arXiv subjects

Diederik Beckers

Publications and source records attributed to Diederik Beckers.

4 recordsLinked to original sources

arXiv2026

Beyond first-order accuracy in continuous-forcing immersed boundary methods, and their well-conditioned projection-based solution

We introduce a refined immersed boundary (IB) methodology that is better-than-first-order accurate in practice, while preserving key properties of "continuous-forcing" IB approaches that retain a singular source term in the governing equations. Our method leverages a smoothed indicator (Heaviside) function, following ideas from multiphase flow and immersed layers formulations, to recast the IB solution as a composite of distinct interior and exterior fields. We demonstrate that, when cast through this composite-solution lens, prior continuous-forcing IB methods can be seen as neglecting terms in the governing and constraint equations that restrict the solution to first-order accuracy. We incorporate these terms to systematically improve accuracy without the need for heuristic corrections. In canonical Poisson problems, we empirically demonstrate second-order convergence, and in incompressible Navier-Stokes simulations the method achieves slightly sub-second-order performance. While our present study focuses on these cases, the framework suggests a path towards second-order accuracy or higher, with further extensions. This perspective reframes accuracy limitations typically attributed to IB schemes. Although continuous-forcing IB methods are often reported to be only first-order accurate, we show that neither smoothing nor interface interpolation inherently restricts attainable order. Moreover, we naturally incorporate this higher-order formulation into a projection-based solution process. The resulting algorithm simultaneously mitigates the spurious surface stresses produced by ill-conditioned linear systems and reduces sensitivity to geometric resolution, addressing both conditioning and accuracy concerns within a unified approach.

math.NA↗

arXiv2025

Model-Based Reinforcement Learning for Control of Strongly-Disturbed Unsteady Aerodynamic Flows

The intrinsic high dimension of fluid dynamics is an inherent challenge to control of aerodynamic flows, and this is further complicated by a flow's nonlinear response to strong disturbances. Deep reinforcement learning, which takes advantage of the exploratory aspects of reinforcement learning (RL) and the rich nonlinearity of a deep neural network, provides a promising approach to discover feasible control strategies. However, the typical model-free approach to reinforcement learning requires a significant amount of interaction between the flow environment and the RL agent during training, and this high training cost impedes its development and application. In this work, we propose a model-based reinforcement learning (MBRL) approach by incorporating a novel reduced-order model as a surrogate for the full environment. The model consists of a physics-augmented autoencoder, which compresses high-dimensional CFD flow field snaphsots into a three-dimensional latent space, and a latent dynamics model that is trained to accurately predict the long-time dynamics of trajectories in the latent space in response to action sequences. The accuracy and robustness of the model are demonstrated in the scenario of a pitching airfoil within a highly disturbed environment. Additionally, an application to a vertical-axis wind turbine in a disturbance-free environment is discussed in the Appendix Based on the model trained in the pitching airfoil problem, we realize an MBRL strategy to mitigate lift variation during gust-airfoil encounters. We demonstrate that the policy learned in the reduced-order environment translates to an effective control strategy in the full CFD environment.

physics.flu-dyn↗

arXiv2024

Deep reinforcement learning of airfoil pitch control in a highly disturbed environment using partial observations

This study explores the application of deep reinforcement learning (RL) to design an airfoil pitch controller capable of minimizing lift variations in randomly disturbed flows. The controller, treated as an agent in a partially observable Markov decision process, receives non-Markovian observations from the environment, simulating practical constraints where flow information is limited to force and pressure sensors. Deep RL, particularly the TD3 algorithm, is used to approximate an optimal control policy under such conditions. Testing is conducted for a flat plate airfoil in two environments: a classical unsteady environment with vertical acceleration disturbances (i.e., a Wagner setup) and a viscous flow model with pulsed point force disturbances. In both cases, augmenting observations of the lift, pitch angle, and angular velocity with extra wake information (e.g., from pressure sensors) and retaining memory of past observations enhances RL control performance. Results demonstrate the capability of RL control to match or exceed standard linear controllers in minimizing lift variations. Special attention is given to the choice of training data and the generalization to unseen disturbances.

physics.flu-dyn↗

arXiv2022

Planar potential flow on Cartesian grids

Potential flow has many applications, including the modelling of unsteady flows in aerodynamics. For these models to work efficiently, it is best to avoid Biot-Savart interactions. This work presents a grid-based treatment of potential flows in two dimensions and its use in a vortex model for simulating unsteady aerodynamic flows. For flows consisting of vortex elements, the treatment follows the vortex-in-cell approach and solves the streamfunction-vorticity Poisson equation on a Cartesian grid after transferring the circulation from the vortices onto the grid. For sources and sinks, an analogous approach can be followed using the scalar potential. The combined velocity field due to vortices, sinks, and sources can then be obtained using the Helmholtz decomposition. In this work, we use several key tools that ensure the approach works on arbitrary geometries, with and without sharp edges. Firstly, the immersed boundary projection method is used to account for bodies in the flow and the resulting body-forcing Lagrange multiplier is identified as the bound vortex sheet strength. Secondly, sharp edges are treated by decomposing the vortex sheet strength into a singular and smooth part. To enforce the Kutta condition, the smooth part can then be constrained to remove the singularity introduced by the sharp edge. These constraints and the Poisson equation are formulated as a saddle-point system and solved using the Schur complement method. The lattice Green's function is used to efficiently solve the discrete Poisson equation with unbounded boundary conditions. The method and its accuracy are demonstrated for several problems.

physics.flu-dyn↗