A new high accuracy meshfree method to directly simulate fluid dynamics and heat transfer of weakly compressible fluids

A Tayler series expansion based high accuracy meshfree method (TS-HAMM) is developed to calculate first and second derivatives of property values stored in dispersed particle clouds. Compared with other meshfree methods such as smoothed particle hydrodynamics (SPH), TS-HAMM can (a) systematically increase accuracies in gradient, derivative and Laplacian calculations with similar computational cost; (b) provide boundary conditions directly from conservation equations at the fluid/solid interfaces with guaranteed order of accuracy; (c) simulate fluid dynamics and heat transfer of low viscous weakly compressible fluid (e.g. water) directly without making incompressible assumptions. Through numerical verifications with water-like low viscous low compressible fluid in Couette flow, lid-driven flow inside a cavity, and natural convection inside an enclosure, we justify the validity of TS-HAMM in simulating fluid dynamics and heat transfer of water-like low viscous weakly compressible fluid, which are challenging with other meshfree methods such as smoothed particle hydrodynamics (SPH).