scholarly journals A Fully Discrete SIPG Method for Solving Two Classes of Vortex Dominated Flows

2020 ◽  
Author(s):  
Lunji Song
Keyword(s):  
Circular Cylinder ◽  
Dynamical Behavior ◽  
Navier Stokes ◽  
Benchmark Problems ◽  
Navier Stokes Equation ◽  
Driven Cavity ◽  
Fully Discrete ◽  
Space Discretization ◽  
Cylinder Flow ◽  
Incompressible Navier Stokes Equation

To simulate incompressible Navier–Stokes equation, a temporal splitting scheme in time and high-order symmetric interior penalty Galerkin (SIPG) method in space discretization are employed, while the local Lax-Friedrichs flux is applied in the discretization of the nonlinear term. Under a constraint of the Courant–Friedrichs–Lewy (CFL) condition, two benchmark problems in 2D are simulated by the fully discrete SIPG method. One is a lid-driven cavity flow and the other is a circular cylinder flow. For the former, we compute velocity field, pressure contour and vorticity contour. In the latter, while the von Kármán vortex street appears with Reynolds number 50≤Re≤400, we simulate different dynamical behavior of circular cylinder flows, and numerically estimate the Strouhal numbers comparable to the existing experimental results. The calculations on vortex dominated flows are carried out to investigate the potential application of the SIPG method.

scholarly journals Lattice Boltzmann Method for Two-Dimensional Unsteady Incompressible Flow

2016 ◽  
Vol 12 (2) ◽  
pp. 122-127
Author(s):  
Juraj Mužík
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Collision Operator ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equation ◽  
Driven Cavity ◽  
Boltzmann Method ◽  
Incompressible Navier Stokes Equation

Abstract A Lattice Boltzmann method is used to analyse incompressible fluid flow in a two-dimensional cavity and flow in the channel past cylindrical obstacle. The method solves the Boltzmann’s transport equation using simple computational grid - lattice. With the proper choice of the collision operator, the Boltzmann’s equation can be converted into incompressible Navier-Stokes equation. Lid-driven cavity benchmark case for various Reynolds numbers and flow past cylinder is presented in the article. The method produces stable solutions with results comparable to those in literature and is very easy to implement.

scholarly journals Unstructured Grid Solutions for Incompressible Laminar Flow over a Circular Cylinder Using a Particular Finite Volume-Finite Element Method

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Mahdi Yousefifard ◽  
Parviz Ghadimi ◽  
Rahim Zamanian
Keyword(s):  
Laminar Flow ◽  
Circular Cylinder ◽  
High Performance ◽  
Unstructured Grid ◽  
Unstructured Grids ◽  
Control Volume ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Benchmark Problems ◽  
Navier Stokes Equation

A numerical modeling of a 2D Navier-Stokes equation by a particular vertex centered control volume framework on an unstructured grid is presented in this paper. Triangular elements are applied with an effective high performance fully coupled algorithm, to simulate incompressible laminar flow over a circular cylinder. The cell face velocities in the discretization of the continuity and momentum equations are calculated by a combined linear and momentum interpolation scheme, respectively, and their performances are compared. Flow analyses have been conducted based on various Reynolds numbers up to 200 for the steady and unsteady flows using structured and unstructured grids. The robustness and accuracy of the scheme in the unstructured mesh are proved using the benchmark problems of incompressible laminar flow over a circular cylinder at low and medium Reynolds numbers. Results have been compared with the structured grid results, both cases with equal cell numbers and same strategy for the mesh refinement. Current results display good agreement with the experimental values. Overall, it is shown that, using the suggested method for the current problem, unstructured grids are highly competitive with the structured grids.

Numerical Simulation of High Reynolds Number Flow Structure in a Lid-Driven Cavity Using MRT-LES

2014 ◽  
Vol 554 ◽  
pp. 665-669
Author(s):  
Leila Jahanshaloo ◽  
Nor Azwadi Che Sidik
Keyword(s):  
Reynolds Number ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Numerical Technique ◽  
Lattice Boltzmann Model ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Driven Cavity ◽  
Reynolds Number Flow ◽  
Boltzmann Method

The Lattice Boltzmann Method (LBM) is a potent numerical technique based on kinetic theory, which has been effectively employed in various complicated physical, chemical and fluid mechanics problems. In this paper multi-relaxation lattice Boltzmann model (MRT) coupled with a Large Eddy Simulation (LES) and the equation are applied for driven cavity flow at different Reynolds number (1000-10000) and the results are compared with the previous published papers which solve the Navier stokes equation directly. The comparisons between the simulated results show that the lattice Boltzmann method has the capacity to solve the complex flows with reasonable accuracy and reliability. Keywords: Two-dimensional flows, Lattice Boltzmann method, Turbulent flow, MRT, LES.

A Study of Bifurcation Design Used in CD-ELISA Micro-Fluidic Platform

2010 ◽  
Author(s):  
Samuel I. En Lin
Keyword(s):  
Coriolis Force ◽  
Clinical Diagnostics ◽  
Biological Molecules ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Safety Testing ◽  
Micro Channels ◽  
Simulation Results ◽  
Incompressible Navier Stokes Equation ◽  
Detection And Quantification

Enzyme-linked immunosorbent assays (ELISA), one of the most common immunoassays, is widely used for detection and quantification of chemical and biological molecules and is becoming more and more important in clinical diagnostics, food safety testing, and environmental monitoring. A major challenge in developing the CD-ELISA is to split the flow (e.g., bio-reagents) evenly on the micro-channels. The Coriolis force resultant from CD rotation can disturb the flow in the splitter region and thus cause the failure mode in delivering the solution from each reservoir in a pre-specified manner. In this study, we investigate on the effects of inlet pressure and Coriolis force on the splitting ratio under two splitter structures. The analysis is based on the incompressible Navier-Stokes equation and the simulation results agree well with our experimental work.

Large-frequency global regularity for the incompressible Navier–Stokes equation

1999 ◽  
Vol 129 (5) ◽  
pp. 903-912
Author(s):  
Joel D. Avrin
Keyword(s):  
Boundary Conditions ◽  
Global Regularity ◽  
Stokes Equations ◽  
Strong Solutions ◽  
Dirichlet Boundary Conditions ◽  
Navier Stokes ◽  
Thin Domains ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Incompressible Navier Stokes Equation

We obtain global existence and regularity of strong solutions to the incompressible Navier–Stokes equations for a variety of boundary conditions in such a way that the initial and forcing data can be large in the high-frequency eigenspaces of the Stokes operator. We do not require that the domain be thin as in previous analyses. But in the case of thin domains (and zero Dirichlet boundary conditions) our results represent a further improvement and refinement of previous results obtained.

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