2019 Volume 2019 Pages 20190012
In this paper, we proposed a novel numerical treatment for no-slip wall boundary conditions for incompressible fluid flow simulations in the LSMPS (least squares moving particle semi-implicit) method. In the conventional wall boundary treatments, velocity and pressure on a wall particle were treated as computational variables to enforce prescribed boundary conditions. However, such a treatment not only increases computational cost but also causes numerical instability. In the proposed treatment, no variable is defined on a wall particle, and boundary conditions themselves are incorporated into the spatial discretization scheme by means of the weighted least squares approach. To verify consistency of the proposed scheme, convergence studies were carried out. As numerical examples for fluid flow simulation, plane Poiseuille flow, three-dimensional square channel flow, rigid rotation problem and lid-driven cavity flow have been calculated. As a result, high accuracy and validity of the proposed method were confirmed.
