Sharif Digital Repository

This paper investigates implementation of upwind compact implicit and explicit high-order finite difference schemes for solution of the level set equation. The upwind compact implicit and explicit high-order finite difference schemes are well-known techniques to descritize spatial derivatives for convection term in hyperbolic equations. Applying of upwind high-order schemes on the level set equation leads to less error and CPU time reduction compared to essential non-oscillatory (ENO), weighted essential non-oscillatory schemes (WENO), and even different particle level set methods. The results indicate the error based on area loss decreases drastically with applying high-order upwind,... 

Flow movement in unsaturated soil can be expressed by a partial differential equation, named Richards equation. The objective of this study is the finding of an appropriate implicit numerical solution for head based Richards equation. Some of the well known finite difference schemes (fully implicit, Crank Nicolson and Runge-Kutta) have been utilized in this study. In addition, the effects of different approximations of moisture capacity function, convergence criteria and time stepping methods were evaluated. Two different infiltration problems were solved to investigate the performance of different schemes. These problems include of vertical water flow in a wet and very dry soils. The... 

Meshless methods are a relatively new type of numerical methods that have attracted the attention of many researchers over the past years. So far, a number of meshless methods have been developed and applied to solve problems in various fields of engineering, including solid mechanics and geotechnical problems. The Element-Free Galerkin (EFG) method is adopted in this study for solving the governing partial differential equations of equilibrium and continuity of pore fluid flow for numerical simulation of coupled hydro-mechanical problems. For this purpose, the weak form of the governing equations is derived by applying the weighted residual method and Galerkin technique. The penalty method...