Stabilization of a meshless method via weighted least squares filtering

Stability of a meshless method proposed for strong form of a linear hyperbolic partial differential equation can be ensured via simple filtering procedure in the weighted least squares sense. This approach overcomes the need for the upwind implementation of numerical fluxes and thus employs central-type scheme that is more suitable for methods constructing the approximations on local clouds of points. The behavior of the filter and the overall performance of the method is verified on a set of benchmark problems, where the propagation of acoustic waves is modeled by linearized Euler equations and the results are compared with analytical and/or numerical reference solutions.