Computers & Fluids最新文献

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.

The advancement in programmable capability of graphics hardware has paved new opportunities in the domain of high performance computing (HPC). The computational fluid dynamics (CFD) community, being a significant user of HPC, has started exploiting the inherent data parallelism in the numerical solvers to be able to make efficient use of these many-core, high throughput accelerator based processors. In the present work, we examine the process of accelerating our CPU based Staggered Update Procedure (SUP) solver, i.e., a higher order accurate cell-centred finite volume solver by off-loading the computationally most expensive region of the code pertaining to the explicit residual computation. We have adopted OpenACC, a directive based programming model to expose parallelism in the code. The framework evolved for GPU porting in the context of SUP is also of value to those intending to port their CFD solvers based on classical finite volume methodology. The performance analysis is conducted using scalar convection–diffusion equations in both two- and three-dimensions. The findings demonstrate a speedup factor of 9 (in case of 2D) and 28 (in case of 3D) when considering the explicit residual alone, achieved with a single NVIDIA Tesla V100 GPU card. In addition, we could establish superior algorithmic scalability by the way of recovering near perfect serial performance, on the heterogeneous CPU+GPU architecture. Further, overall code acceleration can be achieved by porting other parts of the solver on GPU.

This paper presents a state of the art on port-Hamiltonian formulations for the modeling and numerical simulation of open fluid systems. This literature review, with the help of more than one hundred classified references, highlights the main features, the positioning with respect to seminal works from the literature on this topic, and the advantages provided by such a framework. A focus is given on the shallow water equations and the incompressible Navier–Stokes equations in 2D, including numerical simulation results. It is also shown how it opens very stimulating and promising research lines towards thermodynamically consistent modeling and structure-preserving numerical methods for the simulation of complex fluid systems in interaction with their environment.

The primary goal of this study is to introduce deep learning (DL) methods as a cost-effective alternative to the computationally intensive Direct Numerical Simulation (DNS) simulations. We show that one can obtain a parametric field from a low-resolution input and map it to a fine grid output, significantly reducing the computational burden. We assess five super-resolution models for up-scaling low-resolution flow data into fine-grid numerical simulations’ output for accuracy and efficiency. The proposed architectures employ convolutional neural networks interconnected in encoder/decoder branches. We investigate these models using turbulent velocity fields inside a suddenly expanded channel characterized by complex features, including turbulence, instabilities, asymmetries, separation, and reattachment. Our results reveal that an encoder/decoder model with residual connections delivers the fastest results, a U-Net-based model with skip connections excels at producing sharper edges in regions prone to blurring, while deeper models incorporating maximum and average pooling layers show superior performance in reconstructing velocity profiles. These findings significantly contribute to our understanding of the potential of deep learning in fluid mechanics. The models presented in this study are trained and validated on standard computer hardware and can be easily adapted to other problems. The findings are promising for discovering and analyzing flow physics, highlighting the potential for DL techniques to improve the accuracy of the available fluid mechanics computational tools.