International Journal for Numerical Methods in Fluids最新文献

In the present study, a high-order hybrid compact-weighted essentially non-oscillatory (WENO) scheme is applied in conjunction with the immersed boundary method for efficiently computing compressible inviscid flows around two-dimensional solid bodies. For this aim, the two-dimensional unsteady compressible Euler equations written in the conservative form are considered and they are discretized in the space by using the hybrid fifth-order compact-WENO (CW) finite-difference scheme and the third-order explicit TVD Runge–Kutta scheme in the time. The solid bodies are appropriately imposed to the computational domain by using the immersed boundary method as an effective procedure in modeling the complex configurations without the difficulties usually encountered in generating the computational grid over such problems. Different test cases are simulated by applying the hybrid CW immersed boundary method and the present results are compared with those of available finite-difference immersed boundary methods. To further assess the solution method applied, the present results are also obtained by the high-order WENO immersed boundary scheme, and these two high-order accurate solution procedures are thoroughly compared with each other. The main advantage of using the hybrid CW finite-difference immersed boundary method applied here is that it provides a more accurate solution with lower computational cost in comparison with the traditional and high-order WENO finite-difference immersed boundary methods. It is shown that the solution procedure based on the hybrid CW scheme implemented via the immersed boundary method has still reasonable shock-capturing features and it can effectively be applied for accurately computing the compressible inviscid flows with the complicated flow structures and the embedded discontinuities such as the shocks over the complicated geometries.

The application of neural network-based modeling presents an efficient approach for exploring complex fluid dynamics, including droplet flow. In this study, we employ Long Short-Term Memory (LSTM) neural networks to predict energy budgets in droplet dynamics under surface tension effects. Two scenarios are explored: Droplets of various initial shapes impacting on a solid surface and collision of droplets. Using dimensionless numbers and droplet diameter time series data from numerical simulations, LSTM accurately predicts kinetic, dissipative, and surface energy trends at various Reynolds and Weber numbers. Numerical simulations are conducted through an in-house front-tracking code integrated with a finite-difference framework, enhanced by a particle extraction technique for interface acquisition from experimental images. Moreover, a two-stage sequential neural network is introduced to predict energy metrics and subsequently estimate static parameters such as Reynolds and Weber numbers. Although validated primarily on simulation data, the methodology demonstrates the potential for extension to experimental datasets. This approach offers valuable insights for applications such as inkjet printing, combustion engines, and other systems where energy budgets and dissipation rates are important. The study also highlights the importance of machine learning strategies for advancing the analysis of droplet dynamics in combination with numerical and/or experimental data.

In this paper, a novel fourth-order center-upwind WENO scheme is proposed for the fifth-order WENO (Weighted Essentially Non-Oscillatory) scheme with innovative improvements. This scheme achieves an effective reduction in numerical dissipation and a significant improvement in scheme adaptability by introducing a virtual sub-stencil dynamically controlled by a switching function. The core of the study lies in the redesign of the sub-stencil of the fifth-order WENO, which is decomposed into two two-point sub-stencils, and the automatic selection and switching between the sub-stencils is achieved by the switching function. In addition, the new scheme achieves adaptive optimization under different flow conditions by dynamically adjusting the linear weights, allowing flexible switching between the fourth-order central and fifth-order WENO schemes. Through the spectral characterization of the ADR method and the empirical validation of a series of benchmark numerical test cases, the new scheme demonstrates lower power dissipation and higher resolution, verifying its effectiveness and application potential in high-precision numerical simulations.

In this paper, an implicit scheme that uses the least-square method to compute the pressure gradient term in the momentum equation, mainly for coupled algorithm was proposed. Accurate computation of the pressure gradient is crucial in computational fluid dynamics, directly influencing the precision of calculation results. The least-square gradient can reach unconditional second-order accuracy in the finite volume method. Currently, the least-square gradient method is predominantly employed in segregated algorithms, primarily utilizing explicit schemes that are not applicable to coupled algorithms. The scarcity of high-accuracy schemes for computing pressure gradients in coupled algorithms underscores a significant research gap. It contributes by presenting a derivation of an implicit scheme for the least-square gradient, complemented by an extensive discussion on boundary treatment methods. The efficacy of proposed least-square method through comparative analysis involving the Green-Gauss method, as well as benchmarking against existing literature or analytical solutions across distinct cases. The findings demonstrate that, in the majority of cases, the least-square method offers superior accuracy and convergence rates compared with the Green-Gauss method.

In this paper, a high-order lattice Boltzmann flux solver (LBFS) based on flux reconstruction (FR) is presented for simulating the three-dimensional compressible flows. Unlike the original LBFS employing finite volume methods, the current method (FR-LBFS) can achieve arbitrary high-order accuracy with a compact stencil. High-order schemes based on finite volume methods often compromise parallel efficiency and complicate boundary treatment. In contrast, LBFS incorporates physical effects in calculating inviscid fluxes, providing superior shock-capturing capabilities over traditional approximate Riemann solvers. The present method combines the strengths of both FR and LBFS, yielding enhanced performance. Specifically, there is limited analysis of compact high-order LBFS in simulations of three-dimensional compressible flows. Several benchmark test cases are employed to validate the superiority of the current method, and the results show good agreement with established literature values. The shock tube problem and inviscid Taylor-Green vortex demonstrate the shock-capturing capability and low-dissipation characteristics of FR-LBFS. Meanwhile, the decaying homogeneous isotropic turbulent flow and the flow around a triangular airfoil highlight the accuracy of the current method in turbulence simulation. The obtained numerical results demonstrate that the proposed method holds considerable promise for applications in simulations of compressible and turbulent flows.

This paper investigates the accuracy of U-Net++ networks in predicting Reynolds-Averaged Navier-Stokes (RANS) solutions. The study employs the symbolic distance function (SDF) to represent geometry and flow conditions, utilizing parameterized airfoil data from the UIUC (University of Illinois at Urbana-Champaign) airfoil datasets. The research assesses the performance of multiple trained neural networks in predicting pressure and velocity distributions. Specifically, the study examines the influence of varying network weights on solution accuracy. Through the optimization of the model, the research demonstrates that the mean relative error is below 1.72% for a range of previously unseen wing shapes, with a computational speedup factor of up to 1,000× in certain scenarios. The accuracy achieved by this model underscores the significant potential of deep learning-based approaches as reliable tools for aerodynamic design and optimization.

In situations where a wide range of flow scales are involved, the non-linear scheme should be capable of both shock capturing and low-dissipation. Most of the existing Weighted Compact Non-linear Schemes (WCNS) are too dissipative and incapable of achieving fourth-order for the two smooth stencils located on the same side of a discontinuity due to the weight deviations and the defect of the weighting strategy. In this paper, a novel filtered embedded WCNS is introduced for complex flow simulations involving both shock and small-scale structures. To overcome the above deficiency of existing WCNS, a pre-discrete mapping function is proposed to filter the weight deviation out and amend the inappropriate weights to ideal weights in smooth regions. Meanwhile, the embedded process is also implemented by this function, which is utilized to improve the resolution of shock capturing in certain discontinuity distributions. The pre-discrete mapping function is also extended to the WENO framework. The approximate-dispersion-relation analysis indicates that the scheme with the mapping function has lower dispersion and dissipation error than the WCNS-JS, WCNS-Z, and WCNS-T schemes. Numerical results show that WCNS with the new non-linear weights captures discontinuities sharply without obvious oscillation, has a higher resolution than other non-linear schemes, and has an obvious advantage in capturing small-scale structures.

The computation of damping rates of an oscillating fluid with a free surface in which viscosity is small and surface tension high is numerically challenging. A typical application requiring such computation is drop-on-demand (DoD) microfluidic devices that eject liquid metal droplets, where accurate knowledge of the damping rates for the least-damped oscillation modes following droplet ejection is paramount for assessing jetting stability at higher jetting frequencies, as ejection from a nonquiescent meniscus can result in deviations from nominal droplet properties. Computational fluid dynamics (CFD) simulations often struggle to accurately predict meniscus damping unless very fine discretizations are adopted, so calculations are slow and computationally expensive. The faster alternative we adopt here is to compute the damping rate directly from the eigenvalues of the linearized problem. The presence of a surface tension term in Stokes or sloshing problems requires approximation of the meniscus displacements as well, which introduces additional complexity in their numerical solution. In this paper, we consider the combined effects of viscosity and surface tension, approximate the meniscus displacements, and construct a finite element method to compute the fluid's oscillation modes. We prove that if the finite element spaces satisfy a typical inf-sup condition, and the space of the meniscus displacements is a subset of the set of normal traces of the space of velocities, then the method is free of spurious modes with zero or positive damping rates. To construct numerical examples, we implement the method with Taylor-Hood elements for the velocity and pressure fields, and with continuous piecewise quadratic elements for the displacement of the meniscus. We verify the numerical convergence of the method by reproducing the solution to an analytical benchmark problem and two more complex examples with axisymmetric geometry. Remarkably, the spatial shape and temporal evolution (angular frequency and damping rate) of the set of least-damped oscillation modes are obtained in a matter of minutes, compared to days for a CFD simulation. The method's ability to quickly generate accurate estimates of fluid oscillation damping rates makes it suitable for integration into design loops for prototyping microfluidic nozzles.

Direct numerical simulation (DNS) and implicit large-eddy simulation (LES) of turbulent channel flows with isothermal walls, with and without shock trains, are performed using a recently proposed high-order optimized targeted essentially non-oscillatory (TENO) scheme. Mean flow and turbulence statistics are presented and compared with those previously obtained from DNS using a bandwidth-optimized weighted essentially non-oscillatory (WENO) scheme with limiter. It is observed that the TENO scheme performs better than the WENO scheme in predicting the mean flow and Reynolds stresses in these flows. The optimized TENO scheme used here is found to be very suitable for performing implicit LES on a relatively coarse grid.