SMOOTHED PARTICLE INTERPOLATION

Smoothed particle hydrodynamics (SPH) discretization techniques are generalized to develop a method, smoothed particle interpolation (SPI), for solving initial value problems of systems of a nonhydrodynamical nature. Under this approach, SPH is viewed as strictly an interpolation scheme and, as such, suitable for solving general hyperbolic and parabolic equations. The SPI method is tested on (1) the wave equation with inhomogeneous sound speed and (2) Burgers's equation. The efficiency of SPI is studied by comparing SPI solutions to those obtained with standard finite-difference methods. It is shown that the power of SPI arises when the smoothing particles are free to move.