Numerical Simulation Of Incompressible Flows Research Articles

A Fast Hybrid Pressure-Correction Algorithm for Simulating Incompressible Flows by Projection Methods

To enforce the conservation of mass principle, a pressure Poisson equation arises in the numerical solution of incompressible fluid flow using the pressure-based segregated algorithms such as projection methods. For unsteady flows, the pressure Poisson equation is solved at each time step usually in physical space using iterative solvers, and the resulting pressure gradient is then applied to make the velocity field divergence-free. It is generally accepted that this pressure-correction stage is the most time-consuming part of the flow solver and any meaningful acceleration would contribute significantly to the overall computational efficiency. The objective of the present work was to develop a fast hybrid pressure-correction algorithm for numerical simulation of incompressible flows around obstacles in the context of projection methods. The key idea is to adopt different numerical methods/discretisations in the sub-steps of projection methods. Here, a classical second-order time-marching projection method, which consists of two sub-steps, was chosen for the purposes of demonstration. In the first sub-step, the momentum equations were discretised on unstructured grids and solved by conventional numerical methods, here a meshless method. In the second sub-step (pressure-correction), the proposed algorithm adopts a double-discretisation system and combines the weighted least-squares approximation with the essence of immersed boundary methods. Such a design allowed us to develop an FFT-based solver to speed up the solution of the pressure Poisson equation for flow cases with obstacles, while keeping the implementation of the boundary conditions for the momentum equations as easy as conventional numerical methods do with unstructured grids. The numerical experiments of five test cases were performed to verify and validate the proposed hybrid algorithm and evaluate its computational performance. The results showed that the new FFT-based hybrid algorithm works and is robust, and it was significantly faster than the multigrid-based reference method. The hybrid algorithm opens an avenue for the development of next-generation high-performance parallel computational fluid dynamics solvers for incompressible flows.

Super-resolution of low-fidelity flow solutions via generative adversarial networks

While computational fluid dynamics (CFD) can solve a wide variety of fluid flow problems, accurate CFD simulations require significant computational resources and time. We propose a general method for super-resolution of low-fidelity flow simulations using deep learning. The approach is based on a conditional generative adversarial network (GAN) with inexpensive, low-fidelity solutions as inputs and high-fidelity simulations as outputs. The details, including the flexible structure, unique loss functions, and handling strategies, are thoroughly discussed, and the methodology is demonstrated using numerical simulations of incompressible flows. The distinction between low- and high-fidelity solutions is made in terms of discretization and physical modeling errors. Numerical experiments demonstrate that the approach is capable of accurately forecasting high-fidelity simulations.

Aerodynamic Characteristics Analysis of Ultra-High-Speed Elevator with Different Hoistway Structures

The high-speed airflow generated by ultra-high-speed elevators causes significant aerodynamic force, which seriously reduces the comfort and safety of passengers. First, a multi-parameter general model of ultra-high-speed elevator was established, and the three-dimensional numerical simulation of incompressible flow in the ultra-high-speed elevator was simulated. The correctness of the model and method was verified by experiments and grid-independence analyses. On this basis, the variation in the aerodynamic forces and the pressure in the hoistway was analyzed. Finally, the influence of different hoistway structures and parameters of ventilation holes on the aerodynamic forces and hoistway pressure were analyzed. The results showed that the opening of ventilation holes significantly reduced the aerodynamic forces and hoistway pressure for most of the period of the car’s operation period, but both the aerodynamic forces and hoistway pressure showed a sudden increase–decrease process. The aerodynamic forces and hoistway pressure were highly sensitive to changes in the hoistway blockage ratio, the cross-sectional area of the ventilation hole, and the position of the ventilation hole. When a pair of ventilation holes were opened, those in the middle of the hoistway reduced aerodynamic problems in the hoistway to the greatest extent. The increase in the connection angle between the ventilation hole and the hoistway eliminated the low-speed recirculation zone at the ventilation hole and increased the total volume of exhaust air at the ventilation hole.

Direct numerical simulation of incompressible flows on parallel Octree grids

We introduce an approach for solving the incompressible Navier-Stokes equations on a forest of Octree grids in a parallel environment. The methodology uses the p4est library of Burstedde et al. (2011) [15] for the construction and the handling of forests of Octree meshes on massively parallel distributed machines and the framework of Mirzadeh et al. (2016) [54] for the discretizations on Octree data structures. We introduce relevant additional parallel algorithms and provide performance analyses for individual building bricks and for the full solver. We demonstrate strong scaling for the solver up to 32,768 cores for a problem involving O(6.1×108) computational cells. We illustrate the dynamic adaptive capabilities of our approach by simulating flows past a stationary sphere, flows due to an oscillatory sphere in a closed box and transport of a passive scalar. Without sacrificing accuracy nor spatial resolution in regions of interest, our approach successfully reduces the number of computational cells to (at most) a few percents of uniform grids with equivalent resolution. We also perform a numerical simulation of the turbulent flow in a superhydrophobic channel with unparalleled wall grid resolution in the streamwise and spanwise directions.

Lagrangian finite-difference method for predicting green water loadings

A meshless CFD method is proposed for numerical simulation of incompressible flows and estimation of hydrodynamic loads during green water events. In this paper, governing equations are described in Finite Differences context, where spatial operators are derived using Weighted-Least Squares. Volume-conservative Lagrangian advection is handled by solving a set of geometrical constraints, while adjusting to moving boundaries represented by triangulated meshes. The validation of the method is performed by simulating four green-water experiments on fixed and moving structures, and comparing the kinematics of flow and hydrodynamic loads during impacts. It is shown that the method accurately reproduces patterns of waves that are wetting the deck, as well as the pressure distribution along the deck. The resulting method intrinsically handles violent fluid–structure interaction with free surface fragmentation, while providing second-order accurate pressure field.

A Numerical Study on the Flow Mechanism of Performance Improvement of a Wide-Angle Diffuser by Inserting a Short Splitter Vane

Usage of a wide-angle diffuser may result in unfavorable separated flow and a significant diffuser loss. To improve the performance of the diffusers, inserting short splitter vanes is known as a useful method that has been demonstrated experimentally. Regarding the role of the vane in the diffuser flow, Senoo & Nishi (1977) qualitatively explained that the lift force acting on the vane should be a key factor. However, its quantitative verification remains since then. To challenge this issue, numerical simulations of incompressible flow in a wide angle of 28° two-dimensional diffuser with and without a short splitter vane were conducted in the present study. An improvement of pressure-recovery by the vane and oscillatory flows in the diffuser are reasonably reproduced from comparison with the experimental results made by Cochran & Kline (1958). It is also found that the lift force acting on the vane varies periodically in an opposite phase with the detachment point moved back and forth on a diverging wall, since one vane is not sufficient to fully suppress the flow separation that occurred on the wall and the incoming main-flow shifts toward the other diverging wall in the diffuser. Thus, as a role of splitter vane in the diffuser, “the lift force of the vane is a key factor” may be quantitatively verified from the present numerical simulation. Further, it is confirmed by the local loss analysis that the turbulent kinetic energy production observed in mixing layers contributes most of the loss in the diffuser. Consequently, the present numerical technique may be usable to investigate the flow character in a diffuser with splitter vanes at a design stage.

Numerical Analysis of a Projection-Based Stabilized POD-ROM for Incompressible Flows

In this paper, we propose a new stabilized projection-based proper orthogonal decomposition reduced order model (POD-ROM) for the numerical simulation of incompressible flows. The new method draws ...

Unsteady Preconditioned Characteristic Boundary Conditions for Direct Numerical Simulation of Incompressible Flows

The unsteady preconditioned characteristic boundary conditions (UPCBCs) based on the artificial compressibility (AC) method are formulated and applied at artificial boundaries for the direct numerical simulation (DNS) of incompressible flows. The compatibility equations including the unsteady terms are mathematically derived in the generalized curvilinear coordinates and then incorporated as boundary conditions (BCs) in a high-order accurate incompressible flow solver. The spatial derivative terms of the system of equations are discretized using the fourth-order compact finite difference (FD) scheme, consistent with the high-order accuracy required for the DNS. The time integration is carried out using an implicit dual time-stepping method, and the robustness and performance of the numerical algorithm are enhanced by applying the preconditioning technique and calculating the automated AC parameter based on the local flow conditions. At first, the steady viscous incompressible flow for a two-dimensional plane jet is computed to assess the accuracy and performance of the solution method by applying the UPCBCs in comparison with the simplified BCs. Then, the simulation of the unsteady incompressible viscous flow around a two-dimensional NACA0012 airfoil at the Reynolds number 800 and the angle of attack 20° is performed, and it is indicated that the computational cost of the solution is considerably decreased by implementing the UPCBCs at the artificial far-field boundary compared with the simplified BCs, which is remarkably valuable for the DNSs. Finally, the computation of the transition to unsteady for the incompressible flow around a three-dimensional NACA0012 wing at the same conditions of the two-dimensional case is successfully performed, and the results obtained are compared with those of previous studies that exhibit good agreement. Indications are that the present solution method by applying the UPCBCs at the artificial far-field boundary can be effectively used for the DNSs of the incompressible flows.

Flow separation prevention around a NACA0012 profile through multivariable feedback controlled plasma actuators

In the present paper, the problem of controlling the unsteady flow separation over an aerofoil, using plasma actuators, is addressed. Although a plasma flow is essentially a two-phase flow, it has been proved that a local force term may be successfully considered within a flow solver in order to mimic the effect of a local acceleration (see [63]). By exploiting the Chimera Overlapping Grids technique to allow the inclusion of one or more actuators, accurate numerical simulations have been carried out with the in-house Finite Volume solver Xnavis. The effects of varying both number and position of the actuator/sensor pairs along the aerofoil are investigated by focusing on the dynamic control of the boundary layer separation. The capabilities of the proposed control strategy are also examined by showing how the practical flow separation control problem can be formulated as a simple output regulation problem, so that a simple control strategy may be used. Several numerical simulations of incompressible flows around a pitching NACA0012 at Reynolds Re=20,000 illustrate the effectiveness of the proposed approach, in the presence of time-varying angles of attack and complex non-linear dynamics, which are neglected in the control design. The present work extends the former paper of Broglia et al. [2], where the control algorithm was applied to the simple case of single input/single output regulation and implemented in a Finite Elements numerical code; in that work the boundary layer control of an airfoil at fixed angle of attack was addressed. In the present paper a multi input/multi output approach is theoretically developed and numerically implemented. Robust and fast flow reattachment is achieved, along with both stabilisation and increase/reduction of the lift/drag, respectively. A major advantage of the presented method is that the chosen controlled outputs can be easily measured in realistic applications.

Two-Dimensional Numerical Simulation of Fluid Flow using Weakly Compressible Explicit Scheme and Its Verification

This study concerns a numerical simulation method of incompressible fluid flows using a weakly compressible explicit scheme and its verification. The Entropically Damped Artificial Compressibility (EDAC) method, one of weakly compressible explicit schemes, is applied for simulations of low-Reynolds number flows with an inlet and outlet. The non-reflective characteristic boundary condition is imposed on the velocity field, and the convective outflow condition is imposed on the pressure field. The Pseudo Crank-Nicolson method with the upstream-shifted interpolation is used for the time discretization. The implemented numerical method is applied to simulate a lid-driven cavity flow and a plane Poiseuille flow. The simulation results agree well with the existing results, then demonstrating the suitability of the method to numerical simulations of incompressible flows.

Combined immersed boundary method and multiple-relaxation-time lattice Boltzmann flux solver for numerical simulations of incompressible flows

method combining the immersed boundary technique and a multi-relaxation-time (MRT) lattice Boltzmann flux solver (LBFS) is presented for numerical simulation of incompressible flows over circular and elliptic cylinders and NACA 0012 Airfoil. The method uses a simple Cartesian mesh to simulate flows past immersed complicated bodies. With the Chapman-Enskog expansion analysis, a transform is performed between the Navier-Stokes and lattice Boltzmann equations (LBEs). The LBFS is used to discretize the macroscopic differential equations with a finite volume method and evaluate the interface fluxes through local reconstruction of the lattice Boltzmann solution. The immersed boundary technique is used to correct the intermediate velocity around the solid boundary to satisfy the no-slip boundary condition. Agreement of simulation results with the data found in the literature shows reliability of the proposed method in simulating laminar flows on a Cartesian mesh.

A distributed parallel direct simulator for pore-scale two-phase flow on digital rock images using a finite difference implementation of the phase-field method

The phase-field method is a versatile and robust technique for modeling interfacial motion in multiphase flows in pore-scale media. The method provides an effective way to account for surface effects by use of diffuse interfaces. The resulting model significantly simplifies the numerical implementation of mass transport and momentum balance solvers for simulating two-phase flow with a large number of moving interfaces. The thermodynamically consistent governing equations minimize the Helmholtz free energy, leading to formation, transport, and/or destruction of interfaces. The phase-field method accurately conserves mass and is relatively straightforward to implement in conjunction with contact-angle models that account for wettability on rock surfaces. The underlying free-energy minimization framework leads to the advective Cahn-Hilliard equation and modified Navier-Stokes equations that form the phase-field model.We have implemented a particular variant of the phase-field method (PFM) into the computational core of a pore-scale multiphase flow simulator, namely PMFS-PFM, for the numerical simulations of incompressible flow of two immiscible fluid phases. The implementation was discussed in a previous paper for rectangular prism-shaped fully-connected domains, e.g., for simulating two-phase flow in a 2D slit or a 3D duct (Alpak et al., 2016). In this paper, we discuss the recent developments on PMFS-PFM. The main components of the new work are (I) implementation of support for inactive cells that model the solid parts of a rock by extending the original finite difference method (FDM) based discretizations of the underlying partial differential equations (PDEs) in order to solve realistic 3D pore-scale flow problems on rock volumes stemming from imaging, and (II) enhancing the performance of the simulator through implementation of modern sparse linear solvers and distributed parallel computing.It has been shown that the simulations performed on complex pore-scale domains are consistent with the physics of the immiscible two-phase displacement. The parallel scalability of the code is reasonably well varying between 50% and 86% for the investigated test cases of different complexity. Results indicate that the more disconnected the pore-scale domains are, the lower is the parallel efficiency. It has been noted that there is a possibility of improving the parallel efficiency by exploring various grid subdivisions.

Robust control of flow separation over a pitching aerofoil using plasma actuators

We address the problem of controlling the unsteady flow separation over an aerofoil, using plasma actuators. Despite the complexity of the dynamics of interest, we show how the problem of controlling flow separation can be formulated as a simple output regulation problem, so that a simple control strategy may be used. A robust multivariable feedback control is designed and tested in a configuration with two actuator/sensor pairs. Accurate numerical simulations of incompressible flows on a pitching NACA 0012 at Reynolds Re = 20,000 are performed in order to illustrate the effectiveness of the proposed approach. Robust, fast flow reattachment is achieved, along with both stabilisation and increase/reduction of the lift/drag, respectively. The control system shows good dynamic performances, as the angle of attack is varied. The chosen output can be experimentally measured by appropriate sensors and the extension of the proposed approach to 3D configurations is straightforward.

Comparison of Handling Pressure in Poisson Solver for Immersed Boundary Method Considering Pressure Condition

In the Cartesian grid approach, the immersed boundary method (IBM) is well used to handle the boundary of an object with complicated shape on the Cartesian grid. However, the conventional IBM generates the unphysical pressure oscillations near the boundary because of the pressure jump between inside and outside of the boundary. The IBM considering pressure condition was proposed in order to remove the pressure oscillations by solving the governing equations considering the pressure condition on the boundary. In this method, there are two ways of the handling the pressure on the boundary in the Poisson solver. In this paper, the effect of removing the pressure oscillations by the IBM considering the pressure condition is investigated. And, the influence by the difference in the handling of the pressure on the boundary in the Poisson solver is investigated. In the numerical simulations of incompressible flow around a 2D circular cylinder, the present IBM indicates a greate effect of removing the pressure oscillations. And, it does not occur difference of the result by the difference of the handling the pressure on the boundary in the Poisson solver. Therefore, it is possible to select a method with less computational amount in the Poisson solver without degrading the quality of the result. It is concluded that the present IBM is very promising as improved method in order to remove the pressure oscillations in the conventional IBM.

埋め込み境界法を用いた複数微粒子が壁に衝突する非圧縮流体の3次元直接数値解析

埋め込み境界法を用いた複数微粒子が壁に衝突する非圧縮流体の3次元直接数値解析

Simple Finite Element Numerical Simulation of Incompressible Flow Over Non-rectangular Domains and the Super-Convergence Analysis

In this paper, we apply a simple finite element numerical scheme, proposed in an earlier work (Liu in Math Comput 70(234):579–593, 2000), to perform a high resolution numerical simulation of incompressible flow over an irregular domain and analyze its boundary layer separation. Compared with many classical finite element fluid solvers, this numerical method avoids a Stokes solver, and only two Poisson-like equations need to be solved at each time step/stage. In addition, its combination with the fully explicit fourth order Runge–Kutta (RK4) time discretization enables us to compute high Reynolds number flow in a very efficient way. As an application of this robust numerical solver, the dynamical mechanism of the boundary layer separation for a triangular cavity flow with Reynolds numbers $$Re=10^4$$ and $$Re=10^5$$ , including the precise values of bifurcation location and critical time, are reported in this paper. In addition, we provide a super-convergence analysis for the simple finite element numerical scheme, using linear elements over a uniform triangulation with right triangles.

OpenCL-Based GPU Acceleration of ISPH Simulation for Incompressible Flows

Thanks to the recent development of tools such as CUDA and OpenCL it has become possible to fully utilize Graphical Processing Units (GPUs) for scientific computing. OpenCL promises huge savings in parallel code development and optimization efforts due to it is not restricted to a specific architecture. We have developed an OpenCL-based acceleration framework on GPU for numerical simulations of incompressible flows using incompressible Smoothed Particle Hydrodynamics (ISPH). In order to assess the performance of the GPU implementation presented in the present work, a comparison was made against the implementation of the same ISPH in CPU using OpenCL.

A multidimensional characteristic-based method for making incompressible flow calculations on unstructured grids

This paper presents a new multidimensional characteristic-based scheme (MCB) for numerical simulation of incompressible flows on unstructured grids in conjunction with the artificial compressibility method. The original MCB scheme has been proposed by the authors already and this research is the extension of the aforementioned scheme to unstructured grids. The significant difference between MCB and the conventional characteristic-based scheme (CB) is the multidimensional nature of the scheme, which allows information to propagate in any direction instead of only normal to the cell interface. In addition, local time stepping and the residual smoothing technique have been used for convergence acceleration. The accuracy and utility of the proposed scheme have been studied by means of numerical tests for different Reynolds numbers and the results obtained using the new scheme are in good agreement with the standard benchmark solution in the literature.

Numerical Simulation of Incompressible Flows with Heat Transfer using Seamless Immersed Boundary Method

Numerical Simulation of Incompressible Flows with Heat Transfer using Seamless Immersed Boundary Method

Direct Numerical Simulation of Incompressible Flows on Unstructured Meshes Using Hybrid CPU/GPU Supercomputers

This paper describes a hybrid MPI-CUDA parallelization strategy for the direct numerical simulation of incompressible flows using unstructured meshes. Our in-house MPI-based unstructured CFD code has been extended in order to increase its performance by means of GPU co-processors. Therefore, the main goal of this work is to take advantage of the current hybrid supercomputers to increase our computing capabilities. CUDA is used to perform the calculations on the GPU devices and MPI to handle the communications between them. The main drawback for the performance is the slowdown produced by the MPI communication episodes. Consequently, overlapping strategies, to hide MPI communication costs under GPU computations, are studied in detail with the aim to achieve scalability when executing the code on multiple nodes.