Application of local radial basis function-based differential quadrature method in micro flows

Abstract

Numerical simulation of flows in micro geometry is one of the most appealing fields in computational fluid dynamics due to the advent of MEMS. In the present study, a local Radial Basis Function-based Differential Quadrature (RBF-DQ) method is applied to study the flow in micro cavity in the slip flow regime. RBF-DQ method is a natural mesh-free approach. The weighting coefficients of RBF-DQ method are determined by taking Radial Basis Functions (RBF) as test functions instead of using high order polynomials. RBF-DQ method has a unique feature of discretizing derivatives at a knot by a weighted linear sum of functional values at its neighboring knots, which may be distributed randomly. In the paper, two-dimensional incompressible flows in a micro lid-driven cavity are simulated with Knudsen number Kn < 0.1. Maxwell's first-order formula is adopted to treat slip boundary condition on solid walls.