Jun Liu

Morphing aircraft, which are capable of adaptively changing their configurations in response to mission requirements and flight environments to achieve improved aerodynamic performance, have become an important direction in aircraft design. Since the unsteady aerodynamic characteristics during continuous wing morphing differ from those in corresponding quasi-steady states, evaluating dynamic aerodynamic effects during morphing is important. In this study, a surface-based dynamic mesh approach was developed based on a spring-analogy method to simulate continuous wing morphing processes. The method employed a surface-driven mesh motion strategy, in which prescribed analytical motion of surface nodes was propagated into the volume mesh without relying on global interpolation procedures. By coupling this approach with a CFD solver, unsteady simulations of a continuously stretching wing were performed. Numerical examples showed consistent results between moving-mesh and fixed-mesh simulations. Further simulations under subsonic, transonic, and supersonic conditions allowed analysis of aerodynamic responses during continuous morphing. The proposed approach provides a numerical framework for unsteady aerodynamic simulations involving continuous surface deformation.

The Flux Vector Splitting (FVS) scheme tends to produce numerical transition zones and nonphysical oscillations when initialized with mathematical discontinuities. Although the Upwind Flux Scheme based on Characteristics (UFSC) can alleviate such errors, it still exhibits limitations in handling stationary contact discontinuities and high-Mach number shock waves. To overcome these issues, this paper proposes the Optimized-Contact UFSC (OC-UFSC), which achieves strict preservation of stationary contact discontinuities through an improved decoupling strategy. Furthermore, by incorporating a shock detector with the Van Leer scheme, a hybrid scheme OC-UFSC+V, is constructed to enhance stability under high-Mach number shocks. Comparative analyses against the FVS and Flux Difference Splitting (FDS) schemes in both one- and two-dimensional benchmark tests demonstrate that OC-UFSC+V resolves contact discontinuities sharply, expansion waves, and shock waves. Compared with the FVS scheme, it preserves the accuracy of linear and quadratic flows, matches the resolution of FDS schemes, and effectively avoids the common Carbuncle phenomenon in FDS. Overall, OC-UFSC+V exhibits superior resolution and stability.

In the cell-centered unstructured finite volume method for solving the Navier–Stokes equations, the viscous flux is discretized by applying Gauss's theorem, which converts the volume-integrated viscous flux into a surface integral over cell faces. In classical methods, the computation of viscous flux on a face requires both the basic variables and their gradients at the face center. The basic variables are reconstructed from cell-centered values, and the face-centered gradients are typically computed using the gradients from adjacent cell centers. However, when grid quality is poor, this gradient computation method, which strongly depends on the geometric relationship between neighboring cells, often leads to reduced gradient accuracy and numerical instability. To overcome this limitation, the present study proposes a face-averaged gradient method for viscous flux computation. In this method, cell-centered gradients are first interpolated to grid nodes using an inverse distance weighting scheme. The nodal gradients are then averaged back to the target face center through a second inverse distance weighting interpolation. This two-step process provides a more accurate gradient at the face center, which improves the stability of viscous flux calculations. Numerical simulations show that, compared to classical methods, the proposed approach significantly reduces sensitivity to grid quality, while maintaining high accuracy and convergence performance in complex geometries and unstructured grids.

Finite difference methods (FDMs) on curvilinear grids struggle to maintain numerical accuracy due to grid non-uniformity, even when satisfying the requirement of free-stream preservation. To address this issue, we introduce the concept of linear-stream preservation and propose a novel FDM framework based on the discrete equivalence equation and its discrete rule. The proposed method employs a gradient-based interpolation scheme, effectively mitigating spatial coupling errors introduced by traditional interpolation methods. Numerical examples, including linear-stream preservation, isentropic vortex, subsonic channel flow, and supersonic flow past a cylinder, demonstrate that the proposed method significantly reduces numerical errors and enhances computational stability on non-smooth grids. The proposed linear-stream preserving FDM offers substantial advantages in grid adaptability, paving the way for more reliable and robust FDM-based computational fluid dynamics simulations on complex geometries.

The finite volume method is widely applied in computational fluid dynamics engineering practices. Particularly in the computation of compressible flow fields, discontinuous structures often evolve into numerical transition zones spanning multiple grid points. During this process, nonphysical oscillations parallel to the discontinuity are generated and are regularly distributed. Discontinuities such as shock waves are defined by characteristic Euler equations, and the UFSC (Upwind Flux Scheme based on Characteristics) scheme is a flux computation method constructed based on the characteristic upwind properties derived from the equations. This paper presents numerical examples comparing the performance of the UFSC scheme with other conventional flux-splitting schemes (such as Steger–Warming, van Leer) under the finite volume method. The results show that the UFSC scheme effectively eliminates the nonphysical oscillations induced by the initial contact discontinuities in the flux vector splitting scheme. Additionally, it significantly reduces the amplitude of the disturbances caused by the initial shock wave. Moreover, for hypersonic flow problems, the UFSC scheme, compared to Roe and other FDS (flux difference splitting) schemes, does not exhibit shock instability, demonstrating excellent numerical stability. The UFSC scheme shows strong stability in both strongly discontinuous and continuous flow fields, demonstrating its practical value in engineering computations.

For the second-order cell-centered unstructured finite volume method, the variables are linearly distributed inside the grid cell. Classical methods use a first-order extrapolation process in calculating the boundary values, which can lead to loss of second-order accuracy at the boundary. In order to solve the problem, a novel boundary constrained reconstruction method is proposed for boundary values in the unstructured finite volume method. This method first solves for all cell-centered gradients using the weighted least squares method. Subsequently, the boundary cell center gradient is used to reconstruct the boundary face center values. These reconstructed boundary values, corrected by boundary conditions, are then added to the boundary cell gradient calculation stencils to recalculate the boundary cell center gradient. The above-mentioned steps are repeated iteratively, stopping when the boundary face center values stabilize. Numerical case validation shows that this method is able to ensure linear distribution of variables within the boundary cells of the second-order cell-centered unstructured finite volume method, thereby recovering the accuracy of boundary cell calculations.

The computation of the finite difference method in curvilinear coordinates usually necessitates coordinate transformation. Eliminating geometric errors induced by coordinate transformation can be achieved with geometric conservation law. However, no research has been conducted to implement a difference scheme on two-dimensional three-neighboring-node unstructured meshes and achieve a second-order accuracy. In this paper, a new finite difference method is proposed for a numerical simulation on these meshes, and it can achieve a second-order accuracy with the use of the gradient interpolation and the discrete criterion, freezing the metrics and Jacobian at local nodes. The results of several numerical tests demonstrate that the method achieved reliable performance and robustness on unique and randomized unstructured grids for a complex flow with discontinuity, subsonic inflow, and diffraction. The method had comparable accuracy to the second-order difference scheme on structured grids.

In order to overcome the influence of complex environmental disturbance factors such as nonlinear time-varying characteristics on the dynamic control performance of small fixed-wing UAVs, the nonlinear expression relationship of neural networks (NNs) is combined with the recursive least squares (RLSs) identification algorithm. This paper proposes a hybrid aerodynamic parameter identification method based on NN-RLS offline network training and online learning correction. The simulation results show that compared with the real value of the identification value obtained by this algorithm, the residual error of the moment coefficient is reduced by 69%, and the residual error of the force coefficient is reduced by 89%. Under the same identification accuracy, the identification time is shortened from the original 0.1 s to 0.01 s. Compared with traditional identification algorithms, better estimation results can be obtained. By using this algorithm to continuously update the NN model and iterate repeatedly, iterative learning for complex dynamic models can be realized, providing support for the optimization of UAV control schemes.

Wide-speed-range vehicles are characterized by high flight altitude and high speed, with significant changes in the flight environment. Due to the strong uncertainty of its aerodynamic characteristics, higher requirements are imposed on attitude control. In this paper, an adaptive prescribed performance control method based on online aerodynamic identification is proposed, which consists of two parts: an online aerodynamic parameter identification method and an adaptive attitude control method based on the pre-defined parameters of the control system. The aerodynamic parameter identification is divided into offline design and online design. In the offline design, neural networks are used to fit nonlinear aerodynamic characteristics. In the online design, a nonlinear recursive identification method is used to correct the errors of the offline fitted model. The adaptive attitude control is based on the conventional control method and updates the control gain in real time according to the desired system parameters to enhance the robustness of the controller. Finally, the effectiveness of the offline neural network and online discrimination correction is verified by mathematical simulations, and the effectiveness and robustness of the adaptive control proposed in this paper are verified by comparative simulation.