scholarly journals A Review of Vortex Methods and Their Applications: From Creation to Recent Advances

Fluids ◽  
2021 ◽  
Vol 6 (2) ◽  
pp. 68 ◽  
Author(s):  
Chloé Mimeau ◽  
Iraj Mortazavi
Keyword(s):  
Stokes Equations ◽  
Flow Simulation ◽  
Particle Methods ◽  
Navier Stokes ◽  
Numerical Dissipation ◽  
Mathematical Framework ◽  
Vortex Methods ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Present Particle

This review paper presents an overview of Vortex Methods for flow simulation and their different sub-approaches, from their creation to the present. Particle methods distinguish themselves by their intuitive and natural description of the fluid flow as well as their low numerical dissipation and their stability. Vortex methods belong to Lagrangian approaches and allow us to solve the incompressible Navier-Stokes equations in their velocity-vorticity formulation. In the last three decades, the wide range of research works performed on these methods allowed us to highlight their robustness and accuracy while providing efficient computational algorithms and a solid mathematical framework. On the other hand, many efforts have been devoted to overcoming their main intrinsic difficulties, mostly relying on the treatment of the boundary conditions and the distortion of particle distribution. The present review aims to describe the Vortex methods by following their chronological evolution and provides for each step of their development the mathematical framework, the strengths and limits as well as references to applications and numerical simulations. The paper ends with a presentation of some challenging and very recent works based on Vortex methods and successfully applied to problems such as hydrodynamics, turbulent wake dynamics, sediment or porous flows.

scholarly journals High-resolution simulations of the flow around an impulsively started cylinder using vortex methods

1995 ◽  
Vol 296 ◽  
pp. 1-38 ◽  
Author(s):  
P. Koumoutsakos ◽  
A. Leonard
Keyword(s):  
High Resolution ◽  
Stokes Equations ◽  
Slip Boundary Condition ◽  
The Body ◽  
Navier Stokes ◽  
Rectilinear Motion ◽  
Vortex Methods ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Wide Range

The development of a two-dimensional viscous incompressible flow generated from a circular cylinder impulsively started into rectilinear motion is studied computationally. An adaptative numerical scheme, based on vortex methods, is used to integrate the vorticity/velocity formulation of the Navier–Stokes equations for a wide range of Reynolds numbers (Re = 40 to 9500). A novel technique is implemented to resolve diffusion effects and enforce the no-slip boundary condition. The Biot–Savart law is employed to compute the velocities, thus eliminating the need for imposing the far-field boundary conditions. An efficient fast summation algorithm was implemented that allows a large number of computational elements, thus producing unprecedented high-resolution simulations. Results are compared to those from other theoretical, experimental and computational works and the relation between the unsteady vorticity field and the forces experienced by the body is discussed.

Aerodynamic Flow Simulation Using Pressure-Based Method and Normalized Variable Diagram

2002 ◽  
Author(s):  
M. H. Djavareshkian ◽  
S. Baheri Islami
Keyword(s):  
Eddy Viscosity ◽  
Stokes Equations ◽  
Flow Simulation ◽  
Navier Stokes ◽  
Test Cases ◽  
Navier Stokes Equations ◽  
Combine Scheme ◽  
Wide Range ◽  
Minimum Number

This paper a pressure-base finite volume procedure is used in an aerodynamic flow simulation. The boundedness criteria for this procedure are determined from the SBIC, Second and Blending Interpolation Combine, scheme which are used to solve the Euler and Navier-Stokes equations on a nonorthogonal mesh. The scheme with the minimum number of adjustable parameters is robust on the wide range of test cases. The procedure incorporates the k-ε eddy-viscosity turbulence model. The method is then validated against experiment and another numerical solution for the cases of invisicd and turbulent transonic flow around airfoil NACA0012 and RAE2822. The comparisons show that the quality of the resolution of the SBIC scheme is considerable.

scholarly journals Gyrotactic swimmers in turbulence: shape effects and role of the large-scale flow

2018 ◽  
Vol 856 ◽  
Author(s):  
M. Borgnino ◽  
G. Boffetta ◽  
F. De Lillo ◽  
M. Cencini
Keyword(s):  
Large Scale ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Small Scale ◽  
Navier Stokes Equations ◽  
Preferential Sampling ◽  
Wide Range ◽  
Shape Effects ◽  
Dilute Suspensions ◽  
Large Scale Flow

We study the dynamics and the statistics of dilute suspensions of gyrotactic swimmers, a model for many aquatic motile microorganisms. By means of extensive numerical simulations of the Navier–Stokes equations at different Reynolds numbers, we investigate preferential sampling and small-scale clustering as a function of the swimming (stability and speed) and shape parameters, considering in particular the limits of spherical and rod-like particles. While spherical swimmers preferentially sample local downwelling flow, for elongated swimmers we observe a transition from downwelling to upwelling regions at sufficiently high swimming speed. The spatial distribution of both spherical and elongated swimmers is found to be fractal at small scales in a wide range of swimming parameters. The direct comparison between the different shapes shows that spherical swimmers are more clusterized at small stability and speed numbers, while for large values of the parameters elongated cells concentrate more. The relevance of our results for phytoplankton swimming in the ocean is briefly discussed.

Complex dynamics in a stratified lid-driven square cavity flow

2018 ◽  
Vol 855 ◽  
pp. 43-66 ◽  
Author(s):  
Ke Wu ◽  
Bruno D. Welfert ◽  
Juan M. Lopez
Keyword(s):  
Stokes Equations ◽  
Complex Dynamics ◽  
Boussinesq Approximation ◽  
Navier Stokes ◽  
Square Cavity ◽  
Navier Stokes Equations ◽  
Stable Temperature ◽  
Wide Range ◽  
Side Walls ◽  
Steady State Solutions

The dynamic response to shear of a fluid-filled square cavity with stable temperature stratification is investigated numerically. The shear is imposed by the constant translation of the top lid, and is quantified by the associated Reynolds number. The stratification, quantified by a Richardson number, is imposed by maintaining the temperature of the top lid at a higher constant temperature than that of the bottom, and the side walls are insulating. The Navier–Stokes equations under the Boussinesq approximation are solved, using a pseudospectral approximation, over a wide range of Reynolds and Richardson numbers. Particular attention is paid to the dynamical mechanisms associated with the onset of instability of steady state solutions, and to the complex and rich dynamics occurring beyond.

Heat Transfer From a Circular Cylinder at Low Reynolds Numbers

1998 ◽  
Vol 120 (1) ◽  
pp. 72-75 ◽  
Author(s):  
V. N. Kurdyumov ◽  
E. Ferna´ndez
Keyword(s):  
Circular Cylinder ◽  
Energy Equation ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Order Unity ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Prandtl Numbers ◽  
High Degree

A correlation formula, Nu = W0(Re)Pr1/3 + W1(Re), that is valid in a wide range of Reynolds and Prandtl numbers has been developed based on the asymptotic expansion for Pr → ∞ for the forced heat convection from a circular cylinder. For large Prandtl numbers, the boundary layer theory for the energy equation is applied and compared with the numerical solutions of the full Navier Stokes equations for the flow field and energy equation. It is shown that the two-terms asymptotic approximation can be used to calculate the Nusselt number even for Prandtl numbers of order unity to a high degree of accuracy. The formulas for coefficients W0 and W1, are provided.

Lift, drag and added mass of a hemispherical bubble sliding and growing on a wall in a viscous linear shear flow

2008 ◽  
Vol 366 (1873) ◽  
pp. 2233-2248 ◽  
Author(s):  
Dominique Legendre ◽  
Catherine Colin ◽  
Typhaine Coquard
Keyword(s):  
Shear Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Added Mass ◽  
Unsteady Motion ◽  
Navier Stokes ◽  
Mass Force ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Linear Shear

The three-dimensional flow around a hemispherical bubble sliding and growing on a wall in a viscous linear shear flow is studied numerically by solving the full Navier–Stokes equations in a boundary-fitted domain. The main goal of the present study is to provide a complete description of the forces experienced by the bubble (drag, lift and added mass) over a wide range of sliding and shear Reynolds numbers (0.01≤ Re b , Re α ≤2000) and shear rate (0≤ Sr ≤5). The drag and lift forces are computed successively for the following situations: an immobile bubble in a linear shear flow; a bubble sliding on the wall in a fluid at rest; and a bubble sliding in a linear shear flow. The added-mass force is studied by considering an unsteady motion relative to the wall or a time-dependent radius.

Prediction of Wall-Jet and Wall-Wake Flows

1970 ◽  
Vol 12 (6) ◽  
pp. 404-420 ◽  
Author(s):  
S. C. Kacker ◽  
J. H. Whitelaw
Keyword(s):  
Film Cooling ◽  
Stokes Equations ◽  
Numerical Procedure ◽  
Navier Stokes ◽  
Wall Jet ◽  
Two Dimensional ◽  
Constant Property ◽  
Navier Stokes Equations ◽  
Wake Flows ◽  
Wide Range

An existing numerical procedure for solving the steady, two-dimensional, constant property form of the Navier–Stokes equations, has been used to obtain predictions of mean and fluctuating properties downstream of a two-dimensional wall jet. The Prandtl–Kolmogorov model of turbulence, with a simple empirical expression for the length scale, is shown to permit satisfactory predictions over a wide range of flow situations. These flow situations are relevant to the design of film-cooling slots.

scholarly journals Effect of uniform and non-uniform mesh on the development of turbulent boundary layer

2021 ◽  
Author(s):  
Lokesh Kalyan Gutti ◽  
◽  
Bhupendra Singh Chauhan ◽  
Hee-Chang Lim ◽  
◽  
...  
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Stokes Equations ◽  
Flow Simulation ◽  
Navier Stokes ◽  
Uniform Mesh ◽  
Navier Stokes Equations ◽  
Eddy Simulation ◽  
Grid Points ◽  
Long Channel

For incompressible flow simulation, it is commonly accepted to use uniform meshes to solve the governing equation of turbulent boundary layer. It follows the laws of conservation stabilizing the flow field in the domain and preventing odd-even decoupling in the pressure field. In this study, Large Eddy Simulation (LES) has been conducted in a long channel. In order to calculate the turbulent boundary layer in the channel, the unsteady Navier-Stokes equations has been adopted at a Reynolds number =180, which is based on mean centerline velocity and the half-width of the channel. The mesh used in this study was based on both stretch and uniform mesh having grid points, which is corresponding to . Turbulence statistics were also calculated to compare to the existing results. In the results, the turbu lent boundary layer was fully developed at around . In addition, fully developed channel flow was achieved at the non-dimensional time of .

scholarly journals Improved theory for shock waves using the OBurnett equations

2021 ◽  
Vol 929 ◽  
Author(s):  
Ravi Sudam Jadhav ◽  
Abhimanyu Gavasane ◽  
Amit Agrawal
Keyword(s):  
Shock Waves ◽  
Stokes Equations ◽  
Direct Simulation Monte Carlo ◽  
Space Velocity ◽  
Navier Stokes ◽  
Wave Flow ◽  
Complex Flow ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Mach Numbers

The main goal of the present study is to thoroughly test the recently derived OBurnett equations for the normal shock wave flow problem for a wide range of Mach number ( $3 \leq Ma \leq 9$ ). A dilute gas system composed of hard-sphere molecules is considered and the numerical results of the OBurnett equations are validated against in-house results from the direct simulation Monte Carlo method. The primary focus is to study the orbital structures in the phase space (velocity–temperature plane) and the variation of hydrodynamic fields across the shock. From the orbital structures, we observe that the heteroclinic trajectory exists for the OBurnett equations for all the Mach numbers considered, unlike the conventional Burnett equations. The thermodynamic consistency of the equations is also established by showing positive entropy generation across the shock. Further, the equations give smooth shock structures at all Mach numbers and significantly improve upon the results of the Navier–Stokes equations. With no tweaking of the equations in any way, the present work makes two important contributions by putting forward an improved theory of shock waves and establishing the validity of the OBurnett equations for solving complex flow problems.

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