Showing papers on "Incompressible flow published in 2022"

Unsteady mixed convection flow of magneto-Williamson nanofluid due to stretched cylinder with significant non-uniform heat source/sink features

Abstract: This analysis reports an unsteady and incompressible flow of Williamson nanoliquid in presence of variable thermal characteristics are persuaded by a permeable stretching cylinder. The flow field investigation is established with the effect of mixed convection and non-uniform heat source/sink on flow and heat transfer. On the cylinder surface, the analysis is inspected with utilization of zero mass flux constraints. By using the appropriate similarity variables, the framed equations for the energy, momentum and mass is converted into non-linear ODEs. The numerical communication of the boundary value problem is successfully implemented using a computer algorithm programmed into the fifth Runge-Kutta scheme. Additionally, the wall shear factor and rate of heat transfer are calculated in two different cases namely, with curvature and without curvature. In addition, the results obtained are confirmed by making comparisons with previously published articles and we found an excellent match that guarantees the indemnity of current communication. A comprehensive change in velocity, temperature and concentration is examined for involved parameters like local Weissenberg number, space dependent heat source constant, magnetic number, curvature constant, thermophoretic parameter, buoyancy parameter, Brownian motion parameter, Prandtl number, Schmidt number, unsteadiness parameter, reaction rate parameter, activation energy parameter and temperature difference parameter. A reduction in velocity is observed for unsteady parameter and buoyancy constant. An enhanced nanofluid temperature is noted for space dependent heat source parameter, time dependent heat source parameter and unsteady parameter. Moreover, the nanofluid concentration is increases for temperature difference parameter while reverse observations are noticed for chemical reaction rate.

A coupled cell-based smoothed finite element method and discrete phase model for incompressible laminar flow with dilute solid particles

Abstract: In this paper, the cell-based smoothed finite element method (CS-FEM) empowered by the discrete phase model (DPM) is developed to solve dilute solid particles movements induced by incompressible laminar flow. In the present method, the fluid phase is solved by CS-FEM in the Eulerian framework, while particles are treated as discrete phases traced using Newton's second law in the Lagrangian framework. Meanwhile, the fluidic drag force on particles is considered to realize the one-way coupling of fluid to particles. For the fluid phase, the semi-implicit characteristic-based split (CBS) method is employed to suppress the spatial and pressure oscillations arising from the numerical solution of the Navier-Stokes equations discretized by the CS-FEM. To accurately capture the fluid velocity at an arbitrary particle position inside quadrilateral elements, the mean value coordinates interpolation is introduced. Furthermore, the motion equations for particles are solved by the fourth-order Runge-Kutta method to ensure high accuracy on particle trajectories. Several numerical examples in this paper demonstrate that the proposed method can effectively predict the effect of fluid flow on particle trajectories and position distributions in the analysis of practical and complex flow problems.

A Convergent Post-processed Discontinuous Galerkin Method for Incompressible Flow with Variable Density

Abstract: We propose a linearized semi-implicit and decoupled finite element method for the incompressible Navier--Stokes equations with variable density. Our method is fully discrete and shown to be unconditionally stable. The velocity equation is solved by an H1-conforming finite element method, and an upwind discontinuous Galerkin finite element method with post-processed velocity is adopted for the density equation. The proposed method is proved to be convergent in approximating reasonably smooth solutions in three-dimensional convex polyhedral domains.

Vortex induced vibrations of a cylinder at low mass ratio

Abstract: We used the Lattice Boltzmann Method (LBM) to study the vortex-induced vibrations of a circular cylinder in an incompressible flow with a restoring force. The cylinder has three degrees of freedom, two for translation and one for rotation. Results with a wide range of relevant parameters are presented in high resolution simulations. The three detected branches in cross-flow amplitudes were related with flow and cylinder’s dynamics in the limit of low mass ratios. The transition regions between these branches were related with regions where several solutions exist depending on the initial conditions, this solution space is increased with the inclusion of the rotational degree of freedom.

A vector penalty-projection approach for the time-dependent incompressible magnetohydrodynamics flows

Abstract: In this paper, we study a fully discrete vector penalty-projection method for the time-dependent incompressible magnetohydrodynamics flows. This fully discrete scheme is a combination of a mixed finite element approximation for spatial discretization and first-order backward Euler for temporal discretization. Moreover, unconditionally energy stable is established, and error estimates for the fully discrete scheme is also derived. Finally, some numerical experiments are provided to verify the theoretical results and illustrate the accuracy and efficiency of the proposed scheme.

Skeleton-stabilized divergence-conforming B-spline discretizations for incompressible flow problems of high Reynolds number

Abstract: We consider a stabilization method for divergence-conforming B-spline discretizations of the incompressible Navier–Stokes problem wherein jumps in high-order normal derivatives of the velocity field are penalized across interior mesh facets. We prove that this method is pressure robust, consistent, and energy stable, and we show how to select the stabilization parameter appearing in the method so that excessive numerical dissipation is avoided in both the cross-wind direction and in the diffusion-dominated regime. We examine the efficacy of the method using a suite of numerical experiments, and we find the method yields optimal L2 and H1 convergence rates for the velocity field, eliminates spurious small-scale structures that pollute Galerkin approximations, and is effective as an Implicit Large Eddy Simulation (ILES) methodology.

Generalized‐α scheme in the PFEM for velocity‐pressure and displacement‐pressure formulations of the incompressible Navier–Stokes equations

Abstract: Despite the increasing use of the particle finite element method (PFEM) in fluid flow simulation and the outstanding success of the Generalized‐ α$$ \alpha $$ (GA) time integration method, very little discussion has been devoted to their combined performance. This work aims to contribute in this regard by addressing three main aspects. First, it includes a detailed implementation analysis of the GA method in PFEM. The work recognizes and compares different implementation approaches from the literature, which differ mainly in the terms that are α$$ \alpha $$ ‐interpolated (state variables or forces of momentum equation) and the type of treatment for the pressure in the time integration scheme. Second, the work compares the performance of the GA method against the Backward Euler and Newmark schemes for the solution of the incompressible Navier–Stokes equations. Third, the study is enriched by considering not only the classical velocity‐pressure formulation but also the displacement‐pressure formulation that is gaining interest in the fluid‐structure interaction field. The work is carried out using various 2D and 3D benchmark problems such as the fluid sloshing, the solitary wave propagation, the flow around a cylinder, and the collapse of a cylindrical water column.

Variational methods for finding periodic orbits in the incompressible Navier–Stokes equations

Abstract: Unstable periodic orbits are believed to underpin the dynamics of turbulence, but by their nature are hard to find computationally. We present a family of methods to converge such unstable periodic orbits for the incompressible Navier–Stokes equations, based on variations of an integral objective functional, and using traditional gradient-based optimisation strategies. Different approaches for handling the incompressibility condition are considered. The variational methods are applied to the specific case of periodic, two-dimensional Kolmogorov flow and compared against existing Newton iteration-based shooting methods. While computationally slow, our methods converge from very inaccurate initial guesses.

A fully explicit incompressible Smoothed Particle Hydrodynamics method for multiphase flow problems

Abstract: Multiphase flow is a challenging area of computational fluid dynamics (CFD) due to their potential large topological change and close coupling between the interface and fluid flow solvers. As such, Lagrangian meshless methods are very well suited for solving such problems. In this paper, we present a new fully explicit incompressible Smoothed Particle Hydrodynamics approach (EISPH) for solving multiphase flow problems. Assuming that the change in pressure between consecutive time-steps is small, due to small time steps in explicit solvers, an approximation of the pressure for following time-steps is derived. To verify the proposed method, several test cases including both single-phase and multi-phase flows are solved and compared with either analytical solutions or available literature. Additionally, we introduce a novel kernel function, which improves accuracy and stability of the solutions, and the comparison with a well-established quintic spline kernel function is discussed. For the presented benchmark problems, results show very good agreements in velocity and pressure fields and the interface-capturing with those in the literature. To the best knowledge of the authors, the EISPH method is presented for the first time for multiphase flow simulations.

A Cell-Based Smoothed Finite Element Method for Solving Incompressible Reynolds-Averaged Navier–Stokes Equations Using Spalart–Allmaras Turbulence Model

Abstract: In this paper, a leap forward in the development of a cell-based smoothed finite element method (CS-FEM) is presented to solve incompressible turbulent flow treated by Reynolds–averaged Navier–Stokes (RANS) equations and the Spalart–Allmaras (SA) model. The streamline-upwind/Petrov–Galerkin stabilization combined with the stabilized pressure gradient projection (SUPG/SPGP) is used to address oscillation and instability for CS-FEM in calculations of incompressible flow. The capability, accuracy, and validity of presented turbulent CS-FEM were tested by four numerical examples, including turbulent channel flow, a backward-facing step, flow past a circular cylinder, and turbulent flow past multistage Tesla valves. Based on the favorable comparison of numerical results obtained by the presented CS-FEM with experimental results and literature numerical results, CS-FEM is demonstrated to be highly applicable with appealing performances on simulations of incompressible turbulent flows. This new extension of CS-FEM empowers the S-FEM family to solve complex turbulent flows.

Three dimensional ideal MHD equilibria with non-parallel flow and pressure anisotropy

Abstract: We extend previous work of [9], [10] to the case of ideal MHD equations with incompressible flow non-parallel to the magnetic field and pressure anisotropy. Classes of exact three-dimensional solutions are obtained with straight magnetic axes and closed nested pressure-surface intersections with the poloidal plane, for moderate values of the flow velocity parameters whereas these surfaces are destroyed for higher velocities.

A low-degree strictly conservative finite element method for incompressible flows on general triangulations

Abstract: In this study, a new P 2 -P 1 finite element pair is proposed for incompressible fluid. For this pair, the discrete inf-sup condition and the discrete Korn’s inequality hold for general triangulations. It yields strictly conservative velocity approximations when applied to models of incompressible flows. The convergence rate of the scheme can only be proved to be of suboptimal 𝒪(h) order, though, based on the property of strict conservation, the robust capacity of the pair for incompressible flows is verified theoretically and numerically.

Well-posedness of the free boundary problem in incompressible MHD with surface tension

Abstract: In this paper, we study the two phase flow problem with surface tension in the ideal incompressible magnetohydrodynamics. First, we prove the local well-posedness of the two phase flow problem with surface tension. Second, for the initial data satisfying a Syrovatskij type stability condition, we prove that as surface tension tends to zero, the solution of the two phase flow problem with surface tension converges to the solution of the two phase flow problem without surface tension.