Historical Development of Meshless Modeling: On contaminant Transport and Fluid Flow Through porous Media

In retrospect, this is realized that governing equations in all engineering fields such as fluid mechanics, solid mechanics, aerospace issues, groundwater contaminant transport etc. are inherently based on several ordinary or partial differential equations. Partial differential equations characterize the material s behavior during life time under specific conditions. The solution of these governing equations attracted the attentions by mathematicians, physicists and engineers. To this end, different computational techniques including finite element method, finite difference method, finite volume method, boundary element method and scaled-boundary finite element method have been introduced. However, over recent decades, a new type of numerical approaches termed meshless or mesh-free or element-free techniques have been developed and examined over a wide ranges of hydrological sciences and geo-environmental engineering problems. Our major objective in the present study is to describe the historical advances in meshless solutions of partial differential equations governing contaminant transport and fluid flow through landfill liners and saturated/unsaturated porous media.

کلیدواژه ها:

contaminant transport ، fluid flow ، porous media ، meshless methods ، Partial differential equations.