A high-order accurate meshless method for solution of incompressible fluid flow problems

Meshless solution to differential equations using radial basis functions (RBF) is an alternative grid based methods commonly used. Since the meshless method does not need underlying connectivity in form of control volumes or elements, issues such as skewness that adversely impact accuracy are eliminated. Gaussian, Multiquadrics and inverse some most popular RBFs used for solutions fluid flow heat transfer problems. But they have additional shape parameters be fine tuned stability. Moreover, also face stagnation error when point density increased accuracy. Recently, Polyharmonic splines (PHS) with appended polynomials been shown solve above give rapid convergence discretization errors degree polynomials. In this research, we extend PHS-RBF incompressible Navier-Stokes equations. A fractional step explicit convection diffusion terms combined a pressure Poisson equation satisfy momentum continuity Systematic tests performed five model problems two them having analytical solutions. We demonstrate fast both refinement number points The further applied lid-driven cavity vortex shedding over circular cylinder. analyzed performance approach Euler proposed shows promise complex domains high