In this study, a third-order meshless method is presented through adopting WENO-Z reconstruction as a substitute for traditional linear reconstruction. In order to achieve a third-order reconstruction of WENO-Z, the required three-point stencils are created by introducing ghost points on the lines through each pair of the central and satellite points of the meshless cloud. The flow variables of the ghost point are evaluated by a proposed interpolation technique, in which only available information associated with the cloud is utilized. Based on each resultant stencil of the ghost-central-satellite points, the WENO-Z is then implemented for computing the variables at the midpoints between the central and satellite points of the cloud. In this way, the resulting meshless method could be expected to be of third-order accuracy while obtaining an oscillation-free property. A series of typical model cases, including linear advection of sinusoid wave, convection of an isentropic vortex, and two well-known shock-tube problems, are selected to be simulated for validation. The expected third-order of accuracy and inherit ability of shock capturing are achieved regardless of whether the meshless points distributed are regular or irregular. In addition, a set of subsonic, transonic, and supersonic flows over aerodynamic bodies like single-and multi-element airfoils are also demonstrated for the compressible Euler equations, and obtained numerical results compare well with the reference data in the literature.

This study develops and numerically assesses a robust aerodynamic optimization framework for a passive flow deflector on a three-dimensional cambered "Flugzeug n & auml;chster Generation" (FNG) wing. A surrogate-assisted Efficient Global Optimization (EGO) algorithm is employed to automate the design of the deflector configuration. The robustness of the optimized design is evaluated under different side-boundary conditions and turbulence models. At a high angle of attack of 19 degrees, the optimized configuration improves the lift-to-drag ratio by 40.15% under periodic boundary conditions with the Spalart-Allmaras (S-A) model and by 63.86% with the Transition-SST model. Under wall-bounded conditions, which are introduced to better approximate future wind-tunnel configurations, the lift-to-drag ratio is further improved by 53.32%. Across all tested numerical settings, the optimized deflector consistently strengthens the leading-edge suction peak, smooths the upper-surface streamline pattern, suppresses large-scale vortex formation, and delays stall onset. The present work therefore provides a systematic numerical framework for robust aerodynamic design, while experimental validation of the optimized configuration remains a subject for future work.

This study explores the critical role of the flow deflector in suppressing boundary layer separation and enhancing aerodynamic efficiency through systematic geometric parameterization and computational analysis. By defining eight key design variables, this research identifies optimal configurations that significantly delay flow separation at high angles of attack. Computational Fluid Dynamics (CFD) simulations reveal that optimized deflector geometries enhance suction peaks near the airfoil leading edge, redirect separated flow toward the upper surface, and inject momentum into the boundary layer to generate a more positive lift coefficient. The numerical results demonstrate that the optimized design achieves a 58.4% increase in lift coefficient and an 83.3% improvement in the lift–drag ratio by effectively mitigating large-scale vortical structures inherent in baseline configurations. Sensitivity analyses further highlight threshold-dependent “sudden-jump” behaviors in lift coefficients for parameters such as element spacing and deflection angles, while thickness exhibits minimal influence. Additionally, pre-stall optimizations show that strategically aligned deflectors preserve baseline performance with a 0.4% lift gain, whereas misaligned configurations degrade aerodynamic efficiency by up to 9.1%. These findings establish a direct correlation between deflector-induced flow redirection and separation suppression, offering actionable insights for passive flow control in stalled regimes. This research advances fundamental understanding of flow deflector-based separation management and provides practical guidelines for enhancing aerodynamic performance in aerospace applications.

This study introduces a novel hypervolume enhancement approach derived from negative hypervolume improvement (NHVI) concepts, addressing inherent limitations in conventional strategies that generate extensive zero-gradient regions detrimental to late-stage optimization efficiency. In contrast to traditional methodologies that nullify dominated regions, our proposed strategy systematically calculates negative improvements within these domains. This critical modification transforms problematic zero-gradient plateaus into negatively inclined hypervolume regions that actively drive optimization momentum, effectively accelerating the entire multi-objective optimization process. The research implements this negative hypervolume improvement paradigm within multi-objective Efficient Global Optimization (EGO) frameworks. The method's efficacy is rigorously validated against a comprehensive suite of standard multi-objective benchmarks, challenging many-objective test cases, and an aerodynamic airfoil optimization case study. Across all numerical tests, the proposed algorithm demonstrated statistically significant superiority, and in the engineering application, comparative analysis reveals that the enhanced algorithm produces a 485% increase in Pareto solution density (from 7 to 41 solutions) while maintaining superior solution quality. These empirical results substantiate the strategy's effectiveness in addressing real-world engineering challenges, particularly demonstrating its capacity to improve optimization precision through systematic gradient management. The demonstrated performance enhancements highlight the methodology's practical significance for complex multi-objective engineering applications requiring both computational efficiency and solution quality.

This paper presents a novel algorithm, namely the adaptive nested Monte Carlo based multi-objective Efficient Global Optimization (ANMC-MOEGO), which aims to enhance efficiency and accuracy while minimizing programming complexity in contrast to traditional multi-objective Efficient Global Optimization (MOEGO). In this algorithm, the programming complexity is streamlined by employing Monte Carlo simulation for both hypervolume improvement (HVI) and expected hypervolume improvement (EHVI) calculations. Furthermore, the efficiency and accuracy of HVI and EHVI calculations are improved through the utilization of a novel technique called adaptive Monte Carlo hypercube boundaries (AMCHB), which is based on the bisection method. The algorithm is validated via a set of test functions from the open literature. The numerical results demonstrate that the ANMC-MOEGO algorithm produces solutions closer to the theoretical results, with improved distributions on the corresponding Pareto fronts compared to the algorithm without AMCHB technique. Moreover, when obtaining a better Pareto front, the proposed algorithm is found to be more time-efficient, achieving speedups of up to 22.57 times.

In this work, a novel multi-objective efficient global optimization (EGO) algorithm, namely GMOEGO, is presented by proposing an approach of available threads' multi-objective infill criterion. The work applies the outstanding hypervolume-based expected improvement criterion to enhance the Pareto solutions in view of the accuracy and their distribution on the Pareto front, and the values of sophisticated hypervolume improvement (HVI) are technically approximated by counting the Monte Carlo sampling points under the modern GPU (graphics processing unit) architecture. As compared with traditional methods, such as slice-based hypervolume integration, the programing complexity of the present approach is greatly reduced due to such counting-like simple operations. That is, the calculation of the sophisticated HVI, which has proven to be the most time-consuming part with many objectives, can be light in programed implementation. Meanwhile, the time consumption of massive computing associated with such Monte Carlo-based HVI approximation (MCHVI) is greatly alleviated by parallelizing in the GPU. A set of mathematical function cases and a real engineering airfoil shape optimization problem that appeared in the literature are taken to validate the proposed approach. All the results show that, less time-consuming, up to around 13.734 times the speedup is achieved when appropriate Pareto solutions are captured.

A graphics processing unit (GPU)-accelerated discontinuous Galerkin (DG) method is presented for solving two-dimensional laminar flows. The DG method is ported from central processing unit to GPU in a way of achieving GPU speedup through programming under the compute unified device architecture(CUDA)model. The CUDA kernel subroutines are designed to meet with the requirement of high order computing of DG method. The corresponding data structures are constructed in component-wised manners and the thread hierarchy is manipulated in cell-wised or edge-wised manners associated with related integrals involved in solving laminar Navier-Stokes equations,in which the inviscid and viscous flux terms are computed by the local lax-Friedrichs scheme and the second scheme of Bassi & Rebay,respectively. A strong stability preserving Runge-Kutta scheme is then used for time marching of numerical solutions. The resulting GPU-accelerated DG method is first validated by the traditional Couette flow problems with different mesh sizes associated with different orders of approximation,which shows that the orders of convergence,as expected,can be achieved. The numerical simulations of the typical flows over a circular cylinder or a NACA 0012 airfoil are then carried out,and the results are further compared with the analytical solutions or available experimental and numerical values reported in the literature,as well as with a performance analysis of the developed code in terms of GPU speedups. This shows that the costs of computing time of the presented test cases are significantly reduced without losing accuracy,while impressive speedups up to 69.7 times are achieved by the present method in comparison to its CPU counterpart.

为了模拟涡桨发动机等绕固定轴旋转的桨叶流场,发展了一种求解旋转体非定常黏性绕流的无网格/网格混合算法.算法基于求解旋转坐标系纳维尔-斯托克斯方程展开,避免了旋转角速度特征物理量的插值运算;计算域采用整体网格和物面附近局部无网格离散,通过引入无网格和网格对偶点,实现了混合算法绕流信息的跨区交换,并给出了一种对偶点调整选取的方法;基于无网格点云空间导数逼近方法离散控制方程,并结合隐式LU-SGS算法,给出了混合算法求解非定常问题的双时间步隐式推进格式.结果表明:所提算法通过2维振荡翼型非定常绕流、旋转圆柱黏性绕流和模拟发动机桨叶旋转运动的3维悬停旋翼绕流进行了考核,所得升力系数等重要气动数据的变化趋势与文献试验或计算值一致,典型截面处所示的激波强度和位置亦与文献值吻合,展现出算法在模拟旋转部件绕流问题方面具有广阔的工程应用前景.

A high-order discontinuous Galerkin (DG) method is presented for solving the preconditioned Euler equations with an explicit or implicit time marching scheme. A detailed description is given of a practical implementation of a precondition matrix of the type of Weiss and Smith and of the DG spatial discretization scheme employed, with particular emphasis on the artificial viscosity-based shock capturing techniques. The curved boundary treatment is proposed through adopting a NURBS surface equipped with a radial basis function interpolation to propagate the boundary displacement to the interior of the mesh. The resulting methods are verified by simulating flows over two-dimensional airfoils, such as symmetric NACA0012 or asymmetric RAE2822, and over three-dimensional bodies, such as an academic hemispherical headform or aerodynamic ONERA M6 wing. Numerical results show that the present method functions for both transonic and nearly incompressible flow simulations, and the proposed treatment of curved boundaries, play an important role in improving the accuracy of the obtained solutions, which are in good agreement with available experimental data or other numerical solutions reported in literature.

Subjected to the accuracy of surrogate model and premature convergence sometimes occurs, the solution of classical efficient global optimization（EGO） usually can be improved. Regarding this point, this paper presents a thorough study of the EGO with high accuracy optimal solution. The algorithm is based on the Kriging surrogate model, in which the Kriging believe strategy based Expected Improvement（EI） function is adopted, it can help to lead the optimal solution to local optimum in the late period of iteration. Besides, in order to improving the accuracy, cooperating with quasi-Newton method and Powell method are also incorporated. Several representative numerical examples are selected to test the algorithms above, the result shows that the algorithms in this paper can reach more accurate global optimal solution than classical EGO, with less additional cost. At last, an aerodynamic optimization problem is developed, it shows that the drag coefficient decreased 1.11% further than the former EGO, shows its practicability in an engineering environment.

In order to solve Maxwell’s equations so as to study the electromagnetic stealth characteristics of targets, a 3-D meshless method is developed. According to the meshless method, the spatial derivatives on clouds of points are computed by using the weighted least square approach. After that, the Steger-Warming flux vector splitting approach is used to calculate the physical flux of Maxwell’s equations. By using the developed method, the calculated bistatic radar cross sections (RCS) of a 3-D sphere are obtained, which are agree with the series solutions. Finally, the electromagnetic scattering characteristics for a 3-D stealth aircraft model with different situations is given, which shows the developed method has the ability to accommodate complicated 3-D configurations with multi-element.

In order to accurately calculate the radar cross sections (RCS) of stealth aircrafts by using the meshless method, several typical body surface boundary conditions from finite-volume time-domain (FVTD) methods, which are suitable for the meshless method, have been compared. The bistatic RCS of a 2-D cylinder irradiated by transverse magnetic wave (TM wave) or transverse electric wave (TE wave) and a 3-D sphere irradiated by different polarization waves are calculated by the meshless method based on different boundary conditions. The numerical results show that the bistatic RCS calculated by the first boundary condition is closest to the series solution, which indicates that the scattering electric field on the surface of perfect conductors is only related to the incident electric field, and the scattering magnetic field is related to the scattering magnetic field near the body surface and the variation of the normal scattering electric field on the body surface. Finally, based on the selected optimal body surface boundary condition, the paper present the electromagnetic scattering field and the bistatic RCS for a 3-D stealth aircraft model, which shows the ability of the meshless method in dealing with 3-D practical problems to a certain extent.

In this paper, preconditioned gridless methods are developed for solving the three-dimensional (3D) Euler equations at low Mach numbers. The preconditioned system is obtained by multiplying a preconditioning matrix of the type of Weiss and Smith to the time derivative of the 3D Euler equations, which are discretized under the clouds of points distributed in the computational domain by using a gridless technique. The implementations of the preconditioned gridless methods are mainly based on the frame of the traditional gridless method without preconditioning, which may fail to have convergence for flow simulations at low Mach numbers, therefore the modifications corresponding to the affected terms of preconditioning are mainly addressed in the paper. An explicit four-stage Runge–Kutta scheme is first applied for time integration, and the lower-upper symmetric Gauss-Seidel (LU-SGS) algorithm is then introduced to form the implicit counterpart to have the further speed up of the convergence. Both the resulting explicit and implicit preconditioned gridless methods are validated by simulating flows over two academic bodies like sphere or hemispherical headform, and transonic and nearly incompressible flows over one aerodynamic ONERA M6 wing. The gridless clouds of both regular and irregular points are used in the simulations, which demonstrates the ability of the method presented for coping with flows over complicated aerodynamic geometries. Numerical results of surface pressure distributions agree well with available experimental data or simulated solutions in the literature. The numerical results also show that the preconditioned gridless methods presented still functions for compressible transonic flow simulations and additionally, for nearly incompressible flow simulations at low Mach numbers as well. The convergence of the implicit preconditioned gridless method, as expected, is much faster than its explicit counterpart.

This paper presents a novel GPU-parallelized meshless method for solving Reynolds-averaged Navier–Stokes equations with the Spalart–Allmaras turbulence model. Least-square curve fit is utilized to discretize the spatial derivatives of the equations, and a Roe-type upwind scheme is used for computing the flux terms. The compute unified device architecture (CUDA) Fortran programming model is employed to port the meshless method from CPU to GPU in a way of achieving efficiency. For the extracted GPU parallel tasks, a particular two-dimensional thread hierarchy is designed to construct the corresponding computational kernels. Then, a modified strategy, multi-layered point reordering, and a proposed strategy, shared memory access tuning, are used to manage the GPU memory access. A series of typical two- and three-dimensional test cases, including transonic flows over an aerofoil, a wing or a CRM wing-body combination, were carried out to verify the developed method. The computed results agreed well with experimental data and other numerical solutions reported in literature. Impressive speedups, over 40× and up to 79× with respect to a single threaded CPU implementation, are successfully achieved for the benchmark tests.

In this paper, our newly proposed Nash-EGO algorithm is applied to real large-scale airfoil/wing optimizations. A finite wing is represented by mounting control airfoils parameterized with a set of design variables, which are manipulated to be increased gradually in purpose of enriching the searching space to accommodate possible more optimal solutions. The enriched design territory is technically split into small subsets to be assigned to the players of Nash-EGO. Doing this way, the performance of each efficient global optimization (EGO) player could be expected to keep at a high level due to EGO players now take care of only their own small-scale subsets instead of facing the large-scale problem directly. The algorithm is first applied to a constrained drag minimization of RAE 2822 airfoil with 14 to 54 design variables and two to eight Nash players to investigate the performance of Nash-EGO, particularly for having an understanding of the influences of the numbers of design variables and Nash players. Then, more challenging cases, sectional shape optimizations of DLR-F4 wing with up to 84 design variables, are conducted. The results show that, in comparison with the baselines, up to 47.5% drag reductions can be achieved by Nash-EGO optimizer; meanwhile, the CPU costs are greatly reduced (up to 366.8% speedup) as compared with the counterpart of the traditional EGO. The successful applications presented show the capability of Nash-EGO algorithm for solving real engineering optimizations with large scales.

In meshless methods, clouds of points irregularly distributed are widely used in discretizing computational domains and are usually unavoidable to accommodate complex geometries. However, the irregularity of points has been reported to be negative effect on the GPU memory access pattern, which results in low performance in GPU computations. In order to remedy this negative effect, a multi-layered point reordering (MLPRO) approach is proposed in this paper for GPU-based meshless implementations. Layer structures based on the virtual connections between central and satellite points in meshless clouds are constructed and used to reorder the points in a layer-by-layer manner. Besides, point reordering inside each thread warp, which is rarely concerned in GPU implementations, is further considered by proposing a supplemental group satellite reordering to form a modified MLPRO approach. Furthermore, by defining virtual connectivity matrixes of meshless clouds of points in the whole computational domain, the effect of reordering mentioned to the data localities can be visibly observed to have a comprehensive view of the improvement of point locality. Supersonic flows in a rectangular channel are firstly selected to test the effect extent of irregularity of meshless points to the GPU performance by increasing the percentage of irregular points occupied in the computational domain. Then flows over two- and three-dimensional aerodynamic configurations are simulated to show the performances of the reordering approaches presented. Numerical results show that significant enhancements of GPU speedups can be achieved for all test cases, particularly for the three-dimensional M6 wing and RAE wing-body combination cases with up to 2.5x further speedups, which is meaningful for simulations with large-scale irregular meshless clouds of points. (C) 2019 Elsevier B.V. All rights reserved.

Purpose The purpose of this paper is to develop a new approach for rapid computation of subsonic and low-transonic rotary derivatives with the available steady solutions obtained by Euler computational fluid dynamics (CFD) codes. Design/methodology/approach The approach is achieved by the perturbation on the steady-state pressure of Euler CFD codes. The resulting perturbation relation is established at a reference Mach number between rotary derivatives and normal velocity on surface due to angular velocity. The solution of the reference Mach number is generated technically by Prandtl–Glauert compressibility correction based on any Mach number of interest under the assumption of simple strip theory. Rotary derivatives of any Mach number of interest are then inversely predicted by the Prandtl–Glauert rule based on the reference Mach number aforementioned. Findings The resulting method has been verified for three typical different cases of the Basic Finner Reference Projectile, the Standard Dynamics Model Aircraft and the Orion Crew Module. In comparison with the original perturbation method, the performance at subsonic and low-transonic Mach numbers has significantly improved with satisfactory accuracy for most design efforts. Originality/value The approach presented is verified to be an efficient way for computation of subsonic and low-transonic rotary derivatives, which are performed almost at the same time as an accounting solution of steady Euler equations.

为研究飞行器的电磁隐身特性,提出基于计算流体力学(CFD)的时域无网格算法.基于无网格点云结构,由展开的泰勒级数结合最小二乘技术逼近该算法涉及的空间导数;借鉴CFD的无网格方法,采用Steger-Warming通量分裂处理空间离散涉及的通量运算,采用四步Runge-Kutta格式推进求解时间离散,并运用该算法对电磁波从不同方向照射平板飞机模型的电磁散射场和双站雷达散射截面进行分析.结果表明:采用本文算法计算得到的二维圆柱双站雷达散射截面能与级数解吻合;该飞机模型的隐身特性与散射场的叠加作用及飞机外形等因素有关;本文算例在一定程度上验证了本文算法具有处理多体及多部件干扰等复杂情形的能力.

This paper develops a recently proposed GPU based two-dimensional explicit meshless method (Ma et al., 2014) by devising and implementing an efficient parallel LU-SGS implicit algorithm to further improve the computational efficiency. The capability of the original 2D meshless code is extended to deal with 3D complex compressible flow problems. To resolve the inherent data dependency of the standard LU-SGS method, which causes thread-racing conditions destabilizing numerical computation, a generic rainbow coloring method is presented and applied to organize the computational points into different groups by painting neighboring points with different colors. The original LU-SGS method is modified and parallelized accordingly to perform calculations in a color-by-color manner. The CUDA Fortran programming model is employed to develop the key kernel functions to apply boundary conditions, calculate time steps, evaluate residuals as well as advance and update the solution in the temporal space. A series of two- and three-dimensional test cases including compressible flows over single- and multi-element airfoils and a M6 wing are carried out to verify the developed code. The obtained solutions agree well with experimental data and other computational results reported in the literature. Detailed analysis on the performance of the developed code reveals that the developed CPU based implicit meshless method is at least four to eight times faster than its explicit counterpart. The computational efficiency of the implicit method could be further improved by ten to fifteen times on the GPU.

A novel Nash-EGO algorithm is presented to extend the usage of efficient global optimization (EGO) into large-scale optimizations by coupling with Nash game strategy. In our Nash-EGO, the large-scale design variables are split into several subsets by adopting Nash variable territory splitting, and the EGO optimizer acts as a player of specific Nash game. All the EGO players are coupled with each other and assigned to optimize their own subsets synchronously in parallel to produce the corresponding approximate optimal subsets. Doing in this way, the performance of EGO players could be expected to keep at a high level due to the fact that EGO players now take care of only their own small-scale subsets instead of facing the large-scale problem directly. A set of typical cases with a small number of variables are firstly selected to validate the performance of each EGO player mentioned. Then, the Nash-EGO proposed is tested by representative functions with a scale up to 30 design variables. Finally, more challenge cases with 90 design variables are constructed and investigated to mimic the real large-scale optimizations. It can be learned from the tests that, with respect to conventional EGO the present algorithm can always find near optimal solutions, which are more close to the theoretical values, and are achieved, moreover, less CPU time-consuming, up to hundreds times faster. All cases with 30 or 90 design variables have similar efficient performances, which indicates the present algorithm has the potential to cope with real large-scale optimizations.