Lid-driven Cavity Flow Research Articles

Large-Scale Cluster Parallel Strategy for Regularized Lattice Boltzmann Method with Sub-Grid Scale Model in Large Eddy Simulation

As an improved method of the lattice Boltzmann method (LBM), the regularized lattice Boltzmann method (RLBM) has been widely used to simulate fluid flow. For solving high Reynolds number problems, large eddy simulation (LES) and RLBM can be combined. The computation of fluid flow problems often requires a large number of computational grids and large-scale parallel clusters. Therefore, the high scalability parallel algorithm of RLBM with LES on a large-scale cluster has been proposed in this paper. The proposed parallel algorithm can solve complex flow problems with large-scale Cartesian grids and high Reynolds numbers. In order to achieve computational load balancing, the domain decomposition method (DDM) has been used in large-scale mesh generation. Three mesh generation strategies are adopted, namely 1D, 2D and 3D. Then, the buffer on the grid interface is introduced and the corresponding 1D, 2D and 3D parallel data exchange strategies are proposed. For the 3D lid-driven cavity flow and incompressible flow around a sphere under a high Reynolds number, the given parallel algorithm is analyzed in detail. Experimental results show that the proposed parallel algorithm has a high scalability and accuracy on hundreds of thousands of cores.

An optimisation–based domain–decomposition reduced order model for the incompressible Navier-Stokes equations

The aim of this work is to present a model reduction technique in the framework of optimal control problems for partial differential equations. We combine two approaches used for reducing the computational cost of the mathematical numerical models: domain–decomposition (DD) methods and reduced–order modelling (ROM). In particular, we consider an optimisation–based domain–decomposition algorithm for the parameter–dependent stationary incompressible Navier–Stokes equations. Firstly, the problem is described on the subdomains coupled at the interface and solved through an optimal control problem, which leads to the complete separation of the subdomain problems in the DD method. On top of that, a reduced model for the obtained optimal–control problem is built; the procedure is based on the Proper Orthogonal Decomposition technique and a further Galerkin projection. The presented methodology is tested on two fluid dynamics benchmarks: the stationary backward–facing step and lid-driven cavity flow. The numerical tests show a significant reduction of the computational costs in terms of both the problem dimensions and the number of optimisation iterations in the domain–decomposition algorithm.

An efficient framework for solving forward and inverse problems of nonlinear partial differential equations via enhanced physics-informed neural network based on adaptive learning

In recent years, the advancement of deep learning has led to the utilization of related technologies to enhance the efficiency and accuracy of scientific computing. Physics-Informed Neural Networks (PINNs) are a type of deep learning method applied to scientific computing, widely used to solve various partial differential equations (PDEs), demonstrating tremendous potential. This study improved upon original PINNs and applied them to forward and inverse problems in the nonlinear science field. In addition to incorporating the constraints of PDEs, the improved PINNs added constraints on gradient information, which further enhanced the physical constraints. Moreover, an adaptive learning method was used to update the weight coefficients of the loss function and dynamically adjust the weight proportion of each constraint term. In the experiment, the improved PINNs were used to numerically simulate localized waves and two-dimensional lid-driven cavity flow described by partial differential equations. Meanwhile, we critically evaluate the accuracy of the prediction results. Furthermore, the improved PINNs were utilized to solve the inverse problems of nonlinear PDEs, where the results showed that even with noisy data, the unknown parameters could be discovered satisfactorily. The study results indicated that the improved PINNs were significantly superior to original PINNs, with shorter training time, increased accuracy in prediction results, and greater potential for application.

Numerical Simulation and Computational Fluid Dynamics Analysis of Two-Dimensional Lid-Driven Cavity Flow Within the Weapon Bay of an Autonomous Fighter Drone

The efficient deployment of weapons in military operations is critical for mission success, and the flow of air within the weapon bay of an autonomous fighter drone plays a vital role in achieving this objective. In this paper, we present a comprehensive numerical simulation and computational fluid dynamics (CFD) analysis of the three-dimensional lid-driven cavity flow within the weapon bay of an autonomous fighter drone. To address this challenging problem, we employ CFD analysis and a multigrid approach to solve the Navier-Stokes equations for the aerodynamic problem. Our simulations include high Reynolds numbers of up to 10,000, which demonstrates the potential of CFD analysis in optimizing the design of autonomous fighter drones for military operations. We evaluate the effectiveness of the linked strongly implicit multigrid technique in estimating high-Re fine-mesh flow solutions using the vorticity-stream function formulation of the two-dimensional incompressible Navier-Stokes equations. The model issue is the driven flow in a square cavity, and we consider meshes up to 1024 x 1024 points and combinations with Reynolds numbers as high as 1000. To further improve the accuracy of our simulations, we employ one-dimensional grid clustering coordinate transformations instead of uniform mesh refinement, as the flow field exhibits one or more secondary vortices. Our findings demonstrate that CFD analysis can provide valuable insights into the complex flow dynamics within the weapon bay of autonomous fighter drones, which can lead to the optimization of their design for enhanced mission capabilities. Overall, our study highlights the significance of numerical simulations and CFD analysis in the design and optimization of autonomous fighter drones for military applications. Our results can serve as a basis for future research in the field of UAV aerodynamics and contribute to the development of more efficient and effective military operations.

GPU implementation of the discrete unified gas kinetic scheme for low-speed isothermal flows

In this paper, two GPU parallel algorithms are proposed for the discrete unified gas kinetic scheme (DUGKS) for simulating low-speed isothermal flows. Algorithm-I uses a two-level fine-grain technique for the parallelization of physical spatial space, while Algorithm-II adopts this technique for both physical spatial and particle velocity spaces. To evaluate the performance of the proposed algorithms, several typical benchmark problems are simulated, including the two-dimensional (2D) and three-dimensional (3D) lid-driven cavity flows, the micro channel and cavity flows. Numerical results show that our GPU algorithms can achieve satisfactory computational efficiency. For Algorithm-I, the speedup can reach 250 and 338 on a Tesla V100 GPU card for the 2D and 3D continuum cavity flows, respectively, and a hundredfold acceleration can be obtained for the rarefied cases. While for Algorithm-II, a speedup of about 70 can be attained for rarefied cases. However, it is not applied to continuum problems that only require a small number of velocity points. Moreover, comparisons between the two GPU algorithms are also conducted for the rarefied flows with various grid meshes and velocity directions. The results show that Algorithm-I performs better when physical mesh size is large, while Algorithm-II can provide higher efficiency for a coarser mesh with medium number of discrete velocities. Special attention is also paid to comparisons between Algorithm-I and MPI parallelization with 128 CPU cores based on physical space discretization approach, and it is found that Algorithm-I has a clear advantage on V100 GPU when dealing with sparse physical grids in both continuum and rarefied cases.

An incompressible flow solver on a GPU/CPU heterogeneous architecture parallel computing platform

A computational fluid dynamics (CFD) solver for a GPU/CPU heterogeneous architecture parallel computing platform is developed to simulate incompressible flows on billion-level grid points. To solve the Poisson equation, the conjugate gradient method is used as a basic solver, and a Chebyshev method in combination with a Jacobi sub-preconditioner is used as a preconditioner. The developed CFD solver shows good performance on parallel efficiency, which exceeds 90% in the weak-scalability test when the number of grid points allocated to each GPU card is greater than 2083. In the acceleration test, it is found that running a simulation with 10403 grid points on 125 GPU cards accelerates by 203.6x over the same number of CPU cores. The developed solver is then tested in the context of a two-dimensional lid-driven cavity flow and three-dimensional Taylor-Green vortex flow. The results are consistent with previous results in the literature.

Solution of conservative-form transport equations with physics-informed neural network

Physics-informed neural network (PINN) has recently gained significant attention in the field of scientific computing. This paper proposes a PINN framework for solving conservative-form transport equations (PINNforCTE). The PINNforCTE features an accelerated back-propagation in the neural network (NN) training due to low-order derivatives in the governing equations. We demonstrate the application of PINNforCTE in simulating a classical flow and heat transfer problem, i.e., the lid-driven cavity flow and heat transfer under three types of boundary conditions, and the simulation results are compared with those obtained from the traditional PINN and the finite element CFD method. The comparisons indicate that PINNforCTE can significantly accelerate the NN training and potentially shorten the solution time. For all cases considered, the training time of PINNforCTE is reduced by approximately ∼50% compared with the conventional PINN. Furthermore, PINNforCTE can accelerate the Adam optimization algorithm (L-BFGS-B optimization algorithm) by ∼100% (∼80%) compared to the traditional PINN. Additionally, PINNforCTE shows greater convenience in applying the Neumann and Robin boundary conditions directly and higher calculation accuracy than the conventional PINN. Finally, the ability of PINNforCTE to solve the inverse problems is confirmed with an example of 2D steady lid-driven cavity flow and heat transfer. PINNforCTE is an efficient NN solver for conservative-form transport equations (CTEs) that are ubiquitous in science and engineering.

An improved MRT-LBM and investigation to the transition and periodicity of 2D lid-driven cavity flow with high Reynolds numbers

An improved MRT-LBM and investigation to the transition and periodicity of 2D lid-driven cavity flow with high Reynolds numbers

Application of Weighted Least Squares Meshless Method to Incompressible Flows

Meshless methods have been successfully applied to solve a large number of inviscid and viscous compressible flows in both two and three dimensional flow fields. However, the conventional methods of solution for compressible flow equations cannot be applied to incompressible flow equations. This is due to the basic difference in the nature of the pressure variable in the compressible and incompressible flows. Pressure acts as a thermodynamic variable in case of compressible flows and can be easily updated by using the equation of state. In contrast, in case of incompressible flows, the pressure is merely responsible for enforcing the incompressibility constraint and hence cannot be updated by the equation of state. This has led to the development of numerical methods based on Helmholtz Decomposition to solve for the fluid flows in the incompressible flow regimes. Here, we have applied weighted least squares meshless method to solve for the flows in the incompressible flow regime using the projection method based on Helmholtz Decomposition. The standard test cases of two dimensional lid driven cavity flow at Reynolds numbers of 100, 400 and 1000 have been solved using the weighted least squares meshless method. A good match between the results of the test case using the meshless methods and conventional CFD methods for the solution of the incompressible flows has been obtained.

Multi-degree-of-freedom kinetic model and its applications in simulation of three-dimensional nonequilibrium flows

A multi-degree-of-freedom (MDOF) kinetic model is developed to simulate three-dimensional nonequilibrium flows. By modifying collision term of Boltzmann model equation, a multi-scale molecular collision mechanism with translational, rotational and vibrational degrees of freedom is indicated by three coupled relaxation processes. Molecular vibration is modeled by harmonic oscillator. As a result, the degree of freedom of vibration may be directly related to temperature. Internal energy of various degrees of freedom are computed based on the equipartition theorem, and equilibrium distribution functions for each relaxation step are calculated. The present MDOF kinetic model is beneficial for assessing multi-scale evolutions of internal energy and molecular inelastic collisions. Several three-dimensional flow cases, including lid-driven cavity flow and hypersonic flows around a blunt cone at varying angles of attack, are simulated using the current MDOF technique. All numerical results were consistent with the reference data. It was shown that the proposed MDOF kinetic model well explains the vibration–rotation-translation energy exchange of polyatomic molecules in high-temperature gas, and that the current computational technique is a useful engineering tool for nonequilibrium aerodynamic research.

Non-uniform Compact Schemes for Parallel Computing

Here, the performance of a sixth order accurate Non-Uniform Compact Scheme (NUCS6) in a parallel framework using the domain decomposition method is analyzed. Traditional compact schemes are used for uniform grids. However, study of flows involving complicated geometries requires transformation of computational domain onto a uniform grid. Compact schemes developed for physical plane computations eliminate the need for such grid transformations. The first successful implementation of uniform compact schemes on a parallelized framework with Schwartz domain decomposition demonstrated the effect of overlap points in eliminating spurious signals at inter-processor boundaries Sengupta et al. [Jour. Comp. Phy. 220 (2007)]. This paper presents the performance of a high order non-uniform compact scheme (NUCS6) in parallel computations with the domain decomposition method. The results of the benchmark problem of flow in a 2D square lid-driven cavity at post-Hopf bifurcation Reynolds number of 10000 is presented to show how the width of overlap region affects the growth and evolution of gyrating polygonal vortex at the centre of the cavity.

Radial basis function-differential quadrature-based physics-informed neural network for steady incompressible flows

In this work, a radial basis function differential quadrature-based physics-informed neural network (RBFDQ-PINN) is proposed to simulate steady incompressible flows. The conventional physics-informed neural network (PINN) makes use of the physical equation as a constraint to ensure that the solution satisfies the physical law and the automatic differentiation (AD) method to calculate derivatives at collocation points. Although the AD-PINN is expedient in evaluating derivatives at arbitrary points, it is time-consuming with higher-order derivatives and may lead to nonphysical solutions with sparse samples. Alternatively, the finite difference (FD) method can facilitate the calculation of derivatives, but the FD-PINN will increase the computational cost when handling random point distributions, especially with higher-order discretization schemes. To address these issues, the radial basis function differential quadrature (RBFDQ) method is incorporated into the PINN to replace the AD method for the calculation of derivatives. The RBFDQ method equips with high efficiency in the calculation of high-order derivatives as compared with the AD method and great flexibility in the distribution of mesh points as compared with the FD method. As a result, the proposed RBFDQ-PINN is not only more efficient and accurate but also applicable to irregular geometries. To demonstrate its effectiveness, the RBFDQ-PINN is tested in sample problems such as the lid-driven cavity flow, the channel flow over a backward-facing step, and the flow around a circular cylinder. Numerical results reveal that the RBFDQ-PINN achieves satisfactory accuracy without any labeled collocation points, whereas the AD-PINN struggles to solve some cases, especially for high Reynolds number flows.

A theoretical framework of information preservation method and its application to low-speed nonequilibrium gas flows

Simulations of nonequilibrium gas flows have garnered significant interest in modern engineering problems involving rarefied gas flow characteristics. Despite the popularity of the direct simulation Monte Carlo (DSMC) method in simulating such flows, its use in low-speed flows is limited by statistical noises. The information preservation (IP) method is a promising alternative known for its low noise properties. In this study, a new theoretical framework for the IP method based on kinetic theory is introduced to offer complete understanding for the transport properties of the preserved information. Specifically, we introduce a velocity-information joint distribution function (VIJDF) and derive its governing equation as well as the corresponding macroscopic transport equations. To ensure the accuracy of the IP method, the total stress/heat flux in IP, including information stress/heat flux generated during movement and collision steps and compensation stress/heat flux imposed in the compensation step, is matched to the molecular stress/heat flux in DSMC. To this end, a nonequilibrium model for the VIJDF is proposed to evaluate the compensation stress/heat flux. The parameters in the collision model of IP are theoretically determined by equating the transport coefficients associated with the preserved information to the coefficients of viscosity and thermal conductivity in DSMC. Numerical simulations for a variety of nonequilibrium gas flows, including low-speed Couette flow, Fourier flow, high-speed Couette flow, external force-driven Poiseuille flow, lid-driven cavity flow, and thermal creep flow, demonstrate that the IP method can achieve similar accuracy as the DSMC method with a much smaller sampling size.

A multiscale discrete velocity method for diatomic molecular gas

In the previous study, the multiscale discrete velocity method (MDVM) has been developed for monatomic gas with particle translational motion only. Unlike the unified gas-kinetic scheme (UGKS) and discrete unified gas-kinetic scheme, which are the typical representative of multiscale kinetic methods, MDVM achieves multiscale property by mixing the solution of macroscopic control equations and the Boltzmann equation, without the need to calculate complex interface flux. Therefore, MDVM has a higher computational efficiency. To broaden the application scope of MDVM, the Rykov model, which elucidates the exchange of energy between molecular translational and rotational energies, is introduced into MDVM in this paper. Numerical simulations are conducted for various cases, including one-dimensional shock tube, one-dimensional nitrogen shock structure, two-dimensional lid-driven cavity flow, and two-dimensional hypersonic flows around a flat plate and a blunt circular cylinder. The present results agree well with those from the diatomic UGKS method, demonstrating the developed diatomic MDVM can simulate multi-scale, strongly non-equilibrium, diatomic molecular gas flow while exhibiting certain efficiency improvements compared to the diatomic UGKS.

Exploring role of aspect ratio for compressible flow in a rectangular lid-driven cavity with a vertical temperature gradient

Numerical investigation of a compressible fluid in a two-dimensional rectangular lid-driven cavity (LDC) with a vertical temperature gradient is performed by solving the compressible Navier–Stokes equation. Here, we explore the role of aspect ratio (AR) (width/height) on the vorticity dynamics and redistribution by considering three ARs of 1:1, 2:1, and 3:1. The onset and propagation of the instability are explored via time-resolved and instantaneous distributions of vorticity, time-series of streamwise velocity, and its associated spectra. The flow physics reveal that the precessing vortical structures in certain square sub-cells of the rectangular LDC resemble that of orbital motion with a primary core eddy surrounded by gyrating satellite vortices, typical of a supercritical flow in a square LDC. Upon increasing the AR, there is a major shift in the vorticity transfer from the top right corner (acting as the source of maximum vorticity generation) toward the left square sub-cells in the domain. This is further aided by the convective motion due to the imposed destabilizing vertical thermal gradient. The spectra demonstrate that a multi-periodic, chaotic flow is the consistent flow feature for the rectangular LDC for Re = 5500, irrespective of the AR. The compressible enstrophy budget of the rectangular LDC with varying AR is computed for the first time. This shows the dominance of the baroclinic vorticity over the viscous diffusion terms, which was conceived of as the major contributor to the creation of rotational flow structures.

Exploring the periodic behavior of the lid-driven cavity flow filled with a Bingham fluid

Exploring the periodic behavior of the lid-driven cavity flow filled with a Bingham fluid

Novel Schemes of No-Slip Boundary Conditions for the Discrete Unified Gas Kinetic Scheme Based on the Moment Constraints.

The boundary conditions are crucial for numerical methods. This study aims to contribute to this growing area of research by exploring boundary conditions for the discrete unified gas kinetic scheme (DUGKS). The importance and originality of this study are that it assesses and validates the novel schemes of the bounce back (BB), non-equilibrium bounce back (NEBB), and Moment-based boundary conditions for the DUGKS, which translate boundary conditions into constraints on the transformed distribution functions at a half time step based on the moment constraints. A theoretical assessment shows that both present NEBB and Moment-based schemes for the DUGKS can implement a no-slip condition at the wall boundary without slip error. The present schemes are validated by numerical simulations of Couette flow, Poiseuille flow, Lid-driven cavity flow, dipole-wall collision, and Rayleigh-Taylor instability. The present schemes of second-order accuracy are more accurate than the original schemes. Both present NEBB and Moment-based schemes are more accurate than the present BB scheme in most cases and have higher computational efficiency than the present BB scheme in the simulation of Couette flow at high Re. The present Moment-based scheme is more accurate than the present BB, NEBB schemes, and reference schemes in the simulation of Poiseuille flow and dipole-wall collision, compared to the analytical solution and reference data. Good agreement with reference data in the numerical simulation of Rayleigh-Taylor instability shows that they are also of use to the multiphase flow. The present Moment-based scheme is more competitive in boundary conditions for the DUGKS.

Computational study of rarefied gas flow and heat transfer in lid-driven cylindrical cavities

The gas flow characteristics in lid-driven cavities are influenced by several factors, such as the cavity geometry, gas properties, and boundary conditions. In this study, the physics of heat and gas flow in cylindrical lid-driven cavities with various cross sections, including fully or partially rounded edges, is investigated through numerical simulations using the direct simulation Monte Carlo (DSMC) and the discrete unified gas kinetic scheme (DUGKS) methods. The thermal and fluid flow fields are systematically studied for both constant and oscillatory lid velocities, for various degrees of gas rarefaction ranging from the slip to the free-molecular regimes. The impact of expansion cooling and viscous dissipation on the thermal and flow fields, as well as the occurrence of counter-gradient heat transfer (also known as anti-Fourier heat transfer) under non-equilibrium conditions, is explained based on the results obtained from numerical simulations. Furthermore, the influence of the incomplete tangential accommodation coefficient on the thermal and fluid flow fields is discussed. A comparison is made between the thermal and fluid flow fields predicted in cylindrical cavities and those in square-shaped cavities. The present work contributes to the advancement of micro-/nano-electromechanical systems by providing valuable insight into rarefied gas flow and heat transfer in lid-driven cavities.

Streamline analysis of MHD flow in a double lid-driven cavity

The magnetohydrodynamic flow of an incompressible, steady and electrically conducting fluid is considered in double lid-driven square cavity under an inclined magnetic field. The non-dimensional governing equations are solved numerically using a radial basis function (RBF) approximation meshless method in order to obtain the flow patterns. Hartmann number [Formula: see text] and the inclination angle of magnetic field [Formula: see text] are taken as a problem variables that produce various flow transformations by their variation for [Formula: see text]. Streamlines are examined topologically, and it has been observed that the inclination angle and strength of magnetic field have different influence on the bifurcation of flow structures.

A Review Study of Numerical Simulation of Lid-Driven Cavity Flow with Nanofluids

Perhaps the most deliberated fluid problem in the field of Computational Fluid Dynamics is the lid driven cavity flow whose simple geometry is used to study the thermal behavior of many engineering applications such as cooling of electronic equipment, solar collectors, thermal storage systems, food processing, solar ponds, crystal growth, lubrication technologies and cooling of electrical and mechanical components. Researchers have been devoting much of their time in order to discover innovative methods to enhance the thermal conductivity of conventional fluids. With the development of nanotechnology, the concept of nanofluids has gained ground considerably as a new kind of heat transfer fluid. Nanofluid is a new kind of fluid with high thermal conductivity is a mixture of solid nanoparticles and a liquid. This review recapitulates the recent progress of the various numerical methods that are used in predicting the influence of several parameters such as type of nanoparticle and host liquid, particle volume concentration, particle size and shape, Brownian diffusion and thermophoresis effect on hydrodynamic and thermal characteristics of convective heat transfer using nanofluids in a lid driven cavity.