A variational multiscale sugbrid model including an explicit filtering is studied in the framework of an equal-order finite element formulation for solving compressible Navier-Stokes equations in entropy variables. The filtering is here achieved by considering embedded piecewise polynomials, whose implementation is made easier with the use of isoparametric and symmetric elements. A hybrid formulation combining a detached-eddy simulation near the walls is also proposed to be able to tackle realistic industrial configurations. The numerical developments are assessed with the Taylor-Green vortex, by comparison with a reference result provided by direct numerical simulation. Finally, new findings are reported with the direct noise computation of the LEISA-2 configuration, a three-element high-lift airfoil as part of the benchmark for airframe noise computation.

Flow steadiness is often overpredicted near the wall by Detached-Eddy Simulation (DES). This problem is here addressed with a Streamline Upwind Petrov-Galerkin (SUPG) finite element method. An hybrid Variational MultiScale (VMS) model is implemented to enhance the Large-Eddy Simulation (LES) mode of DES computation. An explicit filtering method is developed in order to compute the filtered field involved in a VMS model. Furthermore, these VMS fluctuations are also used to improve unsteadiness in the area close to the walls. This approach is assessed with the Taylor-Green vortices and finally applied to the LEISA II configuration.

In this work, we propose a built-in Deep Learning Physics Optimization (DLPO) framework to set up a shape optimization study of the Duisburg Test Case (DTC) container vessel. We present two different applications: (1) sensitivity analysis to detect the most promising generic basis hull shapes, and (2) multi-objective optimization to quantify the trade-off between optimal hull forms. DLPO framework allows for the evaluation of design iterations automatically in an end-to-end manner. We achieved these results by coupling Extrality's Deep Learning Physics (DLP) model to a CAD engine and an optimizer. Our proposed DLP model is trained on full 3D volume data coming from RANS simulations, and it can provide accurate and high-quality 3D flow predictions in real-time, which makes it a good evaluator to perform optimization of new container vessel designs w.r.t the hydrodynamic efficiency. In particular, it is able to recover the forces acting on the vessel by integration on the hull surface with a mean relative error of 3.84% ± 2.179% on the total resistance. Each iteration takes only 20 seconds, thus leading to a drastic saving of time and engineering efforts, while delivering valuable insight into the performance of the vessel, including RANS-like detailed flow information. We conclude that DLPO framework is a promising tool to accelerate the ship design process and lead to more efficient ships with better hydrodynamic performance.

Recent progress in Geometric Deep Learning (GDL) has shown its potential to provide powerful data-driven models. This gives momentum to explore new methods for learning physical systems governed by Partial Differential Equations (PDEs) from Graph-Mesh data. However, despite the efforts and recent achievements, several research directions remain unexplored and progress is still far from satisfying the physical requirements of real-world phenomena. One of the major impediments is the absence of benchmarking datasets and common physics evaluation protocols. In this paper, we propose a 2-D graph-mesh dataset to study the airflow over airfoils at high Reynolds regime (from 10 6 and beyond). We also introduce metrics on the stress forces over the airfoil in order to evaluate GDL models on important physical quantities. Moreover, we provide extensive GDL baselines.