Tommaso Benacchio

Letizia Bottani, Tommaso Benacchio, Giuseppe Orlando et al.

We present a high-order implicit-explicit discontinuous Galerkin (IMEX-DG) solver for the compressible Euler equations to account for rotational effects within a fully compressible atmospheric framework. Time integration follows a second-order additive Runge-Kutta scheme, treating stiff acoustic modes implicitly and advective terms explicitly. The solver is built on the deal.II finite element library, combining matrix-free operator evaluation, adaptive non-conforming meshes capabilities, and distributed-memory parallelism. Two alternative treatments of the rotational and gravitational source terms within the solution strategy, based on nonlinear fixed-point iterations, are introduced and compared in terms of accuracy, robustness, and computational efficiency. A discrete analysis of the rotational operator is also carried out in order to derive a formulation suitable for efficient matrix-free implementation and to avoid inconsistent naive discretisations. The proposed formulation is validated through convergence studies on rotating inertia-gravity wave benchmarks and further assessed in fully three-dimensional simulations of stratified flow over orography on both uniform and adaptive meshes. The numerical results show that the rotating IMEX-DG framework has the expected accuracy and stability properties while correctly capturing the asymmetry and wave structures induced by rotation in large-scale atmospheric flows.

T. Benacchio, L. Bonaventura

We consider spectral discretizations of hyperbolic problems on unbounded domains using Laguerre basis functions. Taking as model problem the scalar advection equation, we perform a comprehensive stability analysis that includes strong collocation formulations, nodal and modal weak formulations, with either inflow or outflow boundary conditions, using either Gauss - Laguerre or Gauss - Laguerre - Radau quadrature nodes and based on either scaled Laguerre functions or scaled Laguerre polynomials. We show that some of these combinations give rise to intrinsically unstable schemes, while the combination of scaled Laguerre functions with Gauss - Laguerre - Radau nodes appears to be stable for both strong and weak formulations. We then show how a modal discretization approach for hyperbolic systems on an unbounded domain can be naturally and seamlessly coupled to a discontinuous finite element discretization on a finite domain. Examples of one dimensional hyperbolic systems are solved with the proposed domain decomposition technique. The errors obtained with the proposed approach are found to be small, enabling the use of the coupled scheme for the simulation of Rayleigh damping layers in the semi-infinite part. Energy errors and reflection ratios of the scheme in absorbing wavetrains and single Gaussian signals show that a small number of nodes in the semi-infinite domain are sufficient to damp the waves. The theoretical insight and numerical results corroborate previous findings by the authors and establish the scaled Laguerre functions-based discretization as a flexible and efficient tool for absorbing layers as well as for the accurate simulation of waves in unbounded regions.

Damiano Paniccia, Francesco Aldo Tucci, Joel Guerrero et al.

Rotorcraft engines are highly complex, nonlinear thermodynamic systems that operate under varying environmental and flight conditions. Simulating their dynamics is crucial for design, fault diagnostics, and deterioration control phases, and requires robust and reliable control systems to estimate engine performance throughout flight envelope. However, the development of detailed physical models of the engine based on numerical simulations is a very challenging task due to the complex and entangled physics driving the engine. In this scenario, data-driven machine-learning techniques are of great interest to the aircraft engine community, due to their ability to describe nonlinear systems' dynamic behavior and enable online performance estimation, achieving excellent results with accuracy competitive with the state of the art. In this work, we explore different Neural Network architectures to model the turboshaft engine of Leonardo's AW189P4 prototype, aiming to predict the engine torque. The models are trained on an extensive database of real flight tests featuring a variety of operational maneuvers performed under different flight conditions, providing a comprehensive representation of the engine's performance. To complement the neural network approach, we apply Sparse Identification of Nonlinear Dynamics (SINDy) to derive a low-dimensional dynamical model from the available data, describing the relationship between fuel flow and engine torque. The resulting model showcases SINDy's capability to recover the actual physics underlying the engine dynamics and demonstrates its potential for investigating more complex aspects of the engine. The results prove that data-driven engine models can exploit a wider range of parameters than standard transfer function-based approaches, enabling the use of trained schemes to simulate nonlinear effects in different engines and helicopters.