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This paper aims to introduce physics-informed neural networks (PINN) applied to the two-dimensional steady-state laminar Navier–Stokes equations over a flat plate with roughness elements and specified local heating. The method bridges the gap between asymptotics theory and three-dimensional turbulent flow analyses, characterized by high costs in analysis setups and prohibitive computing times. The results indicate the possibility of using surface heating or wavy surface to control the incoming flow field.

The understanding of the flow control mechanism is normally caused by the unsteady interactions between the aircraft structure and the turbulent flows as well as some studies have shown, surface roughness can significantly influence the fluid dynamics by inducing perturbations in the velocity profile.

The description of the boundary-layer flow, based upon a triple-deck structure, shows how a wavy surface and a local surface heating generate an interaction between the inviscid region and the viscous region near the flat plate.

To the best of the authors’ knowledge, the presented approach is especially original in relation to the innovative concept of PINN as a solver of the asymptotic triple-deck method applied to the viscous–inviscid boundary layer interaction.

Aircraft noise is dominant for residents near airports when planes fly at low altitudes such as during departure and landing. Flaps, wings, landing gear contribute significantly to the total sound emission. This paper aims to present a passive flow control (in the sense that there is no power input) to reduce the noise radiation induced by the flow over the cavity of the landing gear during take-off and landing.

The understanding of the noise source mechanism is normally caused by the unsteady interactions between the cavity surface and the turbulent flows as well as some studies that have shown tonal noise because of cavity resonances; this tonal noise is dependent on cavity geometry and incoming flow that lead us to use of a sinusoidal surface modification application upstream of a cavity as a passive acoustics control device in approach conditions.

It is demonstrated that the proposed surface waviness showed a potential reduction in cavity resonance and in the overall sound pressure level at the majority of the points investigated in the low Mach number. Furthermore, optimum sinusoidal amplitude and frequency were determined by the means of a two-dimensional computational fluid dynamics analysis for a cavity with a length to depth ratio of four.

The noise control by surface waviness has not implemented in real flight test yet, as all the tests are conducted in the credible numerical simulation.

The application of passive control method on the cavity requires a global aerodynamic study of the air frame is a matter of ongoing debate between aerodynamicists and acousticians. The latter is aimed at the reduction of the noise, whereas the former fears a corruption of flow conditions. To balance aerodynamic performance and acoustics, the use of the surface waviness in cavity leading edge is the most optimal solution.

The proposed leading-edge modification it has important theoretical basis and reference value for engineering application it can meet the demands of engineering practice. Particularly, to contribute to the reduce the aircraft noise adopted by the “European Visions 2020”.

The investigate cavity noise with and without surface waviness generation and propagation by using a hybrid approach, the computation of flow based on the large-eddy simulation method, is decoupled from the computation of sound, which can be performed during a post-processing based on Curle’s acoustic analogy as implemented in OpenFOAM.