arXiv subjects

Andrés Mateo-Gabín

Publications and source records attributed to Andrés Mateo-Gabín.

5 recordsLinked to original sources

arXiv2024

Generative Aerodynamic Design with Diffusion Probabilistic Models

The optimization of geometries for aerodynamic design often relies on a large number of expensive simulations to evaluate and iteratively improve the geometries. It is possible to reduce the number of simulations by providing a starting geometry that has properties close to the desired requirements, often in terms of lift and drag, aerodynamic moments and surface areas. We show that generative models have the potential to provide such starting geometries by generalizing geometries over a large dataset of simulations. In particular, we leverage diffusion probabilistic models trained on XFOIL simulations to synthesize two-dimensional airfoil geometries conditioned on given aerodynamic features and constraints. The airfoils are parameterized with Bernstein polynomials, ensuring smoothness of the generated designs. We show that the models are able to generate diverse candidate designs for identical requirements and constraints, effectively exploring the design space to provide multiple starting points to optimization procedures. However, the quality of the candidate designs depends on the distribution of the simulated designs in the dataset. Importantly, the geometries in this dataset must satisfy other requirements and constraints that are not used in conditioning of the diffusion model, to ensure that the generated geometries are physical.

cs.CE↗

arXiv2024

Accelerating high order discontinuous Galerkin solvers through a clustering-based viscous/turbulent-inviscid domain decomposition

We explore the unsupervised clustering technique introduced in [25] to identify viscous/turbulent from inviscid regions in incompressible flows. The separation of regions allows solving the Navier-Stokes equations including Large Eddy Simulation closure models only in the viscous/turbulent ones, while solving the Euler equations in the remaining of the computational domain. By solving different sets of equations, the computational cost is significantly reduced. This coupling strategy is implemented within a discontinuous Galerkin numerical framework, which allows discontinuous solutions (i.e., different set of equations) in neighbouring elements that interact through numerical fluxes. The proposed strategy maintains the same accuracy at lower cost, when compared to solving the full Navier-Stokes equations throughout the entire domain. Validation of this approach is conducted across diverse flow regimes, spanning from unsteady laminar flows to unsteady turbulent flows, including an airfoil section at Reynolds numbers Re = 103 and 104 and large angles of attack, and the flow past a wind turbine, modelled using actuator lines. The computational cost is reduced by 25% and 29% for the unsteady turbulent flow around an airfoil section and the flow past the wind turbine, respectively. In addition, to further accelerate the simulations, we combine the proposed decoupling with local P -adaptation, as proposed in [ 30]. When doing so, we reduce the computational cost by 41% and 45% for the flow around the airfoil section and the flow past the wind turbine, respectively

physics.flu-dyn↗

arXiv2023

An unsupervised machine-learning-based shock sensor for high-order supersonic flow solvers

We present a novel unsupervised machine-learning sock sensor based on Gaussian Mixture Models (GMMs). The proposed GMM sensor demonstrates remarkable accuracy in detecting shocks and is robust across diverse test cases with significantly less parameter tuning than other options. We compare the GMM-based sensor with state-of-the-art alternatives. All methods are integrated into a high-order compressible discontinuous Galerkin solver, where two stabilization approaches are coupled to the sensor to provide examples of possible applications. The Sedov blast and double Mach reflection cases demonstrate that our proposed sensor can enhance hybrid sub-cell flux-differencing formulations by providing accurate information of the nodes that require low-order blending. Besides, supersonic test cases including high Reynolds numbers showcase the sensor performance when used to introduce entropy-stable artificial viscosity to capture shocks, demonstrating the same effectiveness as fine-tuned state-of-the-art sensors. The adaptive nature and ability to function without extensive training datasets make this GMM-based sensor suitable for complex geometries and varied flow configurations. Our study reveals the potential of unsupervised machine-learning methods, exemplified by this GMM sensor, to improve the robustness and efficiency of advanced CFD codes.

cs.LG↗

arXiv2023

A flux-differencing formulation with Gauss nodes

In this work, we propose an extension of telescopic derivative operators for the DGSEM with Gauss nodes, and we prove that this formulation is equivalent to its usual matrix counterpart. Among other possible applications, this allows extending the stabilization methods already developed for Gauss-Lobatto nodes to Gauss nodes, also ensuring properties such as entropy stability while retaining their improved accuracy.

math.NA↗

arXiv2022

An entropy stable spectral vanishing viscosity for discontinuous Galerkin schemes: application to shock capturing and LES models

We present a stable spectral vanishing viscosity for discontinuous Galerkin schemes, with applications to turbulent and supersonic flows. The idea behind the SVV is to spatially filter the dissipative fluxes, such that it concentrates in higher wavenumbers, where the flow is typically under-resolved, leaving low wavenumbers dissipation-free. Moreover, we derive a stable approximation of the Guermond-Popov fluxes with the Bassi-Rebay 1 scheme, used to introduce density regularization in shock capturing simulations. This filtering uses a Cholesky decomposition of the fluxes that ensures the entropy stability of the scheme, which also includes a stable approximation of boundary conditions for adiabatic walls. For turbulent flows, we test the method with the three-dimensional Taylor-Green vortex and show that energy is correctly dissipated, and the scheme is stable when a kinetic energy preserving split-form is used in combination with a low dissipation Riemann solver. Finally, we test the shock capturing capabilities of our method with the Shu-Osher and the supersonic forward facing step cases, obtaining good results without spurious oscillations even with coarse meshes.

math.NA↗