Incompressible Fluid Flow Problems Research Articles

Stabilized mixed material point method for incompressible fluid flow analysis

This paper proposes novel and robust stabilization strategies for accurately modeling incompressible fluid flow problems in the material point method (MPM). To address the modeling of Newtonian fluids with incompressibility constraints, a new mixed implicit MPM formulation is proposed. Here, instead of solving the velocity and pressure fields as the unknown variables like the typical Eulerian computational fluid dynamics (CFD) solver, the proposed approach adopts a monolithic displacement–pressure formulation inspired by the mixed-form updated-Lagrangian Finite Element Method (FEM). To satisfy the inf–sup stability condition, two stabilization strategies are integrated into the formulation: the variational multiscale method (VMS) and the pressure-stabilization Petrov–Galerkin method (PSPG). By concurrently solving the displacement and pressure fields, the developed monolithic solver obviates the need for free-surface detection as well as Dirichlet and Neumann pressure imposition, in contrast to the fractional-step method. This attribute mitigates spurious pressure and velocity oscillations in simulating dynamic and transient flow problems. This study also addresses other prevalent challenges in MPM simulations, such as the pressure oscillations triggered by cell-crossing errors, particle-distribution-induced quadrature errors, and particle-grid information transfer. To resolve these issues, the quadratic B-Spline basis function, the delta-correction method, and the Taylor particle-in-cell method are incorporated into the proposed mixed MPM formulation, thereby enhancing numerical stability. The efficacy of the proposed stabilized incompressible MPM framework is validated through several benchmark cases, comparing the obtained results with other numerical methods and analytical solutions. Furthermore, the method’s capability in simulating real-world problems involving violent free-surface fluid motion is demonstrated through comparisons with experimental results of water sloshing and dam break scenarios.

A novel approach to micropolar fluid flow between a non-porous disk and a porous disk with slip

This paper considers the problem of steady, laminar, incompressible, and two-dimensional micropolar fluid flow between two disks. The top disk is considered porous, while the lower one is not. The body forces and body couples were neglected, and the flow was assumed to be fully developed. The governing equations of the problem were reduced to a set of ordinary differential equations (ODEs) by Von-Karman's similarity transformations. Since the obtained governing ODEs have not been solved analytically according to the previous studies, in this article, the Modified Akbari-Ganji method (Modified AGM) and the hybrid analytical and numerical method (HAN-method) have been chosen to solve these equations analytically, which is one of the novelties of this study. However, most of this article's novelty is related to the physical results obtained from the analytical solution of these equations. The effects of various slip coefficients, Reynolds number, and micropolar parameters of vortex viscosity, spin gradient viscosity, and microinertia density on profiles of normal velocity, streamwise velocity, and microrotation. The validity of these two analytical solutions was proved by comparison with previously published results. The results of the two methods are almost the same in all cases, which can be seen as an indirect sign of the validity of the results of this study.

The heat transfer effects of MHD slip flow with suction and injection and radiation over a shrinking sheet by optimal homotopy analysis method

The current study investigates the laminar flow of boundary layer using a porous surface shrinking exponentially under varying magnetic field, suction/injection, radiation on velocity and thermal slips. The dimensionless nonlinear differential equations were also defined in terms of governing partial differential equations and applying similarity transformations. The equations were analytically solved following the homotopy analysis method (HAM). An excellent agreement is observed in comparison with theavailable literature in special case (Skin friction coefficient). In the current study, an analytic solution is obtained for the laminar incompressible MHD boundary layer viscous fluid flow problem on the exponentially electrically conducting porous shrinking surface. The impact of different parameters like injection/suction, Prandtl number, radiation, velocity slip, thermal slip, as well as the magnetic field on different velocity and temperature values have been presented graphically, and have been discussed in detail. The f″(0) skin friction rises with higher suction parameter s(>0) values, magnetic parameter M but it decreases when the slip parameter value is increased. Whereas heat transfer rate −θ′(0) rises with an increasing M, s and λ..

A local domain boundary element method for solving 2D incompressible fluid flow problems

The Boundary Element Method (BEM) is a well-established, accurate numerical method for solving engineering problems described by linear partial differential equations. However, the application of BEM to non-linear problems leads to the appearance of volume integrals in the integral formulation, and combined with the non-local character of the method the required computational effort is dramatically increased. In this work, a Local Domain BEM (LD-BEM) is proposed for solving incompressible fluid flow problems. The domain of interest is fragmented into small subdomains, in each of which the integral representation of the solution is considered separately. Eliminating the fluxes at all subdomain interfaces, the proposed LD-BEM leads to sparse linear system coefficient matrices and reduced computational complexity, overcoming some of the well-known disadvantages of the conventional BEM. The proposed method is applied to the solution of the well-known two-dimensional (2D) lid-driven cavity problem, for Reynolds numbers up to Re=125 × 103, with a discretization involving more than 10 million unknowns.

Performance analysis and comparison of IDEAL and SIMPLERR algorithms for incompressible fluid flow and heat transfer problems

In this paper, the numerical performances of the algorithm IDEAL proposed by the present authors in 2008, and the recently proposed (2017) SIMPLERR are systematically analyzed and compared via six incompressible fluid flow and heat transfer problems. It is found that the two algorithms are almost identical when the second inner iteration number of IDEAL is fixed at 2. In general, the robustness and convergence of IDEAL are much better than SIMPLERR. The reason why the performance of SIMPLERR deteriorates with the increase of the first inner iteration number is analyzed and detailed comparisons in the robustness and computing time are presented.

Fluid Flow Modelling Using Physics-Informed Convolutional Neural Network in Parametrised Domains

We design and implement a physics-informed convolutional neural network (CNN) to solve fluid flow problems on a parametrised domain. The goal is to compare the effectiveness of training based solely on CFD-generated training data with purely physics-informed training and training based on a combination of both. We consider the problem of incompressible fluid flow in a convergent-divergent channel with variable wall shape. A speciality of the designed neural network is the incorporation of the boundary condition directly in the CNN. A physics-informed CNN that uses a non-Cartesian mesh poses a challenge when evaluating partial derivatives. We propose a gradient layer that approximates the first and second partial derivatives by finite differences using Lagrange interpolation. Our analysis shows that the convergence of purely physics-informed training is slow. However, using a small training dataset in combination with physics-informed training can achieve results comparable to physics-uninformed training with a considerably larger training dataset.

Lax-Wendroff method for incompressible flow

The Lax-Wendroff scheme is extended to incompressible fluid flow problems within the framework of artificial compressibility method (ACM) utilizing a “cell-centered finite-volume” Δ-approximation on a non-orthogonal non-staggered grid. An ACM induces a transformation between conservative and primitive variables; the physical relevance of ACM is to bring about “matrix preconditionings”, provoking density perturbations. The coupled algorithm is pressure-based; it benefits from enhanced accuracy and greater flexibility using the “monotone upstream-centered schemes for conservation laws (MUSCL)” approach. Numerical experiments in reference to “buoyancy-driven” flows with strong sources illustrate that the entire strategy augments overall damping capability and robustness adhering to the factored pseudo-time integration method. Conclusively, the associated limiter function has little influence on the high resolution for selected test cases.

An adaptive iterative linearised finite element method for implicitly constituted incompressible fluid flow problems and its application to Bingham fluids

In this work, we further extend the theory in [C. Kreuzer, E. Süli, Adaptive finite element approximation of steady flows of incompressible fluids with implicit power-law-like rheology, ESAIM: Math. Model. Numer. Anal. 50 (5) (2016) 1333–1369] on the adaptive finite element analysis of implicitly constituted incompressible fluid flow problems by taking into account the approximation of the nonlinear finite element solutions by an iterative solver. Thereby we show that the computable sequence generated by the modified algorithm still has a weak limit point, which is a solution of the given problem. Our abstract theory can be applied to Bingham fluids, both with and without the convective term. The performance of the adaptive iterative linearised finite element algorithm in this context is illustrated by two numerical experiments.

Modelling and Simulation of Fluid Flow through a Circular Cylinder with High Reynolds Number: A COMSOL Multiphysics Study

In this study, we intend to investigate the steady-state and laminar flow of a viscous fluid through a circular cylinder fixed between two parallel plates keeping the aspect ratio of 1 : 5 from cylinder radius to height of the channel. The two-dimensional, incompressible fluid flow problem has been simulated using COMSOL Multiphysics 5.4 which implements finite element’s procedure. The flow pattern will be investigated by using the Reynolds number from 100 to 1000. The reattachment length formed at the back of the cylinder and drag force when the fluid comes to strike with the front surface of the cylinder is expressed in terms of Reynolds numbers. We propose to calculate the velocity and the pressure before and after the cylinder. For this purpose, two-line graphs before and after the cylinder will be drawn to check the impact of cylinder on both velocity and pressure. It was found that the percentage change in the velocity as well as pressure before to after the cylinder is changing their behaviours at Re = 700. The study is important because the empirical equations between the vortex’s lengths formed along the cylinder using the linear regression process obtained in this study may be used for future implementation.

ISI TAŞINIMI İÇİN YAPISAL OLMAYAN AĞLARDA BİR HIZLANDIRILMIŞ SÜREKSİZ GALERKİN METDU: FORMÜLASYONU VE DOĞRULANMASI

We present a GPU-accelerated method for large scale, coupled incompressible fluid flow and heat transfer problems. A high-order, nodal discontinuous Galerkin method is utilized to discretize governing equations on unstructured triangular meshes. A semi-implicit scheme with explicit treatment of the advective terms and implicit treatment of the split Stokes operators are used for time discretization. The pressure system is solved with a conjugate gradient method together with a fully GPU-accelerated multigrid preconditioner. The code is built on scalable libParanumal solver which is a library of high-performance kernels for high-order discretizations. Performance portability is achieved by using the open concurrent compute abstraction, OCCA. A set of numerical experiments including free and mixed convection problems indicate that our approach experimentally reaches design order of accuracy.

Performance Analysis and Comparison of Ideal and Simplerr Algorithms for Incompressible Fluid Flow and Heat Transfer Problems

Performance Analysis and Comparison of Ideal and Simplerr Algorithms for Incompressible Fluid Flow and Heat Transfer Problems

A novel stabilized Galerkin meshless method for steady incompressible Navier–Stokes equations

In the paper, a novel stabilized meshless method is presented for solving steady incompressible fluid flow problems. For this method, the standard Galerkin discretization is used to momentum equations, where the variational multiscale method is applied to mass conservation equation. Thus, the novel stabilized method can be regarded as a simplification of the variational multiscale element free Galerkin method, but it still retains the advantages of the variational multiscale element free Galerkin method. The present method allows equal linear basis approximation of both velocity and pressure and avoids the Ladyzhenskaya–Babuška–Breezi(LBB) condition. Meanwhile, it can automatically obtain the stabilization tensor. Three Stokes flow and two Navier–Stokes flow problems are applied to validate the accuracy and feasibility of the present method. It is shown that the present stabilized meshless method can guarantee the numerical stability and accuracy for incompressible fluid flow problems. Moreover, it can save computational cost evidently compared with variational multiscale element free Galerkin method.

A high-order accurate meshless method for solution of incompressible fluid flow problems

Meshless solution to differential equations using radial basis functions (RBF) is an alternative to grid based methods commonly used. Since the meshless method does not need an underlying connectivity in the form of control volumes or elements, issues such as grid skewness that adversely impact accuracy are eliminated. Gaussian, Multiquadrics and inverse Multiquadrics are some of the most popular RBFs used for the solutions of fluid flow and heat transfer problems. But they have additional shape parameters that have to be fine tuned for accuracy and stability. Moreover, they also face stagnation error when the point density is increased for accuracy. Recently, Polyharmonic splines (PHS) with appended polynomials have been shown to solve the above issues and give rapid convergence of discretization errors with the degree of appended polynomials. In this research, we extend the PHS-RBF method for the solution of incompressible Navier-Stokes equations. A fractional step method with explicit convection and explicit diffusion terms is combined with a pressure Poisson equation to satisfy the momentum and continuity equations. Systematic convergence tests have been performed for five model problems with two of them having analytical solutions. We demonstrate fast convergence both with refinement of number of points and degree of appended polynomials. The method is further applied to solve problems such as lid-driven cavity and vortex shedding over circular cylinder. We have also analyzed the performance of this approach for solution of Euler equations. The proposed method shows promise to solve fluid flow and heat transfer problems in complex domains with high accuracy.

Development of artificial compressibility method with elliptic relaxation approach

An artificial compressibility (AC) method resorting to the pressure-based algorithm is developed on a non-orthogonal non-staggered grid using a cell-centered finite-volume Δ-approximation for incompressible fluid flow problems. A pressure time-derivative is used to perturb the equation of continuity. This artifact provokes a density preconditioning which transforms conservative variables to primitive ones; the physical relevance of density preconditioning signifies to convoke compatible linearizations of residuals in collaboration with an AC parameter. The avoidance of pressure-velocity decoupling is enhanced by a consistently formulated cell-face dissipation approach, preserving an increased accuracy with a greater flexibility analogous to the MUSCL (monotone upstream-centered schemes for conservation laws) approach. An elliptic-relaxation scheme having accountability to promoting anisotropic diffusion coefficients is applied to smooth out the pressure residual. Numerical experiments dictate that pertaining to the pseudo-time integration method, the overall contrivance is benefited with an enhanced robustness having sensible oscillation damping characteristics.

On the shape of the free-surface problem of an ideal incompressible fluid flow with a singular sink at the top of a triangular ledge at the bottom

On the shape of the free-surface problem of an ideal incompressible fluid flow with a singular sink at the top of a triangular ledge at the bottom

A volume of solid implicit forcing immersed boundary method for solving incompressible Navier-Stokes equations in complex domain

In this study, a new implicit forcing immersed boundary (IFIB) method is proposed to solve incompressible viscous fluid flow problems involving complex domains. In the conventional immersed boundary (IB) method, a forcing term computed from the volume of solid (VOS) is added to the incompressible Navier-Stokes equations in order to satisfy the velocity condition within the embedded solid body. However, the velocity boundary condition and the divergence-free condition are enforced at different time levels, i.e. intermediate and new time levels. Penetration of streamlines into the stationary solid body is visible as the velocity boundary condition inside the solid body is not strictly enforced at the new time level. In the current work, the proposed IFIB method can ensure velocity field which satisfies both the velocity boundary condition and the divergence-free condition at the same (new) time level. This is accomplished by solving the pressure equation and calculating the forcing term simultaneously (implicitly). A modified pressure Poisson equation (MPPE) is derived in order to couple the pressure and the forcing terms by treating the forcing term as part of the source term of MPPE. Also, a new cell-based method is proposed to compute the VOS for getting a better parallel efficiency. The accuracy of the present IFIB method is then demonstrated by solving several benchmark problems. No penetration of streamlines has been found in the solid body.

Poisson bracket and integrals of motion in the problem of viscous fluid flow around an arbitrary flat contour

The Poisson bracket is used to find the integrals of motion. A numerical and analytical method is suggested to solve Navier-Stokes equations in Helmholtz form. The approximation of the sought solution by a linear combination of basis functions lies in this method’s core. The main idea behind this method is to select basis functions and generalized independent variables. A functional series is taken as the required solution, found from the equation’s solution obtained by equating the Poisson bracket to zero. The substitution of the selected solution into the Helmholtz equation reduces it to a nonlinear algebraic system. This system is solved analytically for a range of cases due to its structure. The authors present an algorithm for solving the boundary problem of viscous incompressible fluid flow around an arbitrary flat contour. In laminar flow around the body, the geometric dimension decreases, and the boundary problem is reduced to a linear system of algebraic equations. The solutions were tested on solving viscous fluid flow around a wedge and a thin plate.

Comparison of Reduced-Basis techniques for the model order reduction of parametric incompressible fluid flows

The applicability of two Reduced-Basis techniques to parametric laminar and turbulent incompressible fluid-flow problems in nuclear engineering is studied in this work. The Reduced-Basis methods are used to generate Reduced-Order Models (ROMs) that can accelerate multi-query problems often encountered in design optimization and uncertainty quantification. Both approaches are intrusive and utilize Proper Orthogonal Decomposition (POD) for data compression. The accuracy of the two methods for reconstructing the velocity, pressure, and turbulent eddy viscosity fields is assessed. The methods are classified based on how many reduced equations are involved. The first approach, often referred to as POD-FV-ROM, only solves one equation with additional physics-based approximations to relate the reduced pressure, velocity, and eddy viscosity fields. The second approach solves two equations and relies on a supremizer stabilization technique. Both methods are reviewed in the finite volume setting and are tested using transient problems: a backward facing step case with an inlet and outlet and a molten-salt closed-loop case. Extension of the methods to parametric reduced-order problems for uncertainty quantification purposes is presented. Conclusions, summarizing the advantages and disadvantages of these two approaches, and recommendations are provided.

A plausible extension of standard penalty, streamline upwind and immersed boundary techniques to the improved element-free Galerkin-based solution of incompressible Navier–Stokes equations

The present work has been conducted in order to propose the extension of standard penalty and stabilization techniques to the improved element-free Galerkin (IEFG) method, for the numerical solution of incompressible fluid flow problems. In principle, the numerical procedures to be implemented in this communication have been conceived for finite element method (FEM)-based solutions, and these include the reduced integration penalty method (RIPM), the streamline upwind Petrov–Galerkin (SUPG) scheme, and a penalty-based immersed boundary method (PBIBM) for the imposition of essential boundary conditions along internal fluid–solid interfaces. The linear momentum balance and mass conservation equations have been coupled via the RIPM, in order to obtain a global weak formulation where the IEFG model is entirely developed in terms of improved moving least squares (IMLS) approximations of the velocity field. A detailed explanation concerning the appropriate extension of both the RIPM and SUPG procedures to the context of IEFG formulations, has also been provided. The resulting formulation has been applied to the solution of two well-known benchmark problems: i) Lid-driven square cavity flow, and ii) Flow past a fixed cylinder. Regarding the flow past a fixed cylinder benchmark problem, the fluid–solid interaction has been imposed as an internal immersed boundary condition via the PBIBM. The feasibility and reliability of implementing the RIPM, SUPG and PBIBM procedures in the IEFG formulation, have been proven by comparison with experimental and mesh-based numerical results reported in the literature. The results obtained in this study have revealed that a proper extension of the aforementioned penalty and stabilization techniques to the IEFG formulation, allows the achievement of accurate and stable numerical results during the solution of incompressible fluid-dynamics problems.

Incompressible Viscous Flow Simulation Using the Quasi-Hydrodynamic Equations’ System

In this paper, we consider the problem of modeling viscous incompressible fluid flow using the quasi-hydrodynamic (QHD) system of equations. The use of this approach makes it possible to avoid instability in the pressure calculation when using the classical formulation of the Navier–Stokes equations, which is manifested when using cellular numerical schemes. For the numerical implementation of QHD equations, the finite volume method is used with cell-center approximation. In the case of a two-dimensional problem a square mesh is used. A cubic mesh is used in the case of a three-dimensional problem. Two series of calculations are performed for testing in areas of complex geometry for several Reynolds numbers. The results are compared with the ANSYS CFX software package. The comparison shows the high quality of the numerical simulation results using the QHD system of equations.