Point Cloud Movement For Fully Lagrangian Meshfree Methods
For researchers using Lagrangian meshfree methods, this work addresses a critical accuracy bottleneck in point cloud movement, though the improvement is incremental.
The paper identifies that the commonly used first-order point movement method in Lagrangian meshfree methods introduces volume and mass conservation errors. It proposes two new methods based on characteristic velocity and streamline tracing, which are shown to be vastly superior to the first-order method.
In Lagrangian meshfree methods, the underlying spatial discretization, referred to as a point cloud or a particle cloud, moves with the flow velocity. In this paper, we consider different numerical methods of performing this movement of points or particles. The movement is most commonly done by a first order method, which assumes the velocity to be constant within a time step. We show that this method is very inaccurate and that it introduces volume and mass conservation errors. We further propose new methods for the same which prescribe an additional ODE system that describes the characteristic velocity. Movement is then performed along this characteristic velocity. The first new way of moving points is an extension of mesh-based streamline tracing ideas to meshfree methods. In the second way, the movement is done based on the difference in approximated streamlines between two time levels, which approximates the pathlines in unsteady flow. Numerical comparisons show these method to be vastly superior to the conventionally used first order method.