A Meshless Discretization Methodology Based on Lennard-Jones Forces

A meshless discretization methodology based on the Lennard-Jones force is presented. The new methodology, named Lennard-Jones discretization method (LJDM), can be seen as an enhancement of Coulomb's Law discretization method (CLDM). Because CLDM is based on the repulsive Coulomb's forces, it can produce conformal discretization node sets with soft transitions in the space surrounding geometrically different objects. However, in CLDM, reference nodal arrangement (RNA) can be drastically modified, making it difficult to deterministically define a stop criterion and convergence using an invariable set of values for free parameters. This problem is solved in this letter by employing an adapted version of the Lennard-Jones vector force, which is a composition of repulsive and attractive contributions. The main role of attractive forces is preserving RNA, while repulsive forces produce conformal discretization. Analysis of simulation error as function of LJDM and CLDM iterations shows that the inclusion of attractive forces makes LJDM superior to CLDM because convergence and stability are found to be assured for constant sets of free parameters over the discretization iterations.