Developing the Computation of Mountain Groundwater with σ-Transform

Groundwater distribution in the mountain area is very wide. The tremendous order difference of the horizontal distance and vertical depth scales in completing three dimensional groundwater flow often causes the problem of massive computation or low accuracy. Therefore, in dealing with such large areas, this study continues and improves the development of groundwater flow computation model of Tung-Lin Tsai (2001) by using semi-three dimensional groundwater model, that making models can be efficiently applied to large area and can be accurately simulated the simulation for a small range. To overcome the undulating terrain, using σ- transform to calculate mountainous terrain will supplement the shortcoming that complex terrain of the mountain can’t be presented.

In this study, firstly mountain groundwater flow governing equation are divided into two parts considered individually, that are dismantling the slope disturbance for the non-pumping effect of gravity and pumping disturbance without considering the slope effect of gravity, and then transform a very complicated mountainous terrain into a unchanged level coordinate and the thickness of the vertical coordinates of the soil layers are 1 by σ-coordinates. In computation, the governing equation for every layer is assumed to satisfy quadratic polynomial function. At the interface between two layers the continuity of pore pressure and the continuity of flux must be satisfied. According to soil properties﹐ doing the vertical stratification and horizontal partitions, the simultaneous vertical and horizontal two-dimensional calculations, complete this mountainous area of the proposed semi-three dimensional groundwater flow model.

In this study, a simple case of the model is validated. Aiming at no pumping effect to consider the mountain groundwater of slope gravitational perturbation and the pumping disturbance of the mountain groundwater, verify and display the model reasonable. In addition, the study designs two conceptual models to simulate the actual mountainous terrain, high mountain terrain and gentle slope respectively, discussing the simulation of different mountainous terrain situation.