Computational efficiency and precision pose a classic contradiction in aerodynamic shape optimization. To address this challenge, this study introduces an effective optimization framework based on multi-fidelity fully connected neural network (MFFCN). The framework utilizes transfer learning (TL) to train a multi-fidelity surrogate model that establishes direct mappings between geometric configuration parameters and aerodynamic performance by adaptively capturing linear or nonlinear relationships concealed between high-fidelity (HF) and low-fidelity (LF) information. The HF and LF data are derived from fine and coarse grids, respectively, evaluated using the same computational fluid dynamics (CFD) model. The MFFCN-TL framework is applied to optimize the National Advisory Committee for Aeronautics 0012 (NACA0012) airfoil (12 design variables) and the Office National d'Études et de Recherches Aérospatiales M6 (ONERA M6) wing (50 design variables). Simulation results demonstrate that the NACA0012 airfoil achieves a 69.47% enhancement in lift–drag ratio in 1.069 s, compared to a 12.76% gain over 24.8 h in single-fidelity CFD-based optimization. The ONERA M6 wing achieves a 24.66% reduction in drag coefficient in 694 ms compared to 18.37% over 237.3 h in the CFD model. Statistical results show that the MFFCN-TL framework can reduce optimization cost by more than 90% compared to the single-fidelity CFD-based model. These findings suggest that the MFFCN-TL framework significantly enhances optimization efficiency and provides superior feasible solutions over single-fidelity methods.

The Richtmyer–Meshkov instability (RMI) is caused by an incident planar shock wave impinging on the heavy-gas-density interface. We have numerically investigated the RMI controlled by different transverse magnetic-field strengths based on the ideal compressible magnetohydrodynamics (MHD) equations. The MHD equations are solved by the corner transport upwind + constrained transport algorithm, which guarantees a divergence-free constraint on the magnetic field. We discuss the flow characteristics and shock patterns in both classical hydrodynamic and MHD situations and verify our conclusions by comparing the experimental results with the numerical results. The results show that the magnetic field modifies the pressure-gradient distribution, and the baroclinic vorticity splits and attaches to the MHD shock waves. In addition, the results indicate that the interaction of shock wave and density interface changes the distribution of magnetic-field energy and distorts the magnetic induction line in the region of magnetic-field energy accumulation. The distortion of the magnetic induction lines alters the magnetic field gradient and creates a magnetic tension that produces a torque opposing that generated by the shear force on the vorticity layer, so the Kelvin–Helmholtz instability is effectively suppressed and no Kelvin–Helmholtz vortex appears on the vorticity layer. The result is that the interface instability is suppressed.

To enhance the power gain of vortex-induced vibration of a circular cylinder, the active control method of pulsed blowing jets located at θ = 90° is utilized to intensify its oscillation with the two-dimensional simulation of Reynolds-averaged Navier–Stokes at 2.0 × 104 ≤ Re ≤ 9.6 × 104. Different from traditional continuous jets, the blowing jets used in this paper start once the cylinder moves to the upper limited position and last for a certain duration. Based on the combination of nine momentum coefficients and four pulse durations of the jets, the oscillation responses of the cylinder at a series of reduced velocities are calculated and distinct responses are observed in three branches. In the initial branch (U* ≤ 4.27), no matter what the values of Cμ and n are, the vortex patterns keep 2S accompanied by the amplitude ratios vibrating around the benchmarks. In the fore part of the upper branch (4.27 < U* ≤ 6.17), as Cμ ≤ 0.1005, the control effect is similar to that at U* ≤ 4.27; as Cμ > 0.1005, both slight enhancement and suppression in amplitude ratios are observed, as well as the small values of power gain ratios. In the rear part of the upper branch and lower branch (U* > 6.17), the enlarged disturbance of the jets to wake results in enhanced amplitude ratios for most cases. Galloping is observed at n = 1/4 and 1/2 with a maximum amplitude ratio 13 times the benchmark, except for some suppressed cases at Cμ > 0.1005, n = 1/16, and 1/8. Though large amplitude ratios are achieved, considering more energy consumed as Cμ increases, the better control strategy with η ranging from 5.45% to 19.78% falls in U* > 6.17 and Cμ < 0.1005.