A Meshless Volume Scheme

Development of a new meshless technique is described, called the meshless volume scheme. The method is completely meshless, yet retains the low storage and simple flux distribution technique characteristic of finite volume methods. The new method is based on the well-known Taylor series expansion method with least squares. A least squares weighting scheme is introduced that 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 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 which agree well with established methods.