PARTICLE METHOD FOR THE SOLUTION OF STOCHASTIC PROBLEMS: FORMULATION

This work presents the initial approach to a novel method for numerical solution of stochastic differential equations, showing the proper formulation for the stochastic term in a Lagrangian method. The mathematical formulation for the uncertainty properties terms of the model is based in the Karhunen -Loeve expansions used in the spectral stochastic finite ele- ment method (SSFEM). The particle method used is the Smoothed Particle Hydrodynamics (SPH), which is modified to represent the randomness of the output variables that are affected by the stochastic inlet properties behavior. This method formulation acquires importance for the solution of high deformation problems where there exists an uncertainty on the model properties.