Rbf-Fd Discretization of the Navier-Stokes Equations Using Staggered Nodes

A semi-implicit fractional-step method that uses a staggered node layout and radial basis function-finite differences (RBF-FD) to solve the incompressible Navier-Stokes equations is developed. Polyharmonic splines (PHS) with polynomial augmentation (PHS+poly) are used construct global differentiation matrices. systematic parameter study identifies combination of stencil size, PHS exponent, degree minimizes truncation error for wave-like test function on scattered nodes. Classical modified wavenumber analysis extended RBF-FDs heterogeneous distributions confirm accuracy selected 28-point comparable spectral-like, 6th-order Pad\'e-type finite differences. The solver demonstrated two benchmark problems, internal flow in lid-driven cavity Reynolds number regime $10^2 \leq \mathrm{Re}\leq 10^4$, open around cylinder at $\mathrm{Re}= 100$ $200$. grid staggering careful selection facilitates accurate stable simulations significantly lower resolutions than previously reported, using more compact RBF-FD stencils, without special treatment near solid walls, need hyperviscosity or other means regularization.