Simulation Of Incompressible Flows Research Articles

A duality-preserving adjoint method for segregated Navier–Stokes solvers

Adjoint methods efficiently compute gradients for systems with many inputs and have been widely used for large-scale gradient-based optimization in fluid mechanics. To ensure optimization's numerical robustness, we need to develop an adjoint solution algorithm that has a similar, if not the same, convergence rate as the primal flow solver at each optimization iteration. This consistent primal-adjoint convergence behavior is also called duality-preserving (DP). Existing DP adjoint methods are mostly for fully coupled Navier–Stokes (NS) solvers with compressible flows. However, few DP adjoints have been proposed for segregated NS solvers, e.g., the semi-implicit method for pressure-linked equations (SIMPLE) algorithm solvers widely used for incompressible flow simulations. This study will fill this gap by deriving a fixed-point segregated adjoint formulation that fully preserves the convergence behavior of primal solvers. We first rewrite the steady-state segregated NS primal solution process into a fully coupled left-preconditioned Richardson format. Then, we transpose the preconditioner matrix to obtain a DP iterative adjoint formulation. In addition to algebraic derivation, we create a new graph representation that significantly streamlines the DP adjoint development for new segregated solvers. We prove that the proposed graph representation is equivalent to the above preconditioner transpose approach and guarantees duality. We evaluate our proposed algorithm using three cases with increasing complexity: a miniature-sized problem, an airfoil, and a wing. To quantify duality, we compare the eigenvalues between the primal and adjoint solvers and observe excellent agreements. We also evaluate to what extent various numerical settings (e.g., inner iteration tolerances and non-dual preconditioner) impact the eigenvalue distributions. Our proposed adjoint achieves machine-precision accurate gradient computation with competitive speed. Finally, we incorporate our adjoint solver into a large-scale gradient-based optimization framework and demonstrate its capability for wing aerodynamic shape optimization. The proposed fixed-point adjoint approach has the potential to make the adjoint solution more robust and efficient for any segregated NS solvers.

Lattice Boltzmann Simulation of Incompressible Fluid Flow in Two-sided Converging and Diverging Lid-driven Square Cavity

The present study focuses on the predictions of flow behavior, streamlines and some other factors of a two adjacent-sided converging and diverging lid-driven square cavity filled with fluid. In the diverging case, the top wall of the cavity is considered to be in motion from left to right, and the left wall is considered to be in motion from top to bottom simultaneously with identical speeds. It is found that for a low Reynolds number, the flow behavior seems to be symmetric with respect to one of the diagonals of the cavity, and at a critical Reynolds number 1121, the symmetry of the flow behavior blows up, and an asymmetric form is obtained due to the increased inertia and turbulence effects. Any increment in the Reynolds number above the critical Reynolds number develops this asymmetry gradually more and more. In the second phenomenon, the converging phenomenon, the top wall of the cavity is assumed to be in motion from left to right, and the right wall is assumed to be in motion from bottom to top simultaneously with identical speeds so that they converge at the corner of the cavity. This case gives rise to two critical Reynolds numbers Re = 969 and Re = 2053 and the flow behavior for both asymmetric states was found to be opposite. Furthermore, the rate of convergence of the present methodology, lattice Boltzmann methodology, for various Reynolds numbers is found to be very high except for the critical and their nearby Reynolds numbers.

An immersed boundary velocity correction method combined with virtual body-fitted grid for simulation of incompressible flows

In this work, a virtual body-fitted grid is introduced into the velocity correction-based immersed boundary method (IBM) to simulate incompressible flows. The impact of the immersed boundary is indirectly transmitted to the flow field via a virtual body-fitted grid. In this method, the fractional step technique consisting of the predictor and the corrector is adopted. The prediction step is executed on the Eulerian mesh, and the correction step is done on the virtual grid to fulfill the no-slip boundary condition. After the correction step, the corrected velocity field on the virtual grid is then assigned to that on the Eulerian mesh to update the flow field. Being able to adjust the grid spacing flexibly, the virtual body-fitted grid alleviates the shortcomings of the conventional IBM that uses the smooth Dirac delta function to associate Lagrangian points with their surrounding Eulerian points. As a result, the present method is easy to apply to non-uniform Cartesian grids, which is inapplicable to the conventional IBM with the smooth Dirac delta function. Numerical experiments concerning flow past a circular cylinder and a NACA0012 airfoil demonstrate the advantages of the present method, i.e., fewer Lagrangian points are required to avoid the streamline penetration of boundary and the range of “diffuse interface” can be narrowed by reducing the normal grid spacing of the virtual body-fitted grid to improve numerical results on a coarse mesh. In addition, an accuracy assessment on the decaying vortex problem reveals that the present IBM has a second-order accuracy.

Stable nodal projection method on octree grids

We propose a novel collocated projection method for solving the incompressible Navier-Stokes equations with arbitrary boundaries. Our approach employs non-graded octree grids, where all variables are stored at the nodes. To discretize the viscosity and projection steps, we utilize supra-convergent finite difference approximations with sharp boundary treatments. We demonstrate the stability of our projection on uniform grids, identify a sufficient stability condition on adaptive grids, and validate these findings numerically. We further demonstrate the accuracy and capabilities of our solver with several canonical two- and three-dimensional simulations of incompressible fluid flows. Overall, our method is second-order accurate, allows for dynamic grid adaptivity with arbitrary geometries, and reduces the overhead in code development through data collocation.

A machine learning based acceleration of segregated pressure correction algorithms for incompressible fluid flow

Segregated pressure correction algorithms are widely used in the simulation of steady-state incompressible fluid flow. However, these traditional solution algorithms usually require high computational resources for design optimization problems. To resolve this issue, we propose an advanced tree-based Machine Learning (ML) model named Extremely Randomized Trees (ERT) for speeding up the convergence of segregated pressure correction algorithms. Then, its prediction performance is compared with the widely used Decision Tree (DT) and Random Forest (RF) with its prediction results finally incorporated into simulation process as an intermediate flow field. The ML model is designed to predict the primary flow properties including turbulent kinetic energy, turbulent dissipation rate, turbulent viscosity, pressure and velocity, whose modeling capability is assessed by the interpolation generalization and extrapolation generalization. Our assessments are on the basis of flow past a surface-mounted obstacle with apparent flow separation and considerable mesh anisotropy to represent a practical CFD application. For the generalization investigation with either varying inlet velocity conditions or aspect ratios of the obstacle, the pressure correction algorithms hybridized with the ML model both achieve high-resolution steady-state results with a significant reduction in iteration steps and computational cost comparing with those without ML acceleration, which is due to that the selected ML model gives more satisfactory initial conditions for the traditional pressure correction algorithms. The results provide a reference for the rapid exploration of parameter spaces in design optimization problems.

Mathematical analysis for simulation of incompressible fluid flow

The omnipresence and complexity of physical phenomena drive the strong search for tools capable of simulating them, since many applications require computationally viable, reliable and, preferably, low-cost simulations. Thus, a priori, this work has two objectives: i) understand the theoretical foundations of fluid dynamics with an important computational method aimed at simulating incompressible flows, called SPH (Smoothed Particle Hydrodynamic), which will subsequently be implemented; and ii) assist in the consolidation and application of key concepts in mathematical analysis for computer simulation. Our efforts in this work provide mathematical foundations, which in turn, describe the dynamics of fluid dynamic motion.

Fluid Simulation on Neural Flow Maps

We introduce Neural Flow Maps, a novel simulation method bridging the emerging paradigm of implicit neural representations with fluid simulation based on the theory of flow maps, to achieve state-of-the-art simulation of in-viscid fluid phenomena. We devise a novel hybrid neural field representation, Spatially Sparse Neural Fields (SSNF), which fuses small neural networks with a pyramid of overlapping, multi-resolution, and spatially sparse grids, to compactly represent long-term spatiotemporal velocity fields at high accuracy. With this neural velocity buffer in hand, we compute long-term, bidirectional flow maps and their Jacobians in a mechanistically symmetric manner, to facilitate drastic accuracy improvement over existing solutions. These long-range, bidirectional flow maps enable high advection accuracy with low dissipation, which in turn facilitates high-fidelity incompressible flow simulations that manifest intricate vortical structures. We demonstrate the efficacy of our neural fluid simulation in a variety of challenging simulation scenarios, including leapfrogging vortices, colliding vortices, vortex reconnections, as well as vortex generation from moving obstacles and density differences. Our examples show increased performance over existing methods in terms of energy conservation, visual complexity, adherence to experimental observations, and preservation of detailed vortical structures.

Employment of roughened absorber palate and jet nozzles with different hole shapes for performance boost of solar-air-heaters

In this study, roughened absorber plate and jet nozzle are simultaneously employed to enhance the efficiency of a solar based air heater. The impact of jet nozzle hole shape is comprehensively investigated for the mentioned system which have not been investigated before. Three-dimensional steady-state simulations of incompressible turbulent fluid flow and heat transfer are performed using the Reynolds-Averaged Navier-Stokes (RANS) equations to model the jet solar air heater (JSAH). Five different jet hole shapes (circular, triangular, square, hexagonal, and rectangular) are examined and results are compared with conventional structure. The thermal and hydraulic performance of the JSAH is assessed using a variety of geometric and operating parameters, including jet diameter ratio (dj/Dh), jet hole streamwise pitch (Lj/Dh), and Re number (Re). The results show that the ratio of (Nu/Nus) initially increases and then decreases as the hydraulic diameter of the jet holes increases. Circular jet holes consistently outperform other shapes, while rectangular and triangular jet holes perform poorly. The pressure penalty (f/fs) decreases with increasing (dj/Dh), with circular jet holes exhibiting the lowest value. Increasing the Reynolds number enhances heat transfer and pumping power but leads to a decrease in (Nu/Nus) and negatively affects the THPP of the JSAH compared to a conventional smooth solar air heater. The study also reveals that the THPP initially increases with streamwise pitch (Lj/Dh) but then declines, following the trend of (Nu/Nus). The results demonstrate up to 4.5 times higher Nusselt numbers with a jet solar air heater versus a smooth solar heater. A maximum thermal-hydraulic performance parameter of 1.64 indicates the proposed design's efficacy. This research furnishes critical insights into optimizing solar air heater performance by examining jet nozzle hole shape, streamwise pitch, and Reynolds number. It enables enhancing thermal efficiency and thermo-hydraulic performance.

Numerical simulation of incompressible interfacial flows by a level set re-distancing method with improved mass conservation

This paper presents a level set re-distancing (NLS) method to better preserve mass conservation and more accurately predict interface evolution in the simulation of incompressible interfacial flows. In this method, the level set function is first advected by an advection equation. The key to this method depends on the simulation of the re-distancing equation subject to a proper mass-correction term. The performance of the proposed NLS method is verified against benchmark cases such as vortex deforming and Zalesak’s cases. The NLS method is then combined with an explicit Adams–Bashforth scheme on a staggered Eulerian grid to obtain Navier–Stokes solutions. Two-layer liquid sloshing, dam-break flow and Rayleigh–Taylor instability are simulated and compared with numerical or experimental results reported in literature. Two-phase flows that involve nonlinear phenomena such as bubble rising and bubble bursting at a free-surface are also chosen to demonstrate the ability of the proposed method in considering surface tension. The NLS method proposed in this paper is compared with the CLSVOF method of Li and Yu (2019) in terms of computational time in dam-break flow and Rayleigh–Taylor instability cases.

A continuous one-domain framework for fluid flow in superposed clear and porous media

Based on generalized porous flow model, we present a one-domain framework for the simulation of incompressible flow in superposed clear and porous media. The continuous change in the characteristics of the porous medium is naturally taken into account by the model. In presence of any strong discontinuities in the domain, the sudden changes are approximated as a continuous but rapid variations over a thin layer across the regions of contrast. The governing equations are solved by a consistent second-order projection scheme on finite volume octree cells. The numerical scheme evaluates advection as well as porous drag terms at fractional time step and employs Godunov type procedure to obtain fractional step velocity at face center. The consistent property of the scheme ensures a discrete balance between pressure gradient and porous drags and, thereby, recovers Darcy-Forchheimer law exactly. The implication of inconsistent discretization of porous drags and pressure gradient is also highlighted. Benchmark problems with flow parallel and perpendicular to the homogeneous porous layer are considered to test the accuracy of the proposed numerical model especially with regard to the artificial transition region. Although the incorporation of the transition layer introduces error into the system, it reduces non-linearity in the field variables and, therefore, decreases the demand of higher grid density near the interface in one-domain approach. Furthermore, we simulate a series of physical problems with varying complexity in flow and characteristics of porous medium. The simulation results illustrate the ability of our solver to handle flows with viscous as well as inertial effects around a planar or circular interface geometry without loss of stability.

A subgrid model with multiple relaxation time for lattice Boltzmann method based on the Cartesian grid

Purpose The paper aims to expand the scope of application of the lattice Boltzmann method (LBM), especially in the field of aircraft engineering. The traditional LBM is usually applied to incompressible flows at a low Reynolds number, which is not sufficient to satisfy the needs of aircraft engineering. Devoted to tackling the defect, the paper proposes a developed LBM combining the subgrid model and the multiple relaxation time (MRT) approach. A multilayer adaptive Cartesian grid method to improve the computing efficiency of the traditional LBM is also employed.Design/methodology/approach The subgrid model and the multilayer adaptive Cartesian grid are introduced into MRT-LBM for simulations of incompressible flows at a high Reynolds number. Validated by several typical flow simulations, the numerical methods in this paper can efficiently study the flows under high Reynolds numbers.Findings Some numerical simulations for the lid-driven flow of cavity, flow around iced GLC305, LB606b and ONERA-M6 are completed. The paper presents the investigation results, indicating that the methods are accurate and effective for the separated flow after icing.Originality/value LBM is developed with the addition of the subgrid model and the MRT method. A numerical strategy is proposed using a multilayer adaptive Cartesian grid method and its treatment of boundary conditions. The paper refers to innovative algorithm developments and applications to the aircraft engineering, especially for iced wing simulations with flow separations.

A semi‐hybrid‐mixed method for Stokes–Brinkman–Darcy flows with H(div)‐velocity fields

SummaryWe consider new semi‐hybrid‐mixed finite element formulations for Stokes–Brinkman problems. Using ‐conforming approximate velocity fields, the continuity of normal components over element interfaces is taken for granted, and pressure is searched in discontinuous spaces preserving the divergence compatibility property. Tangential continuity is weakly imposed by a Lagrange multiplier playing the role of tangential traction. The method is strongly mass‐conservative, leading to exact divergence‐free simulations of incompressible flows. The Lagrange multiplier space requires specific choices according to the velocity approximations implemented in each element geometry. In certain cases, classic divergence‐compatible pairs adopted for Darcy flows may require divergence‐free bubble enrichment to enforce tangential continuity in some extent, avoiding any extra stabilization technique. Considerable improvement in computational performance is achieved by the application of static condensation: the global system is solved only for a piecewise constant pressure variable, velocity normal trace and tangential traction over interfaces. The remaining solution components are recovered by solving independent local Neumann problems in each element. Numerical results are presented for a set of standard test cases in the field of Stokes–Brinkman–Darcy flows with known analytical solutions. The main convergence properties of the method are verified in the whole range of parameters, from Stokes to Darcy limits, as well as for the combined Stokes–Darcy scenario. The robustness of the method is also demonstrated for more challenging test problems with complex non‐conforming meshes with local refinement patterns as well as for curved geometry.

An enhanced moving particle semi-implicit method for simulation of incompressible fluid flow and fluid-structure interaction

An enhanced moving particle semi-implicit method for simulation of incompressible fluid flow and fluid-structure interaction

Comprehensive assessment of the partially-saturated-cells framework for convective problems

We present a comprehensive investigation of Partially-Saturated-Cells method (PSC) for the simulations of incompressible thermal flows. The methodology comprises an additional collision operator introduced into the conventional simplified thermal lattice-Boltzmann (STLBM) method that offers a unified evolution equation for solid and fluid media present in the computational domain. It is a type of diffuse-interface immersed-boundary method that is dictated by the volume fraction of the solid medium and facilitates a smooth transition of boundary conditions at the solid-fluid interface. In this work, we devise a mechanism to evaluate local heat flux at the solid-fluid interface and present its congruity with several heat transfer problems. We also derive the recovery of the macroscopic energy equation from PSC's evolution equation through Chapman-Enskog multiscale expansion. Our investigation also reveals that the method is first-order accurate for moving body simulations irrespective of the straight or curved boundary. It is also Galilean invariant and demonstrates identical heat transfer characteristics in stationary and moving reference frames. A comprehensive analysis of the PSC algorithm is presented to enlighten its suitability for predicting thermo-hydrodynamic characteristics in free, forced, and mixed convection phenomena involving both stationary and moving boundary scenarios. To the best of our knowledge, these aspects pertaining to PSC methodology have not been discussed in the literature so far.

On the convergence of statistics in simulations of stationary incompressible turbulent flows

When reporting statistics from simulations of statistically stationary chaotic phenomenon, it is important to verify that the simulations are time-converged. This condition is connected with the statistical error or number of digits with which statistics can be reliably reported. In this work we consider numerical experiments of low Reynolds number incompressible homogeneous and isotropic turbulence as a model problem to investigate statistical convergence over finite simulation times. Specifically, we investigate the time integration requirements that allow meaningful reporting of the statistical error associated with finiteness of the temporal domain. We address two key questions: (1) How long should a simulation be performed in terms of large eddy time, and (2) How should the simulation time be divided among temporal windows over which a quantity of interest is estimated so that its statistical error could be reliably reported? We find that reliable reporting of statistical errors requires simulations on the order of 104 large eddy times, which is orders of magnitude longer than typically performed. Additionally, data post-processing should employ windows of at least ten times the large eddy time scale, with the most robust computation of statistical error of the mean requiring window sizes of an additional factor of ten. For practical simulations, we demonstrate that it is possible to estimate the statistical error within a factor of two under a less stringent condition in which a minimum of four windows with size at least ten large eddy times are used. Our observations for homogeneous isotropic turbulence are also shown to hold in turbulent channel flow.

Numerical investigation of turbulent flow and heat transfer characteristics in the improved Kenics static mixer

AbstractThis study focuses on using computational fluid dynamics to explore how well a modified static mixing component called the Kenics static mixer (KSM) increases heat transfer. The purpose of the study is to assess this new static mixer's pressure drop and heat transfer properties. Convective heat transport of water within the improved Kenics static mixer (IKSM) was examined using three‐dimensional turbulent, steady, and incompressible flow simulations. The Nusselt number and friction factor simulation results in the KSM are in good agreement with previous literature findings. Between the simulated outcomes of the IKSM, empty pipe, and standard KSM, a comparison analysis was done. The study considered a range of Reynolds number (Re) values from 2000 to 20,000 and investigated the effects of the Re, slit width configuration (), as well as an aspect ratio () on heat transfer and mixing. Based on the performance evaluation criteria and field synergy number characteristics, the hydrothermal efficiency of the IKSM was evaluated, allowing the geometry to be modified for better heat transmission while lowering the friction factor. Notably, in the 2000–20,000 Reynolds number range, the IKSM with four slits showed a 38%–52% greater heat transfer coefficient than the traditional KSM.

3D simulation of incompressible flow a rounda rotating turbulator: Effect of rotational and direction speed

3D simulation of incompressible flow a rounda rotating turbulator: Effect of rotational and direction speed

Inverse distance weighting interpolation-based immersed boundary velocity correction method for incompressible flows

In this work, the inverse distance weighting (IDW) interpolation is introduced into the implicit velocity correction-based immersed boundary method (IBM) for simulation of incompressible flows. In the original implicit velocity correction-based IBM, the solid body must be immersed in a uniform mesh region due to the use of the smooth Dirac delta function, which is utilized to associate Lagrangian points with their surrounding Eulerian points and only works with uniform meshes. The IDW method has the advantage that the interpolation range can be set flexibly. The introduction of the IDW interpolation can extend the application of the IBM to non-uniform meshes while reducing the number of Lagrangian points. The numerical test by the decaying vortex problem proves that the IDW interpolation does not significantly affect the overall accuracy of the IBM. In addition, numerical experiments for the flows around a circular cylinder and a NACA0012 airfoil demonstrate the advantages of the proposed method, including allowing fewer Lagrangian points while ensuring no streamline penetration to the solid body, as well as its adaptability to non-uniform meshes which can improve the computational efficiency due to the use of fewer mesh points. Finally, the simulation of the flow past a stationary sphere illustrates that the proposed method can effectively simulate the three-dimensional flow.

Coupling SPH with a mesh-based Eulerian approach for simulation of incompressible free-surface flows

This paper presents a coupling algorithm for the simulation of incompressible free-surface flows over the near and far fields by solving the Navier-Stokes equations. The coupling combines the Smoothed Particle Hydrodynamics (SPH) with the Finite Difference (FD) method implemented on structured Eulerian grids. Based on the domain decomposition, the SPH is applied to the near-field core region for modeling with high-fidelity the severe free-surface deformation and even fragmentation of flow, while the FD method is used to resolve the remaining far-field region with relatively high efficiency. The primary purpose of the hybrid approach is to mitigate the computational load of SPH applications through combination with a mesh-based Eulerian method while maintaining high accuracy for both the near-field and far-field simulations. Two-way coupling between the FD and SPH models is achieved by the overlapping region between the computational subdomains, in which the Eulerian solutions and the Lagrangian solutions are coupled with each other through interpolation in the overlapping region for the fluid transfer and free-surface movement between the near-field and far-field regions. The proposed algorithm is validated by several test cases, showing favorable accuracy, convergence, and applicability in the simulation of wave interactions with complex bathymetry and structures.

Three-dimensional simulations of fluid flows in oscillating lid-driven cavities using lattice Boltzmann method

Abstract We utilize the lattice Boltzmann method to conduct three-dimensional simulations of incompressible flows in oscillating cubic lid-driven cavities. Our investigation focuses on examining the impact of Reynolds number and oscillating frequency on the flow field. Notably, we observe that the flow field can be adequately approximated as two-dimensional within the low and intermediate Reynolds number range, but this approximation is no longer valid for high Reynolds numbers. Additionally, we find that high Reynolds numbers correspond to transient flow fields, while low and moderate Reynolds numbers exhibit quasi-steady periodic flow fields. Our study holds significant relevance for industrial processing applications, where the Reynolds numbers and oscillating frequencies can be optimized to achieve a desired flow field.