posteriori tests on the output data generated by thermodynamic models for dense gases with uncertain input parameters. A priori tests check the sensitivity of each equation of state to uncertain input data via some reference thermodynamic outputs, such as the saturation curve and the critical isotherm. A posteriori tests investigate how the uncertainties propagate to the computed field properties and aerodynamic coefficients for a flow around an airfoil placed into a transonic dense gas stream.

Multi-fidelity Gaussian process regression for prediction of random fields

We propose a new multi-fidelity Gaussian process regression (GPR) approach for prediction of random fields based on observations of surrogate models or hierarchies of surrogate models. Our method builds upon recent work on recursive Bayesian techniques, in particular recursive co-kriging, and extends it to vector-valued fields and various types of covariances, including separable and non-separable ones. The framework we propose is general and can be used to perform uncertainty propagation and quantification in model-based simulations, multi-fidelity data fusion, and surrogate-based optimization. We demonstrate the effectiveness of the proposed recursive GPR techniques through various examples. Specifically, we study the stochastic Burgers equation and the stochastic OberbeckBoussinesq equations describing natural convection within a square enclosure. In both cases we find that the standard deviation of the Gaussian predictors as well as the absolute errors relative to benchmark stochastic solutions are very small, suggesting that the proposed multi-fidelity GPR approaches can yield highly accurate results.

TSI metamodels-based multi-objective robust optimization

Purpose – This paper aims to deal with an efficient strategy for robust optimization when a large number of uncertainties are taken into account. Design/methodology/approach – ANOVA analysis is used in order to perform a variance-based decomposition and to reduce stochastic dimension based on an appropriate criterion. A massive use of metamodels allows reconstructing response surfaces for sensitivity indexes in the design variables plan. To validate the proposed approach, a simplified configuration, an inverse problem on a 1D nozzle flow, is solved and the performances compared to an exact Monte Carlo reference solution. Then, the same approach is applied to the robust optimization of a turbine cascade for thermodynamically complex flows. Findings – First, when the stochastic dimension is reduced, the error on the variance between the reduced and the complete problem was found to be roughly estimated by the quantity (1−T¯ TSI )×100, where T¯ TSI is the summation of TSI concerning the variables respecting ...

Quantification of thermodynamic uncertainties in real gas flows

A tensorial-expanded chaos collocation method is developed to take into account uncertainties on thermodynamic properties of complex organic substances. Precisely, we analyse the effect of uncertainties introduced by several thermodynamic models on the numerical results provided by a computational fluid dynamics solver for flows of molecularly complex gases close to saturation condition (dense gas flows). The tensorial-expanded chaos collocation method is used to perform both a priori and a posteriori tests on the output data generated by three popular thermodynamic models for dense gases with uncertain input parameters. A priori tests check the sensitivity of each equation of state to uncertain input data via some reference thermodynamic outputs, such as the saturation curve and the critical isotherm. A posteriori tests investigate how uncertainties propagate to the computed field properties and aerodynamic coefficients for a flow around an airfoil placed into a transonic dense gas stream.

Distributed Lagrange Multiplier Functions for Fictitious Domain Method with Spectral/hp Element Discretization

A fictitious domain approach for the solution of second-order linear differential problems is proposed; spectral/hp elements have been used for the discretization of the domain. The peculiarity of our approach is that the Lagrange multipliers are particular distributed functions, instead of classical

Prediction of geometric uncertainty effects on Fluid Dynamics by Polynomial Chaos and Fictitious Domain method

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