Document Type: Article
Golestan University, Faculty of Engineering, Gorgan, Iran
Temperature difference in the soil and its environments is a common phenomenon. The permeability of the soil changes with the temperature mostly because of the variation of the viscosity of water in different temperatures. More realistic estimation of the seepage value through and beneath hydraulic structures leads to more efficient design of them. In this paper, the heat conduction equation is solved by a least squares based meshfree method to calculate the distribution of the temperature in a soil. The distribution of the permeability coefficients can be varied irregularly that may make some difficulties in the mesh-based methods. In these methods the permeability changes in each mesh and finer mesh or some kinds of interpolation are required in the solution procedure. Since there is no need to form elements or grids in a meshfree method, it can handle this irregular variation simply. Here, the seepage equation is solved by the same least squares based meshfree method. The method is integral free, simple and efficient in calculation thanks to its sparse and positive definite matrices. The scheme is validated by solving a simplified version of the governing equations. More complicated problems are dealt with to investigate the phenomenon numerically.