Tommaso Benacchio

Tommaso Benacchio, Rupert Klein

We introduce a second-order numerical scheme for compressible atmospheric motions at small to planetary scales. The collocated finite volume method treats the advection of mass, momentum, and mass-weighted potential temperature in conservation form while relying on Exner pressure for the pressure gradient term. It discretises the rotating compressible equations by evolving full variables rather than perturbations around a background state, and operates with time steps constrained by the advection speed only. Perturbation variables are only used as auxiliary quantities in the formulation of the elliptic problem. Borrowing ideas on forward-in-time differencing, the algorithm reframes the authors' previously proposed schemes into a sequence of implicit midpoint, advection, and implicit trapezoidal steps that allows for a time integration unconstrained by the internal gravity wave speed. Compared with existing approaches, results on a range of benchmarks of nonhydrostatic- and hydrostatic-scale dynamics are competitive. The test suite includes a new planetary-scale inertia-gravity wave test highlighting the properties of the scheme and its large time step capabilities. In the hydrostatic-scale cases the model is run in pseudo-incompressible and hydrostatic mode with simple switching within a uniform discretization framework. The differences with the compressible runs return expected relative magnitudes. By providing seamless access to soundproof and hydrostatic dynamics, the developments represent a necessary step towards an all-scale blended multimodel solver.

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.

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.