The Moving Least Squares (MLS) grid-free method, a simple, flexible finite difference method for solution of general continuum mechanics problems, especially detonation problems, is proposed in this paper. The spatial points that carry time dependent data are distributed in space in such a way that provides nearly uniform spacing of points, accurate presentation of boundaries, easy variation of resolution and arbitrary reorganization of the computational domain. Local finite difference operators are obtained with simple MLS differentiation. There is no specific topological or geometrical restriction of the distribution of data points. Therefore this method avoids many drawbacks of the traditional methods. Because of its flexibility, it can be used to simulate a wide range of mechanics problems. Because of its simplicity, it has the potential to become a preferred method. Most traditional computational continuum mechanics (CCM) methods, from a Smooth Particle Hydrodynamics (SPH) view, can be considered as special cases of grid-free methods of specific kernel functions. Such a generalization allows the development of a unified grid-free method that can represent most finite difference methods by switching the kernel functions. The flexible management and ease of coding make such a unified code attractive for many applications. A simple three-dimensional narrow-band level-set algorithm, which is associated with the MLS grid free data point distribution in three dimensions, is also proposed.
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