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Solution of 2D Navier-Stokes equations in velocity-vorticity formulation using FD

Solution of 2D Navier-Stokes equations in velocity-vorticity formulation using FD. Remo Minero Scientific Computing Group – Dep. Mathematics and Computer Science. y. (-1,1). (1,1). D. O. (-1,-1). (1,-1). 2D NAVIER-STOKES EQUATIONS. where D is [-1; 1] x [-1; 1]. x. NUMERICAL METHOD.

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Solution of 2D Navier-Stokes equations in velocity-vorticity formulation using FD

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  1. Solution of 2D Navier-Stokes equations in velocity-vorticity formulation using FD Remo Minero Scientific Computing Group – Dep. Mathematics and Computer Science SMARTER meeting

  2. y (-1,1) (1,1) D O (-1,-1) (1,-1) 2D NAVIER-STOKES EQUATIONS where D is [-1; 1] x [-1; 1] x SMARTER meeting

  3. NUMERICAL METHOD • Temporal discretization: • Advection term: Adams-Bashforth scheme • Convection term: Crank Nicolson scheme • 2nd order Runge-Kutta scheme for the 1st time step • Spatial discretization: • Finite differences • Influence matrix technique to enforce boundary condition for  2nd order accuracy Accuracy dependent on derivatives’ discretization (e.g. 1st order for upwind, 2nd for centred differences, etc.) SMARTER meeting

  4. SELF ORGANIZATION OF VORTICES • Random initial condition for u, initial value for  follows consistently. (1 – Re=1000 ) (11 – Re=2500 ) SMARTER meeting

  5. Comparing results and performances with already existing codes FUTURE PERSPECTIVES Investigation on time evolution of some physical quantities like E,  and L Different initial conditions/ boundary conditions Steep gradient of  near the walls: LDC SMARTER meeting

  6. BC Coarse grid Fine grid Defect Max t non to have instabilities t x x x tn+1 tn-1 tn tn+2 LDC IN TRANSIENT PROBLEMS SMARTER meeting

  7. BC Coarse grid Fine grid Defect x x x x x x x x 0 0 L L LDC WITH SPECTRAL METHODS ? SMARTER meeting

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