International Journal for Numerical Methods in Fluids最新文献

Exponential and trigonometric functions have been extensively employed as the kernel of reconstruction operators within numerous WENO (Weighted Essentially Non-oscillatory) schemes to accelerate the convergence rate. However, most of them are scale-dependent, compromising the robustness required for multi-scale flow simulations. Thus, this work aims to develop novel three-cell-based scale-invariant WENO schemes that use exponential and trigonometric functions as the kernel of non-linear weights. First, to achieve the scale-invariant property, this work reformulates the newly proposed scale-invariant ROUND (Reconstruction Operators in Unified Normalized-variable Diagram) schemes into the form of WENO weighting functions, thereby facilitating the design of scale-invariant WENO schemes. Then, this work proposes new WENO non-linear weights using exponential and trigonometric functions—such as Gaussian, hyperbolic, and cosine functions—to enhance the accuracy of the three-cell-based WENO scheme. The proposed WENO weights contain a shape parameter that controls the errors between the non-linear weight and the ideal weight. As the value of the shape parameter increases, the non-linear weight converges towards the ideal weight but also becomes more likely to produce numerical oscillations. To approximate the optimal value of the shape parameter, the WENO reconstruction operator is projected into normalized variable space, and the shape parameters are fine-tuned to ensure the normalized reconstruction operator falls into the CBC (Convection Bounded Criterion) region of UND (Unified Normalized-variable Diagram). The accuracy analysis reveals that the proposed weighting functions outperform classical WENO schemes, particularly when the smooth function contains a first-order critical point. The accuracy and shock-capturing properties of the proposed schemes are further validated through benchmark tests. Thus, this work demonstrates using the ROUND framework to design scale-invariant three-cell-based WENO schemes with exponential and trigonometric functions and optimal shape parameters.

We consider the numerical resolution of the incompressible Navier-Stokes equations. We present a new compatible Finite Volume discretisation that generalises the famous Marker-and-Cell (MAC) method to polyhedral meshes that we call PolyMAC. In the first part of the paper, we recall the principles of compatible schemes and detail the key operators of the discretisation. The convergence and robustness of PolyMAC are assessed numerically first on a benchmark from the FVCA conferences. We then consider a problem of industrial complexity that allows us to confirm the robustness of PolyMAC on more complex problems. The second part of the article is dedicated to the efficient numerical resolution of the resulting linear system. Concretely, we use a PISO-like prediction-correction approach and develop efficient preconditioners for linear systems. In particular, we show that the saddle-point system arising from the correction step is very challenging for iterative methods on distorted meshes. In this work, we develop a robust preconditioner based on an algebraic transformation of the system. In particular, this new preconditioner shows impressive convergence on problems of industrial complexity.

This work investigates the optimization of airfoil shapes using various reinforcement learning (RL) algorithms, including Deep Deterministic Policy Gradient (DDPG), Twin Delayed Deep Deterministic Policy Gradient (TD3), and Trust Region Policy Optimization (TRPO). The primary objective is to enhance the aerodynamic performance of airfoils by maximizing lift forces across different angles of attack (AoA). The study compares the optimized airfoils against the standard NACA 2412 airfoil. The DDPG-optimized airfoil demonstrated superior performance at lower and moderate AoAs, while the TRPO-optimized airfoil excelled at higher AoAs. In contrast, the TD3-optimized airfoil consistently underperformed. The results indicate that RL algorithms, particularly DDPG and TRPO, can effectively improve airfoil designs, offering substantial benefits in lift generation. This paper underscores the potential of RL techniques in aerodynamic shape optimization, presenting significant implications for aerospace and related industries.

The CIP-Soroban method is an excellent adaptive meshless method capable of solving advection problems with 3rd-order accuracy by combining the Constrained Interpolation Profile/Cubic Interpolated Pseudo-particle (CIP) method. This study proposes a modified version of the CIP-Soroban method specifically designed to address severe compressible hydrodynamic scenarios. The proposed method includes a material distinguishing approach, incorporates a modified form of monitoring functions for grid generation, utilizes a staggered grid arrangement, incorporates the Maximum and minimum Bounds method, solves non-advection terms using a finite difference method, and employs an adjusted procedure for stably solving the governing equations. We applied the modified CIP-Soroban method to simulate the implosion process in inertial confinement fusion (ICF), which is commonly modeled by compressible fluid and has the problems of large gradients of physical values and strong nonlinearity for stable and accurate numerical analysis. Implosion simulations were performed using a series of grids with increasing resolutions, ranging from coarse to fine grid settings, as one of the application examples. The results indicated that compared to the conventional uniform grid CIP method, the modified CIP-Soroban method reduced computational costs (calculation time, memory occupancy, and grid number) for obtaining the same precision results.

In nature, many complex multi-physics coupling problems exhibit significant diffusivity inhomogeneity, where one process occurs several orders of magnitude faster than others temporally. Simulating rapid diffusion alongside slower processes demands intensive computational resources due to the necessity for small time steps. To address these computational challenges, we have developed an efficient numerical solver named Finite Difference informed Random Walker (FDiRW). In this study, we propose a GPU-accelerated, mixed-precision configuration for the FDiRW solver to maximize efficiency through GPU multi-threaded parallel computation and lower precision computation. Numerical evaluation results reveal that the proposed GPU-accelerated mixed-precision FDiRW solver can achieve a 117× speedup over the CPU baseline, while an additional 1.75× speedup is achieved by employing lower precision GPU computation. Notably, for large model sizes, the GPU-accelerated mixed-precision FDiRW solver demonstrates strong scaling with the number of nodes used in simulation. When simulating radionuclide absorption processes by porous wasteform particles with a medium-sized model of 192 × 192 × 192, this approach reduces the total computational time to 10 min, enabling the simulation of larger systems with strongly inhomogeneous diffusivity.