Solution of 2-D Incompressible Navier Stokes Equations with Artificial Compressibility Method Using Ftcs Scheme
SOLUTION OF 2-D INCOMPRESSIBLE NAVIER STOKES EQUATIONS WITH ARTIFICIAL COMRESSIBILITY METHOD USING FTCS SCHEME
IMRAN AZIZ
Department of Mechanical Engineering College of EME
National University of Science and Technology
Islamabad, Pakistan
Imran_9697@hotmail.com
Abstract— The paper deals with the 2-D lid-driven cavity flow governed by the non dimensional incompressible Navier-Stokes theorem in the rectangular domain. Specific boundary conditions for this case study have been defined and the flow characteristics pertaining to the scenario have been coded in MATLAB using artificial compressibility method and FTCS scheme. The results are compared successfully with an authentic research paper by Ghia, Ghia & Shin.
Keywords: Navier stokes equations, Artificial Compressibility, FTCS scheme.
Introduction
The Navier-Stokes equations describe the motion of fluid substances and are used to solve wide range of problems in Fluid Dynamics. These equations include conservations of mass, momentum and energy. In this documentation we present the solution of 2-d navier stokes equations in a flow driven lid cavity used as a model for subsonic bombers weapons bay. The weapons bay is a compartment on fighter aircrafts to carry bombs [1].It is a highly critical area for any bomber design in the aeronautical industry. The design optimization of weapon bay involves various considerations namely weapon load capacity, extent of vibration and severe aerodynamic drag. In order to approximate the problem, a MATLAB code is developed to solve two dimensional incompressible navier stokes equations. Incompressible flows are those in which density variation is not linked to the pressure. The mass conservation is a constraint on velocity field. The continuity equation can be combined with momentum equation to derive the equation for pressure or it can be solved independently by applying artificial compressibility.
We have used the later approach by employing FTCS scheme. The
IMRAN AZIZ
Department of Mechanical Engineering College of EME
National University of Science and Technology
Islamabad, Pakistan
Imran_9697@hotmail.com
Abstract— The paper deals with the 2-D lid-driven cavity flow governed by the non dimensional incompressible Navier-Stokes theorem in the rectangular domain. Specific boundary conditions for this case study have been defined and the flow characteristics pertaining to the scenario have been coded in MATLAB using artificial compressibility method and FTCS scheme. The results are compared successfully with an authentic research paper by Ghia, Ghia & Shin.
Keywords: Navier stokes equations, Artificial Compressibility, FTCS scheme.
Introduction
The Navier-Stokes equations describe the motion of fluid substances and are used to solve wide range of problems in Fluid Dynamics. These equations include conservations of mass, momentum and energy. In this documentation we present the solution of 2-d navier stokes equations in a flow driven lid cavity used as a model for subsonic bombers weapons bay. The weapons bay is a compartment on fighter aircrafts to carry bombs [1].It is a highly critical area for any bomber design in the aeronautical industry. The design optimization of weapon bay involves various considerations namely weapon load capacity, extent of vibration and severe aerodynamic drag. In order to approximate the problem, a MATLAB code is developed to solve two dimensional incompressible navier stokes equations. Incompressible flows are those in which density variation is not linked to the pressure. The mass conservation is a constraint on velocity field. The continuity equation can be combined with momentum equation to derive the equation for pressure or it can be solved independently by applying artificial compressibility.
We have used the later approach by employing FTCS scheme. The
References: Klaus A. Hoffmann, Steve T. Chiang “Computational Fluid Dynamics,” Engineering eduaction system,Wichita, Kansas, 67208-1078, USA, vol. I, pp. 316–317,August 2001. Klaus A. Hoffmann, Steve T. Chiang “Computational Fluid Dynamics,” Engineering eduaction system,Wichita, Kansas, 67208-1078, USA, vol. I, pp. 316–317, August 2001. U. Ghia, K. N. Ghia, And C. T. Shin, Journal of Computational Physis(1982),pp 396-397 U U. Ghia, K. N. Ghia, And C. T. Shin, Journal of Computational Physis(1982),pp 396-397 Dale A