A semi-implicit meshless method for incompressible flows in complex geometries

We present an exponentially convergent semi-implicit meshless algorithm for the solution of Navier-Stokes equations in complex domains. The discretizes partial derivatives at scattered points using radial basis functions (RBF) as interpolants. Higher-order polynomials are appended to polyharmonic splines (PHS-RBF) and a collocation method is used derive interpolation coefficients. interpolating kernels then differentiated partial-differential satisfied by points. PHS-RBF shown be with discretization errors decreasing high power representative distance between here time-dependent steady state fluid flows At each time step, several iterations performed converge momentum continuity equations. A Poisson equation pressure corrections formulated imposing divergence free condition on iterated velocity field. correction repeatedly solved until velocities pre-specified tolerance. have demonstrated convergence accuracy two model problems simulated four other problems. In all cases, stable Courant numbers excess ten. has potential accurately efficiently solve many flow heat transfer An open source code Meshless Multi-Physics Software (MeMPhyS) [1] available interested users algorithm.