ANALYSIS OF THE 2-D FLUID VORTICES FORMATION BY FINITE DIFFERENCE METHOD - AJI HAPSORO (NIM : 20211002), CAHYO
Navier-Stokes equation is a complex non-linear second-order partial differential equation describing a fluid flow. To solve and model the fluid flow, a numerical method called the finite difference method is frequently used. Several assumptions are incorporated in numerically solving the Navier-Stokes equation: the fluid is incompressible, fluid flow parameters depend on its positions, and all variables are considered as periodic function. In this paper numerical calculation has been carried out to model the Kelvin-Helmholtz instability of mixed layer and evolution of vortex structure and vortex dipole. The calculation is done by varying the value of perturbation wavelength 0.5 x l = L and 0.25 x l = L . The smaller the value of perturbation wavelength or is called ratio λ/Lx the more larger vortices formed and its position will be close to others. In other hand, the larger ratio λ/Lx the more little the vortices formed. The variation of perturbation wavelength is also influences final condition time. Perturbation wavelength λ=0.25Lx will needs double time from time which needed by perturbation wavelength λ=0.5Lx to aim the same final condition. Reynolds number (Re) is also varied at 1000, 3000, 5000. The results show that for the three values of Re, the properties of the flows are laminar, critical, and turbulent, respectively as indicated by the vortices direction and distribution of fluid density. The larger the value of fluid velocity is, the more random and turbulent the fluid is.