International Journal for Numerical Methods in Fluids最新文献

An extended height-function (HF) method that can be consistently utilized for 3D volume of fluid (VOF) simulations of wetting phenomena on super-hydrophilic and super-hydrophobic surfaces, is proposed. First, the standard HF method is briefly explained. Then, 2D and 3D HF methods that reflect the contact angles reported so far are described, with their limitations discussed. Finally, specific treatments of contact line identification and HF construction reflecting the contact angle boundary condition, required to overcome such limitations, are presented in detail. Numerical tests for a sessile droplet reveal that the contact line identification and HF construction are conducted appropriately with respect to the imposed contact angles ranging from $��1�{�5�}^{�\circ �}�$ to $��16�{�5�}^{�\circ �}�$ in the proposed numerical scheme. Additionally, the present method shows approximately first- or second-order convergence of the curvature at the contact line for a wide range of contact angles. Moreover, simulations of droplet spreading driven by surface tension reveal that the proposed method can reasonably reproduce the behavior of a droplet reaching an equilibrium state defined by an imposed contact angle.

In the present study, a cavitation implementation algorithm is developed using a pressure-based method for incompressible flows with three-phase interactions. Central to this implementation algorithm is the treatment of the velocity jump due to the phase change, which is included in both the cavitation transport and pressure equations. The velocity jump, as a function of the phase change rate, is added as a source term to the pressure Poisson equation. A non-conservative form of the vapor transport equation is derived, and the velocity divergence is replaced by a term related to the mass phase change rate. An algorithm for the three-phase (air, water, and vapor) interactions is also developed. The VOF method is modified and used to identify the ‘dry’ (air) phase and the ‘wet’ (water/vapor mixture) phase, since the cavitation can only occur inside the water phase. The liquid volume fraction is used to distinguish water and vapor phases. The numerical results of the 2D NACA66MOD and 3D Delft Twist 11 hydrofoils show good agreement with the experimental measurement. The forced unsteady cavitation flows are investigated using a pitching foil with the results compared with the experimental observations. Air–water interface effect on the cavitation is investigated using the NACA66MOD hydrofoil. The code is applied to simulate a surface piercing super cavitating hydrofoil with both ventilation and cavitation involved.

In this article, a local and parallel mixed-precision finite element method is applied for solving the time-dependent incompressible flows. We decompose the solution into the large eddy components and small eddy components based on two-grid method. The analysis shows that the small eddy components carry little part of the total energy compared with the large eddy components. In view of this character, we first obtain the large eddy components by solving the standard nonlinear equation using the high-precision solvers globally in the coarse mesh space, then get the small eddy components by solving a series of local linearized residual equation using the low-precision solvers locally and parallel based on the partition of unity. The performance advantages of the mixed-precision methods are tested with respect to speedups over a high-precision implementation in time and less storage requirements in space.

This study introduces a hybrid element-free Galerkin (HEFG) method to analyze the 3D steady convection–diffusion-reaction equation. By introducing the dimension-splitting method, the governing equation can be split into 2D form in each layer. The 2D form can be solved using the improved element-free Galerkin (IEFG) method with improved moving least-squares (IMLS) approximation as shape function, and discretized equations of 2D form are derived. The finite difference method (FDM) is selected to handle first- and second-order derivatives in the splitting direction. Thus, new 2D discretized equations in each plane are derived, and the final solved equation of the original 3D problem is obtained by coupling these 2D discretized equations. In numerical examples, we study the astringency of the HEFG method by examining the impact of layer and node on relative errors, and the computing time and accuracy of numerical solutions are compared with the dimension-coupling method (DCM), IEFG method, and exact one. The HEFG method can significantly reduce the calculation times of the IEFG method. Compared with the DCM, the advantage of the proposed method is its shorter computing time when dealing with essential boundaries in a splitting direction.

High-fidelity computational fluid dynamics (CFD) simulation usually carries a heavy computational burden, especially for parametric CFD simulations requiring multiple calculations. To address this challenge, researchers have developed reduced-order modeling (ROM) to significantly decrease the computational burden by building a simplified model. This article proposes a hybrid method of weighted proper orthogonal decomposition and Kriging, a novel reduced-order method. This method improves the accuracy of the reduced-order model by assigning appropriate weights to the samples while estimating the specific design parameters. The main innovation of this work is the development of the optimized method for generating the weights. Firstly, the leave-one-out method is employed to divide the samples into the training set and test set, and the multivariate Gaussian distribution is used to convert the Euclidean distance between the training set and test set into weight. Then, we adopt the WPOD-Kriging method to construct a reduced-order model using the training set. This model is compared with the test set to obtain the error. By repeatedly resetting the training set and the test set, we receive multiple errors and average them to calculate the global error. This process involves an important parameter, which is the covariance matrix of multivariate Gaussian distribution. We can generate the optimal covariance matrix by minimizing the global error to achieve the optimized method for generating the weights. The efficacy of the WPOD-Kriging method is validated through three parametric CFD simulations. Compared to other similar approaches, the proposed method offers a more accurate reduced-order model.

The use of well-designed nanoparticles in blood fluid can enhance heat transfer during medical interventions by improving thermophysical characteristics. It enables for targeted heat delivery to specific sites by increasing surface area for better heat exchange, which is crucial in more efficient treatments. The current attempt emphasizes on the enhanced thermal transport mechanism in an aluminium alloy suspended Copper-based blood nanofluid over an inclined cylindrical surface containing motile gyrotactic microbes. The Carreau fluid viscosity model is implemented to expose the intricate nature of bio-nanofluid, while the heating source is used to simulate the bio-convective heat transport mechanism. In addition, the viscosity of hybrid bio-nanofluids exhibits temperature effects that depend on nanoparticle volume friction dependencies related to the dynamics of spherical and cylindrical shapes with distinct shape factors. The physical generated system of partial differential equations (PDEs) is derived and then transformed into a dimensionless system of ordinary differential equations (ODEs) using similarity functions. The resulting system is reduced into first-order differential equations and a numerical solution is obtained by using a hybrid computational procedure. The trend of fluid profiles is examined by mean of governing parameters. Results are interpreted via tabular data and MATLAB visualization. It is observed that gravity and surface friction impede the flow direction with inclined magnetic field orientation which causes a decrease in velocity and an increase in the temperature profile. A declining trend is noted in the microbe profile due to higher values of the Peclet number and numeric growth in the value of the motile microbe's factor. Heat transport rate and drag force coefficients for both spherical and cylindrical nanoparticles differ by reasonable amounts. The proposed results build a bridge between traditional computational-based simulations and advanced ANN-based approaches, establishing a robust foundation for advanced applications in biomedical engineering.

The B-spline Quasi-Interpolation (BSQI) based numerical scheme is a successful method for obtaining the solution to partial differential equations under sufficient regularity conditions. However, it can lead to instability and spurious oscillations in the numerical solution when high gradients or discontinuities are present. To address this issue, this article proposes a hybrid version of the BSQI scheme to solve convection-diffusion problems. The hybrid scheme combines the Cubic BSQI (CBSQI) scheme with the fifth-order Weighted Essentially Non-Oscillatory (WENO) method to approximate the convective flux, and is able to compute the solution in a non-oscillatory manner. Further, we have introduced an approximate smoothness indicator for the larger stencil of the WENO scheme, derived from the smoothness indicator of the lower-order stencils. The approximate smoothness indicator is used as a troubled-cell indicator in a hybrid scheme and has allowed us to develop an efficient version of the WENO-AO(5,3) scheme (Balsara et al. J. Comp. Phy. 2016), which we call WENO-AOA(5,3) scheme. Additionally, we propose a fifth-order hybrid scheme that combines a finite-difference approximation with the WENO-AOA(5,3) scheme to solve convection-diffusion equations. To validate the proposed schemes, we conduct tests on multiple 1D and 2D cases. The hybrid schemes produce comparable results to the WENO scheme while being more computationally efficient. Specifically, the hybrid schemes are 50%–70% more efficient than the WENO-AOA(5,3) scheme, while the WENO-AOA(5,3) scheme has a 2%–15% advantage over the WENO-AO(5,3) scheme.