A Space-Time Meshless Method That Removes Numerical Oscillations When Solving PDEs with High Discontinuities

Abstract

A space-time diffuse approximation method avoiding any secondary finite-difference time-stepping procedure, is presented to solve partial differential equations (PDEs) containing high discontinuities. This method is validated with a non-inner source heat equation. It is shown that its accuracy is improved when using a new proposed weight function. Furthermore, the application of the new weight function, respecting the principle of causality, removes some spurious oscillations appearing with high temporally discontinuous heat sources (such as Heaviside). Results, presented as isotherms or temperature fields, get closer to those obtained with an implicit first-order backward finite–difference scheme.