Direct Numerical Simulation (DNS) code for simulating incompressible

laminar flows

Name: Manmeet Singh

Guide’s name: Dr S.A. Dixit

Institute: IITM Pune

Direct Numerical Simulation is a method of solving the equations of

motion(Navier-Stokes(NS) Equations), without any turbulence model, by

directly discretizing the equations alongwith the initial and boundary con-

ditions. In this study a code is developed to solve the NS equations using

fractional step method over a 2D rectangular cartesian domain. The present

mesh size is 32 x 32 and is solved by finite volume method via finite dif-

ference method. The Pressure Poisson Equation is solved by the Successive

Over Relaxation method with β =1.2. The present code is for dimensional

NS equations for now but will be non dimensionalized in the future. For

validating the code the standard test case of lid-driven cavity flow(Re=1000)

is chosen. The trends in the results of the present code show reasonable

match with the benchmark data to within the present limited spatial reso-

lution. For the initial studies, MATLAB is used whereas the code is written

in FORTRAN 90 for further computations. The output from FORTRAN 90

program is written on netcdf files and visualized on MATLAB and Ferret.

After validation, the code is tested for the case of laminar jet flow entering

the box domain from the bottom boundary and exiting smoothly through

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the top boundary. Side walls carry no-slip boundary conditions, bottom wall

carries no-slip boundary condition in addition to jet velocity profile and the

boundary top wall carries zero gradient(in the direction of flow) condition.

For the initial conditions, it is assumed that the fluid is at rest at the start

of simulation. The vorticity plots from the simulated flow appear to be were

found to be qualitatively satisfactory.

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