  This work deals with a novel Gaussian filter-based pressure correction
technique with a super compact higher order finite difference scheme for
solving unsteady three-dimensional (3D) incompressible, viscous flows. This
pressure correction technique offers significant advantages in terms of
optimizing computational time by taking minimum iterations to reach the
required accuracy, making it highly efficient and cost-effective. Pressure
fields often exhibit highly nonlinear behavior, and employing the Gaussian
filter can help to enhance their reliability by reducing noise and
uncertainties. On the other hand, the super compact scheme uses minimum grid
points to produce second-order accuracy in time and fourth-order accuracy in
space variables. The main focus of this study is to enhance the accuracy and
efficiency and minimize the computational cost of solving complex fluid flow
problems. The super compact scheme utilizes 19 grid points at the known time
level (i.e., $n^{th}$ time level) and only seven grid points from the unknown
time level (i.e., $n + 1$ time level). By employing the above strategies, it
becomes possible to notably decrease computational expenses while maintaining
the accuracy of the computational scheme for solving complex fluid flow
problems. We have implemented our methodology across three distinct scenarios:
the 3D Burger's equation having analytical solution, and two variations of the
lid-driven cavity problem. The outcomes of our numerical simulations exhibit a
remarkable concordance, aligning exceptionally well with both the analytical
benchmarks and previously validated numerical findings for the cavity problems.
