Proper evaluation of spherical harmonics-based expressions for the velocity and vortex stretching vectors in three-dimensional grid-free vortex methods

2020 ◽  
Vol 418 ◽  
pp. 109603
Author(s):  
Samer Salloum ◽  
Issam Lakkis
Keyword(s):  
Spherical Harmonics ◽  
Three Dimensional ◽  
Vortex Methods ◽  
Free Vortex

Grid-Free Vortex Methods for Natural Convection in Two-Dimensional Domains

2012 ◽  
Author(s):  
Issam Lakkis
Keyword(s):  
Natural Convection ◽  
Nonlinear Diffusion ◽  
Reacting Flows ◽  
Ideal Gas ◽  
Two Dimensional ◽  
Vortex Methods ◽  
Free Vortex ◽  
Low Mach Number ◽  
Buoyancy Driven Flows ◽  
Vorticity Generation

Vortex methods for simulating natural convection of an ideal gas in unbounded two-dimensional domains are presented. In particular, the redistribution method for diffusion is extended to enable simulation of nonlinear diffusion of an ideal gas in isobaric conditions encountered in unbounded low-Mach number flows. We also address the problem of handling source terms in grid-free vortex methods and propose a fast, accurate, and physically motivated method for solving the associated inverse problems. Examples include generation of baroclinic vorticity in non-reacting buoyancy driven flows, and in addition, generation of internal energy and species in buoyant reacting flows. Accuracy and speed of the proposed algorithms for nonlinear diffusion and vorticity generation are investigated separately. Simulations of natural convection of a “thermal patch” for Grashof number ranging from to 1562.5 to 25000 are presented.

Simulation of Artificial Turbulence by the Vortex Method

2002 ◽  
Author(s):  
Yoshifumi Ogami ◽  
Kazuie Nishiwaki ◽  
Yoshinobu Yoshihara
Keyword(s):  
Turbulent Flows ◽  
Three Dimensional ◽  
Vortex Method ◽  
Energy Spectra ◽  
System Of Nonlinear Equations ◽  
Vortex Methods ◽  
Velocity Fluctuations ◽  
Integral Scales ◽  
Relative Errors ◽  
Les Model

First, a simple and accurate numerical method is presented to produce velocity fluctuations that are determined by the prescribed physical quantities and qualities of turbulence such as longitudinal and lateral spectra, and integral scales. The fluctuations are obtained by solving a system of nonlinear equations that are derived from the equations of energy spectra and of root mean square of the fluctuations. This method requires as many computer memories and computations as one-dimensional case even for the three dimensional calculations. It is shown that there is a strong resemblance of the simulated velocity fluctuations and experimental data. The energy spectra of these velocity fluctuations are quite accurate with less than 0.01% relative errors to the prescribed spectra. Secondly, these solutions are used to examine the capability of the vortex methods to produce turbulent flows with the prescribed parameters. It is found that although the energy spectra by the vortex method scatter to some extent, they are distributed along the prescribed spectra. It can be said that the vortex methods are able to simulate the target turbulence fairly well. Also it is found that the solutions with the LES model increase and deviate from the target spectrum at the higher frequency regions. This may suggest the nonessentiality of the LES model for the vortex method.

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