A REPRODUCING KERNEL FORMULATION FOR MODELING SHOCKS

A reproducing kernel particle method formulation for modeling shocks formed by non- linear hyperbolic partial differential equations is developed using a flux-based velocity correction technique. The technique is coupled with a spectral decomposition shock detection algorithm to isolate corrections to the jump location. For this class of model problems, the technique is shown to accurately capture the physically correct solution and minimize oscillatory error due to Gibbs phenomenon. The approach provides a basis for further investigation on the extension to the equation of motion and shock-forming solid dynamics problems.