Computers & Fluids最新文献

In this paper, we propose a new high-order finite volume method for solving the multicomponent fluids problem with Mie–Grüneisen EOS. Firstly, based on the cell averages of conservative variables, we develop a procedure to reconstruct the cell averages of the primitive variables in a high-order manner. Secondly, the high-order reconstructions employed in computing numerical fluxes are implemented in a characteristic-wise manner to reduce numerical oscillations as much as possible and obtain high-resolution results. Thirdly, advection equation within the governing system is rewritten in a conservative form with a source term to enhance the scheme’s performance. We utilize integration by parts and high-order numerical integration techniques to handle the source terms. Finally, all variables are evolved by using Runge–Kutta time discretization. All steps are carefully designed to maintain the equilibrium of pressure and velocity for the interface-only problem, which is crucial in designing a high-resolution scheme and adapting to more complex multicomponent problems. We have performed extensive numerical tests for both one- and two-dimensional problems to verify our scheme’s high resolution and accuracy.

A fully coupled matrix-free method is developed for solving the incompressible steady-state Navier–Stokes equations on a collocated finite volume grid. This is achieved by offsetting the momentum equations relative to the continuity equation they are implicitly coupled to at each cell and updating the solution by sweeping planes in 3D and lines in 2D. The effect of sweeping direction on convergence rate is investigated for the 3D laminar lid driven cavity at Reynolds number 200 and 1000 and 3D laminar backwards facing step at Reynolds number 100 and 200. For these flow cases, a speed-up of up to an order of magnitude compared to SIMPLE schemes of OpenFOAM and ANSYS Fluent and the coupled solver of ANSYS Fluent was observed.

A high-order flux reconstruction solver has been developed and validated to perform implicit large-eddy simulations of industrially representative turbomachinery flows. The T106c low-pressure turbine and VKI LS89 high-pressure turbine cases are studied. The solver uses the Rusanov Riemann solver to compute the inviscid fluxes on the wall boundaries, and HLLC or Roe to evaluate inviscid fluxes for internal faces. The impact of Riemann solvers is demonstrated in terms of accuracy and non-linear stability for turbomachinery flows. It is found that HLLC is more robust than Roe, but both Riemann solvers produce very similar results if stable solutions can be obtained. For non-linear stabilization, a local modal filter, which combines a smooth indicator and a modal filter, is used to stabilize the solution. This approach requires a tuning parameter for the smoothness criterion. Detailed analysis has been provided to guide the selection of a suitable value for different spatial orders of accuracy. This local modal filter is also compared with the recent positivity-preserving entropy filter in terms of accuracy and stability for the LS89 turbine case. The entropy filter could stabilize the computation but is more dissipative than the local modal filter. Regarding the spanwise spacing of the grid, the case of the LS89 turbine shows that a $z^{+}$ of approximately $45-60$ is suitable for obtaining a satisfactory prediction of the heat transfer coefficient of the mean flow. This would allow for a coarse grid spacing in the spanwise direction and a cost-effective ILES aerothermal simulation for turbomachinery flows.

Microfluidic systems have various scientific and industrial applications, providing a powerful means to manipulate fluids and particles on a small scale. As a crucial method to underlying mechanisms and guiding the design of microfluidic devices, traditional numerical methods such as the Finite Element Method (FEM) simulating microfluidic systems are limited by the computational cost and mesh generating of resolving the smaller spatiotemporal features. Recently, a Physics-informed neural network (PINN) was introduced as a powerful numerical tool for solving partial differential equations (PDEs). PINN simplifies discretizing computational domains, ensuring accurate results and significantly improving computational efficiency after training. Therefore, we propose a PINN-based modeling framework to solve the governing equations of electrokinetic microfluidic systems. The neural networks, designed to respect the governing physics law such as Nernst-Planck, Poisson, and Navier-Stokes (NPN) equations defined by PDEs, are trained to approximate accurate solutions without requiring any labeled data. Several typical electrokinetic problems, such as Electromigration, Ion concentration polarization (ICP), and Electroosmotic flow (EOF), were investigated in this study. Notably, the findings demonstrate the exceptional capacity of the PINN framework to deliver high-precision outcomes for highly coupled multi-physics problems, particularly highlighted by the EOF case. When using 20 × 10 sample points to train the model (the same mesh nodes used for FEM), the relative error of EOF velocity from the PINN is ∼0.02 %, whereas the relative error of the FEM is ∼1.23 %. In addition, PINNs demonstrate excellent interpolation capability, the relative error of the EOF velocity decreases slightly at the interpolation points compared to training points, approximately 0.0001 %. More importantly, in simulating strongly nonlinear problems such as the ICP case, PINNs exhibit a unique advantage as they can provide accurate solutions with sparse sample points, whereas FEM fails to produce correct physical results using the same mesh nodes. Although the training time for PINN (100–200 min) is higher than the FEM computational time, the ability of PINN to achieve high accuracy results on sparse sample points, strong capability to fit nonlinear problems highlights its potential for reducing computational resources. We also demonstrate the ability of PINN to solve inverse problems in microfluidic systems and use transfer learning to accelerate PINN training for various species parameter settings. The numerical results demonstrate that the PINN model shows promising advantages in achieving high-accuracy solutions, modeling strong nolinear problems, strong interpolation capability, and inferring unknown parameters in simulating multi-physics coupling microfluidic systems.

It is well known that the collapse of heterogeneous multi-cavity near the wall will induce the fluctuation of the load field. To address this problem, the Lattice Boltzmann Method (LBM) is applied to model the three-phase coupling between gas-liquid-solid. The objective is to investigate the evolution of heterogeneous double bubbles and the spatial-temporal distribution characteristics of wall loads induced near the wall. In this study, the pseudopotential Multi-Relaxation-Time Lattice Boltzmann Model (MRT-LBM) and the Carnahan-Starling Equation of State (C-S-EOS) with an extended format for the external force term are used. The effects of the distance of the bubble to the wall, the pressure differences between the inside and outside of the bubble, and the relative size of the bubble on the dynamic evolution and the load distribution characteristics of heterogeneous multi-bubbles near the wall are investigated in order to determine the influence of these factors. Under a two-dimensional pressure field, the collapse process of double cavitation bubbles is visualized. Through the flow field, the morphological changes of the cavitation bubble collapse near the wall are also described. Various parameters are found to have an influence on the evolution of double cavitation bubbles near the wall and the resulting load field. The study employs the Lattice Boltzmann Method and the Potential Model for the analysis of the heterogeneous bubble collapses in the near wall region.

The present paper reports on the ability of neural networks (NN) and linear stochastic estimation (LSE) tools to predict the evolution of skin friction in a minimal turbulent channel ($R{e}_{\tau }=165$) after applying an actuation near the wall that is localized in space and time. Two different NN architectures are compared, namely multilayer perceptrons (MLP) and convolutional neural networks (CNN). The paper describes the effect that the predictive horizon and the type/size/number of wall-based sensors have on the performance of each estimator. The performance of MLPs and LSEs is very similar, and becomes independent of the sensor’s size when they are smaller than 60 wall units. For sufficiently small sensors, the CNN outperforms MLPs and LSEs, suggesting that CNNs are able incorporate some of the non-linearities of the near-wall cycle in their prediction of the skin friction evolution after the actuation. Indeed, the CNN is the only architecture able to achieve reasonable predictive capabilities using pressure sensors only. The predictive horizon has a strong effect on the predictive capacity of both NN and LSE, with a Pearson correlation coefficient that varies from 0.95 for short times (i.e., of the order of the actuation time) to less than 0.4 for times of the order of an eddy turn-over time. The analysis of the weights and filters in the LSE and NNs show that all estimators are targeting wall-signatures consistent with streaks, which is interpreted as the streak being the most causal feature in the near-wall cycle for the present forcing.

A hybrid neural network based on Densely Connected Convolutional Networks (DenseNet), Convolutional Long Short-Term Memory Neural Network (ConvLSTM), and Deconvolutional Neural Network (DeCNN) is employed to predict unsteady flow fields. The utilization of DenseNet makes the model more compact and makes the prediction of three-dimensional flow affordable. The ConvLSTM is implemented to predict multiple future time steps which improves prediction efficiency. The proposed model transforms the time sequences of velocity and pressure fields into uniform spatial–temporal topology as input and captures nonlinear feature information in the spatial–temporal domain. Numerical simulations are conducted for the flow around cylinder at different Reynolds numbers and the near-wall flow around cylinder with different gap ratios, and training samples for the neural network inputs are established. The predicted results are compared with the numerical simulation results, showing good agreement. From the prediction cycle, it can be seen that good prediction results can be maintained in the first three prediction cycles. The prediction results of the three-dimensional unsteady flow around a cylinder near a plane wall, exhibit remarkable accuracy, successfully capturing the evolution of turbulent vortex structures. This signifies that the prediction model is highly effective in capturing the spatial–temporal variations of complex unsteady flows.

We apply physics-informed neural networks to three-dimensional Rayleigh–Bénard convection in a cubic cell with a Rayleigh number of $\mathrm{Ra}=10^6$ and a Prandtl number of $\mathrm{Pr}=0.7$ to assimilate the velocity vector field from given temperature fields and vice versa. With the respective ground truth data provided by a direct numerical simulation, we are able to evaluate the performance of the different activation functions applied (sine, hyperbolic tangent and exponential linear unit) and different numbers of neurons (32, 64, 128, 256) for each of the five hidden layers of the multi-layer perceptron. The main result is that the use of a periodic activation function (sine) typically benefits the assimilation performance in terms of the analyzed metrics, correlation with the ground truth and mean average error. The higher quality of results from sine-activated physics-informed neural networks is also manifested in the probability density function and power spectra of the inferred velocity or temperature fields. Regarding the two assimilation directions, the assimilation of temperature fields based on velocities appears to be more challenging in the sense that it exhibits a sharper limit on the number of neurons below which viable assimilation results cannot be achieved.

The level-set based immersed interface method (IIM) for the elliptic interface problem is generalized to accommodate the interface intersecting the boundary. Finite difference schemes accounting for the jump conditions together with Neumann/periodic boundary condition are derived. It is easy for implementation. Numerical evidence indicates that the generalized IIM achieves the second-order accuracy in both solution and gradient. The method is coupled with a continuum surface method for simulating electrohydrodynamics with moving contact lines. Simulations demonstrate rich behaviors of the droplet. The effect of the electric field is studied. Although the method is presented in 2D, its extension to 3D is straight forward.

In this contribution, we address the numerical solutions of high-order asymptotic equivalent partial differential equations with the results of a lattice Boltzmann scheme for an inhomogeneous advection problem in one spatial dimension. We first derive a family of equivalent partial differential equations at various orders, and we compare the lattice Boltzmann experimental results with a spectral approximation of the differential equations. For an unsteady situation, we show that the initialization scheme at a sufficiently high order of the microscopic moments plays a crucial role to observe an asymptotic error consistent with the order of approximation. For a stationary long-time limit, we observe that the measured asymptotic error converges with a reduced order of precision compared to the one suggested by asymptotic analysis.