Non-smooth kernels for meshfree methods in fluid dynamics

A function and its first two derivatives are estimated by convolutions with well-chosen non-differentiable kernels. The convolutions are in turn approximated by Newton-Cotes integration techniques with the aid of a polynomial interpolation based on an arbitrary finite set of points. Precise numerical results are obtained with far fewer points than that in classic SPH, and error bounds are derived. (C) 2009 Elsevier Ltd. All rights reserved.