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Multi-Fidelity Approaches for Modeling, Simulation and Validation in Fluid Dynamics

A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Fluid Science and Technology".

Deadline for manuscript submissions: 20 November 2025 | Viewed by 428

Special Issue Editors


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Guest Editor
Dipartimento di Scienze e Tecnologie Aerospaziali, Politecnico di Milano, Via La Masa 34, 20156 Milan, Italy
Interests: aerodynamics; computational fluid dynamics; fluid mechanics; wind tunnel modeling; wind tunnel testing; aeroelasticity; multibody system dynamics

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Guest Editor
Department of Aerospace Science and Technology, Politecnico di Milano, 20156 Milano, Italy
Interests: aerodynamics; rotorcraft; wind tunnel tests; computational fluid dynamics; flow control; fluid structure interactions; wind turbine; eVTOLs
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Special Issue Information

Dear Colleagues,

This Special Issue highlights the use of multi-fidelity approaches in the modeling, simulation, and validation of fluid dynamics problems. It encourages studies that combine high-fidelity simulations with reduced- or mid-fidelity models, particularly those supported by experimental validation. Contributions may address model fusion, surrogate modeling, uncertainty quantification, and digital twin development. We also welcome innovative methodologies that leverage artificial intelligence and machine learning for reduced-order modeling, data assimilation, or hybrid physics-informed approaches. A special focus will be given to complex, multi-scale problems involving strong interactions such as fluid–structure interaction, aerodynamic interference effects, and unsteady flow phenomena, where multi-fidelity strategies can play a key role in balancing accuracy and computational efficiency. Both methodological innovations and application-driven research across different fluid dynamic contexts are welcome, including aerospace, energy, and environmental flows.

Dr. Alberto Savino
Dr. Alex Zanotti
Guest Editors

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Keywords

  • multi-fidelity
  • mid-fidelity
  • fluid dynamics
  • simulation
  • model validation
  • wind tunnel
  • surrogate modeling
  • digital twin
  • reduced-order models
  • experimental correlation
  • uncertainty quantification

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Published Papers (1 paper)

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Research

24 pages, 3795 KB  
Article
An Improved Galerkin Framework for Solving Unsteady High-Reynolds Navier–Stokes Equations
by Jinlin Tang and Qiang Ma
Appl. Sci. 2025, 15(15), 8606; https://doi.org/10.3390/app15158606 - 3 Aug 2025
Viewed by 285
Abstract
The numerical simulation of unsteady, high-Reynolds-number incompressible flows governed by the Navier–Stokes (NS) equations presents significant challenges in computational fluid dynamics, primarily concerning numerical stability and computational efficiency. Standard Galerkin finite element methods often suffer from non-physical oscillations in convection-dominated regimes, while the [...] Read more.
The numerical simulation of unsteady, high-Reynolds-number incompressible flows governed by the Navier–Stokes (NS) equations presents significant challenges in computational fluid dynamics, primarily concerning numerical stability and computational efficiency. Standard Galerkin finite element methods often suffer from non-physical oscillations in convection-dominated regimes, while the multiscale nature of these flows demands prohibitively high computational resources for uniformly refined meshes. This paper proposes an improved Galerkin framework that synergistically integrates a Variational Multiscale Stabilization (VMS) method with an adaptive mesh refinement (AMR) strategy to overcome these dual challenges. Based on the Ritz–Galerkin formulation with the stable Taylor–Hood (P2P1) element, a VMS term is introduced, derived from a generalized θ-scheme. This explicitly constructs a subgrid-scale model to effectively suppress numerical oscillations without introducing excessive artificial diffusion. To enhance computational efficiency, a novel a posteriori error estimator is developed based on dual residuals. This estimator provides the robust and accurate localization of numerical errors by dynamically weighting the momentum and continuity residuals within each element, as well as the flux jumps across element boundaries. This error indicator guides an AMR algorithm that combines longest-edge bisection with local Delaunay re-triangulation, ensuring optimal mesh adaptation to complex flow features such as boundary layers and vortices. Furthermore, the stability of the Taylor–Hood element, essential for stable velocity–pressure coupling, is preserved within this integrated framework. Numerical experiments are presented to verify the effectiveness of the proposed method, demonstrating its ability to achieve stable, high-fidelity solutions on adaptively refined grids with a substantial reduction in computational cost. Full article
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