Meshless Scheme Based on Alignment Constraints

Development of a new meshless technique is described that presents certain advantages over conventional meshless schemes due to unique weights that force alignment of the derivative approximation. The method is completelymeshless, yet retains the low storage and simple fluxdistribution technique that are characteristic of finite volumemethods. The newmethod is based on thewell-knownTaylor series expansionmethodwith least squares. The proposed weighting scheme significantly reduces storage and computational requirements compared to other meshless schemes. The scheme is shown to be analogous to finite volume schemes in many ways, but it still lacks a discrete telescoping property and is not discretely conservative. The method is applied to the Euler equations in two dimensions. Results are presented that agree well with established methods.