Numerical validation of the volume penalization method in three-dimensional pseudo-spectral simulations

2012 ◽  
Vol 67 ◽  
pp. 41-56 ◽  
Author(s):  
C. Jause-Labert ◽  
F.S. Godeferd ◽  
B. Favier
Keyword(s):  
Three Dimensional ◽  
Penalization Method ◽  
Numerical Validation ◽  
Spectral Simulations ◽  
Pseudo Spectral ◽  
Volume Penalization Method

scholarly journals Numerical Simulation of Wall-Bounded Flows using a Spectral Method with Volume Penalization

2018 ◽  
Vol 63 ◽  
pp. 280-289
Author(s):  
Yoichi Sawamura ◽  
Katsunori Yoshimatsu ◽  
Kai Schneider
Keyword(s):  
Numerical Solution ◽  
Spectral Method ◽  
Three Dimensional ◽  
Turbulent Channel Flow ◽  
Navier Stokes ◽  
Penalization Method ◽  
Constant Flow Rate ◽  
Slip Boundary ◽  
Wall Bounded Flows ◽  
Volume Penalization Method

The volume penalization method, which allows to impose no-slip boundary conditions, is assessed for wall-bounded flows. For the numerical solution of the penalized equations a spectral method is used. Considering a two-dimensional Poiseuille flow, the solution of the Navier-Stokes penalized equation is computed analytically and the convergence of the numerical solution is studied. To illustrate the properties of the approach we compute a three-dimensional turbulent channel flow imposing a constant flow rate. The obtained results are compared with reference data of Kim et al. [10].

Interaction of Transient Waves With a Circular Surface-Piercing Body

1995 ◽  
Vol 117 (3) ◽  
pp. 382-388 ◽  
Author(s):  
Xing Yu ◽  
Ronald W. Yeung
Keyword(s):  
Large Time ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Transient Waves ◽  
Generalized Poisson ◽  
Poisson Solver ◽  
Potential Applications ◽  
Circular Surface ◽  
High Degree ◽  
Pseudo Spectral

A pseudo-spectral formulation for solving unsteady, three-dimensional fluid motion with a free surface in cylindrical coordinates is presented. An effective method for treating the Laplace equation, as a special application of a generalized Poisson solver, is developed. This approach is demonstrated by studying the evolution of transient surface waves near a vertical circular cylinder enclosed in open or closed domains. Results are observed to have a high degree of precision and spatial resolution even at large time. Potential applications of this method to other problems are discussed.

Numerical simulation of bubbly flow around a cylinder by semi-Lagrangian–Lagrangian method

2019 ◽  
Vol 29 (12) ◽  
pp. 4660-4683 ◽  
Author(s):  
Van Luc Nguyen ◽  
Tomohiro Degawa ◽  
Tomomi Uchiyama ◽  
Kotaro Takamure
Keyword(s):  
Circular Cylinder ◽  
Vortex Structure ◽  
Bubbly Flow ◽  
Three Dimensional ◽  
Lagrangian Method ◽  
Lagrangian Description ◽  
Penalization Method ◽  
Flow Around A Cylinder ◽  
Content Type ◽  
Flow Phenomena

Purpose The purpose of this study is to design numerical simulations of bubbly flow around a cylinder to better understand the characteristics of flow around a rigid obstacle. Design/methodology/approach The bubbly flow around a circular cylinder was numerically simulated using a semi-Lagrangian–Lagrangian method composed of a vortex-in-cell method for the liquid phase and a Lagrangian description of the gas phase. Additionally, a penalization method was applied to account for the cylinder inside the flow. The slip condition of the bubbles on the cylinder’s surface was enforced, and the outflow conditions were applied to the liquid flow at the far field. Findings The simulation clarified the characteristics of a bubbly flow around a circular cylinder. The bubbles were shown to move around and separate from both sides of the cylinder, because of entrainment by the liquid shear layers. Once the bubbly flow fully developed, the bubbles distributed into groups and were dispersed downstream of the cylinder. A three-dimensional vortex structure of various scales was also shown to form downstream, whereas a quasi-stable two-dimensional vortex structure was observed upstream. Overall, the proposed method captured the characteristics of a bubbly flow around a cylinder well. Originality/value A semi-Lagrangian–Lagrangian approach was applied to simulate a bubbly flow around a circular cylinder. The simulations provided the detail features of these flow phenomena.

scholarly journals Laguerre–Hermite pseudo-spectral velocity formulation of gyrokinetics

2018 ◽  
Vol 84 (1) ◽  
Author(s):  
N. R. Mandell ◽  
W. Dorland ◽  
M. Landreman
Keyword(s):  
Three Dimensional ◽  
Collision Operator ◽  
Zonal Flow ◽  
Phase Mixing ◽  
Final Model ◽  
Nonlinear Phase ◽  
Wide Range ◽  
H Theorem ◽  
Spectral Velocity ◽  
Pseudo Spectral

First-principles simulations of tokamak turbulence have proven to be of great value in recent decades. We develop a pseudo-spectral velocity formulation of the turbulence equations that smoothly interpolates between the highly efficient but lower resolution three-dimensional (3-D) gyrofluid representation and the conventional but more expensive 5-D gyrokinetic representation. Our formulation is a projection of the nonlinear gyrokinetic equation onto a Laguerre–Hermite velocity-space basis. We discuss issues related to collisions, closures and entropy. While any collision operator can be used in the formulation, we highlight a model operator that has a particularly sparse Laguerre–Hermite representation, while satisfying conservation laws and the H theorem. Free streaming, magnetic drifts and nonlinear phase mixing each give rise to closure problems, which we discuss in relation to the instabilities of interest and to free energy conservation. We show that the model is capable of reproducing gyrokinetic results for linear instabilities and zonal flow dynamics. Thus the final model is appropriate for the study of instabilities, turbulence and transport in a wide range of geometries, including tokamaks and stellarators.

A Pseudo-Spectral Numerical Scheme for the Simulation of Convective Flows

2002 ◽  
Author(s):  
Laila Guessous ◽  
Yuehong Zheng
Keyword(s):  
Variational Formulation ◽  
Numerical Scheme ◽  
Mass Matrix ◽  
Three Dimensional ◽  
Vertical Direction ◽  
The Novel ◽  
Convective Flows ◽  
Development And Validation ◽  
Pseudo Spectral ◽  
Unsteady Channel Flow

This paper focuses on the development and validation of a pseudo-spectral numerical scheme, based on a variational formulation, for the solution of the three-dimensional, time-dependent governing equations in wall bounded forced and natural convective flows. One of the novel aspects of this numerical scheme is the use of rescaled Legendre-Lagrangian interpolants to represent the velocity and temperature in the vertical direction. These interpolants were obtained by dividing the Legendre Lagrangian interpolants of same order by the square root of the corresponding weight used for Gauss-Lobatto quadrature. By rescaling the interpolants in such a manner, the mass matrix resulting from the variational formulation becomes the identity matrix, thus simplifying the numerical algorithm. Two specific problems have been investigated as part of the validation process: Steady and unsteady channel flow driven by an external streamwise oscillating pressure gradient and Rayleigh Be´nard convection. In all cases, comparison with exact solutions and published results yield excellent agreement.

Symmetry-breaking bifurcations in spherical Couette flow

1996 ◽  
Vol 310 ◽  
pp. 293-324 ◽  
Author(s):  
Oleg Yu. Zikanov
Keyword(s):  
Symmetry Breaking ◽  
Stokes Equations ◽  
Numerical Technique ◽  
Three Dimensional ◽  
Travelling Wave ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Basic Equilibrium ◽  
Spherical Couette ◽  
Pseudo Spectral

The solutions of the nonlinear and linearized Navier-Stokes equations are computed to investigate the instabilities and the secondary two- and three-dimensional regimes in the flow of an incompressible viscous fluid in a thin gap between two concentric differentially rotating spheres. The numerical technique is finite difference in the radial direction, spectral in the azimuthal direction, and pseudo-spectral in the meridional direction. The study follows the experiments by Yavorskaya, Belyaev and co-workers in which a variety of steady axisymmetric and three-dimensional travelling wave secondary regimes was observed in the case of a thin layer and both boundary spheres rotating. In agreement with the experimental results three different types of symmetry-breaking primary bifurcations of the basic equilibrium are detected in the parameter range under consideration.

Turbulent relaxation of a confined magnetofluid to a force-free state

1987 ◽  
Vol 37 (2) ◽  
pp. 299-321 ◽  
Author(s):  
Jill P. Dahlburg ◽  
David Montgomery ◽  
Gary D. Doolen ◽  
Leaf Turner
Keyword(s):  
Magnetic Field ◽  
Energy State ◽  
Minimum Energy ◽  
Three Dimensional ◽  
Small Scale ◽  
Current Profile ◽  
Transit Times ◽  
Uniform Current ◽  
Scale Turbulence ◽  
Pseudo Spectral

Three-dimensional, pseudo-spectral computation is used to follow the evolution of a resistive, incompressible magnetofluid. The magnetofluid is confined by rigid, free-slip, perfectly-conducting square boundaries in the x, y directions (‘poloidal’ boundaries), and periodic boundary conditions are assumed in the z direction (‘toroidal’ direction). A constant, uniform d.c. magnetic field B0 is assumed in the z direction and a non-uniform current density j flows along it initially. Starting from a non-equilibrium hollow current profile, the evolution is followed for several tens of Alfvén transit times. Considerable small-scale turbulence develops, which causes energy to decay more rapidly than magnetic helicity. The average toroidal magnetic field at the (x, y) boundary reverses sign spontaneously. The near spatial constancy of the ratio jB/(jB) ≡ cos θ, in the relaxed state at late times, suggests that the state is nearly force-free. However, the ratio j. B/B2 ≡ α is considerably less uniform than is cos θ suggesting more residual disorder than a pure minimum-energy state would display.

Sign in / Sign up

Export Citation Format

Share Document