arXiv subjects

Oscar A. Marino

Publications and source records attributed to Oscar A. Marino.

7 recordsLinked to original sources

arXiv2026

Projection-Based Reconstruction for Achieving High-Order Accuracy from Low-Order DGSEM Simulations

High-order discontinuous Galerkin spectral element methods (DGSEM) based on Legendre-Gauss-Lobatto (LGL) nodes provide accurate and efficient discretizations for conservation laws. However, their cost, memory footprint, and time-step restrictions increase rapidly when the degree of the polynomial increases. This paper develops a corrected $\mathbb{P}_n\mathbb{P}_m$ ($c\mathbb{P}_n\mathbb{P}_m$) approach for DGSEM-LGL discretizations that aims to recover the accuracy of an $m^{th}$-order approximation while evolving only the degrees of freedom associated with an $n^{th}$-order representation, with $n<m$. The projected evolution of the high-order components is derived first at the continuous level and then in the fully discrete DGSEM-LGL setting. The discrete analysis shows that because LGL quadrature is not exact for the highest Legendre mode, a correction term for that mode is required to preserve the order of convergence. A compact projection-based reconstruction operator is then introduced to recover high-order components without solving the enlarged constrained least-squares systems used in standard reconstruction procedures. For sufficiently smooth solutions, the resulting $c\mathbb{P}_n\mathbb{P}_m$ scheme is shown to achieve the expected $m+1^{th}$ convergence order. Numerical experiments for one- and two-dimensional conservation laws, including Euler, viscous Burgers, and 2D decaying homogeneous isotropic turbulence, confirm theoretical convergence behavior and demonstrate competitive accuracy relative to computational cost, with particularly clear efficiency gains for viscous flows.

math.NA↗

arXiv2025

Accelerating high-order energy-stable discontinous Galerkin solver using auto-differentiation and neural networks

High-order Discontinuous Galerkin Spectral Element Methods (DGSEM) provide excellent accuracy for complex flow simulations, but their computational cost increases sharply with higher polynomial orders. %that provide very accurate solutions. To alleviate these limitations, this work presents a differentiable DG solver coupled with neural networks (NNs) that learn corrective forcing terms to correct low-order simulations and provide high-order accuracy. The solver's full differentiability enables gradient-based optimization and interactive (solver-in-the-loop) training, mitigating the data-shift problem typically encountered in static, offline learning. Two representative test cases are considered: the one-dimensional viscous Burgers' equation and two-dimensional decaying homogeneous isotropic turbulence (DHIT). The results demonstrate that interactive training with extended unrolling horizons substantially improves the precision and long-term stability of the simulation compared to static training. For the Burgers' equation, a $\mathbb{P}_2$ simulation corrected using a NN-correction achieves the accuracy of a $\mathbb{P}_4$ solution with eight times reduction in computational cost. For the DHIT case, the NN-corrected low-order simulations successfully achieve high-order accuracy while reduce the error beyond the training interval. These results highlight the potential of differentiable solvers combined with neural networks as a robust and efficient framework for accelerating high-fidelity DG-based fluid simulations.

physics.flu-dyn↗

arXiv2025

Acoustic Propagation/Refraction Through Diffuse Interface Models

We present a novel approach for simulating acoustic (pressure) wave propagation across different media separated by a diffuse interface through the use of a weak compressibility formulation. Our method builds on our previous work on an entropy-stable discontinuous Galerkin spectral element method for the incompressible Navier-Stokes/Cahn-Hilliard system %\cite{manzanero2020entropyNSCH}% (Manzanero et al. (2020)), and incorporates a modified weak compressibility formulation that allows different sound speeds in each phase. We validate our method through numerical experiments, demonstrating spectral convergence for acoustic transmission and reflection coefficients in one dimension and for the angle defined by Snell's law in two dimensions. Special attention is given to quantifying the modeling errors introduced by the width of the diffuse interface. Our results show that the method successfully captures the behavior of acoustic waves across interfaces, allowing exponential convergence in transmitted waves. The transmitted angles in two dimensions are accurately captured for air-water conditions, up to the critical angle of $13^\circ$. In a final example, we show a three-dimensional wave transmission from air into water to demonstrate the potential of this methodology for addressing general multiphase acoustic problems. This work represents a step forward in modeling acoustic propagation in incompressible multiphase systems, with potential applications to marine aeroacoustics.

math.NA↗

arXiv2024

Reinforcement learning for anisotropic p-adaptation and error estimation in high-order solvers

We present a novel approach to automate and optimize anisotropic p-adaptation in high-order h/p solvers using Reinforcement Learning (RL). The dynamic RL adaptation uses the evolving solution to adjust the high-order polynomials. We develop an offline training approach, decoupled from the main solver, which shows minimal overcost when performing simulations. In addition, we derive an inexpensive RL-based error estimation approach that enables the quantification of local discretization errors. The proposed methodology is agnostic to both the computational mesh and the partial differential equation to be solved. The application of RL to mesh adaptation offers several benefits. It enables automated and adaptive mesh refinement, reducing the need for manual intervention. It optimizes computational resources by dynamically allocating high-order polynomials where necessary and minimizing refinement in stable regions. This leads to computational cost savings while maintaining the accuracy of the solution. Furthermore, RL allows for the exploration of unconventional mesh adaptations, potentially enhancing the accuracy and robustness of simulations. This work extends our original research, offering a more robust, reproducible, and generalizable approach applicable to complex three-dimensional problems. We provide validation for laminar and turbulent cases: circular cylinders, Taylor Green Vortex and a 10MW wind turbine to illustrate the flexibility of the proposed approach.

physics.flu-dyn↗

arXiv2024

Deep Reinforcement Learning for Multi-Objective Optimization: Enhancing Wind Turbine Energy Generation while Mitigating Noise Emissions

We develop a torque-pitch control framework using deep reinforcement learning for wind turbines to optimize the generation of wind turbine energy while minimizing operational noise. We employ a double deep Q-learning, coupled to a blade element momentum solver, to enable precise control over wind turbine parameters. In addition to the blade element momentum, we use the wind turbine acoustic model of Brooks Pope and Marcolini. Through training with simple winds, the agent learns optimal control policies that allow efficient control for complex turbulent winds. Our experiments demonstrate that the reinforcement learning is able to find optima at the Pareto front, when maximizing energy while minimizing noise. In addition, the adaptability of the reinforcement learning agent to changing turbulent wind conditions, underscores its efficacy for real-world applications. We validate the methodology using a SWT2.3-93 wind turbine with a rated power of 2.3 MW. We compare the reinforcement learning control to classic controls to show that they are comparable when not taking into account noise emissions. When including a maximum limit of 45 dB to the noise produced (100 meters downwind of the turbine), the extracted yearly energy decreases by 22%. The methodology is flexible and allows for easy tuning of the objectives and constraints through the reward definitions, resulting in a flexible multi-objective optimization framework for wind turbine control. Overall, our findings highlight the potential of RL-based control strategies to improve wind turbine efficiency while mitigating noise pollution, thus advancing sustainable energy generation technologies

eess.SY↗

arXiv2024

Modelling Wind Turbines via Actuator Lines in High-Order h/p Solvers

This paper compares two actuator line methodologies for modelling wind turbines employing high-order h/p solvers and large-eddy simulations. The methods combine the accuracy of high-order solvers (in this work the maximum order is 6) with the computational efficiency of actuator lines to capture the aerodynamic effects of wind turbine blades. Comparisons with experiments validate the actuator line methodologies. We explore the effects of the polynomial order and the smoothing parameter associated with the Gaussian regularization function, and use them to blend the actuator line forcing in the high-order computational mesh, to show that both parameters influence the distribution of forces along the blades and the turbine wake. The greatest impact is obtained when the polynomial order is increased, allowing one to better capture the physics without requiring new meshes. When comparing the actuator line methodologies, we show the advantages of performing weighted sums, over element averages, to compute the blade velocities and forces in high-order solvers. For low-order simulations (low polynomial orders), both methods provide similar results, but as the polynomial order is increased, the weighted sum method shows smoother thrust/torque distributions and better wake resolution. Furthermore, cell averaging introduces nonphysical oscillations when increasing the polynomial order beyond 3 (4th order accuracy).

physics.flu-dyn↗

arXiv2022

Jump penalty stabilisation techniques for under-resolved turbulence in discontinuous Galerkin schemes

Jump penalty stabilisation techniques have been recently proposed for continuous and discontinuous high order Galerkin schemes [1,2,3]. The stabilisation relies on the gradient or solution discontinuity at element interfaces to incorporate localised numerical diffusion in the numerical scheme. This diffusion acts as an implicit subgrid model and stablises under-resolved turbulent simulations. This paper investigates the effect of jump penalty stabilisation methods (penalising gradient or solution) for stabilisation and improvement of high-order discontinuous Galerkin schemes in turbulent regime. We analyse these schemes using an eigensolution analysis, a 1D non-linear Burgers equation (mimicking a turbulent cascade) and 3D turbulent Navier-Stokes simulations (Taylor-Green Vortex problem). We show that the two jump penalty stabilisation techniques can stabilise under-resolved simulations thanks to the improved dispersion-dissipation characteristics (when compared to non-penalised schemes) and provide accurate results for turbulent flows. The numerical results indicate that the proposed jump penalty stabilise under-resolved simulations and improve the simulations, when compared to the original unpenalised scheme and to classic explicit subgrid models (Smagorisnky and Vreman).

physics.flu-dyn↗