advanced numerical simulations of lid-driven cavity flows using an optimized parallelized fractional step method

This work presents a numerical simulation of lid-driven cavity flows by solving the incompressible navier-stokes equations, with results validated against established benchmarks. the developed code uses a fractional step method combined with second-order adams-bashforth time discretization and crank-nicolson spatial discretization to achieve both accuracy and stability. a finite difference method is applied on a staggered grid to implement key operators such as gradient, divergence, laplace, and advection, all computed with second-order central differencing. to efficiently solve the pressure poisson equation, the conjugate gradient algorithm is employed. the code is vectorized and parallelized to enhance computational performance. an intriguing case involving opposite moving walls is also explored, revealing altered flow dynamics. this robust and efficient cfd code enables fast, accurate simulations of various fluid flow cases, providing deeper insights into complex flow phenomena.