Use of a Solution-Adaptive Grid (SAG) Method for the Solution of the Unsaturated Flow Equation = 불포화 유동 방정식의 해를 위한 해적응격자법의 이용 연구

다국어 초록 (Multilingual Abstract)

A new numerical method using solution-adaptive grids (SAG) is developed to solve the Richards' equation (RE) for unsaturated flow in porous media. Using a grid generation technique, the SAG method automatically redistributes a fixed number of grid points during the flow process, so that more grid points are clustered in regions of large solution gradients. The method uses the coordinate transformation technique to employ a new transformed RE, which is solved with the standard finite difference method. The movement of grid points is incorporated into the transformed RE, and therefore all computation is performed on fixed grid points of the transformed domain without using any interpolation techniques. Thus, numerical difficulties arising from the movement of the wetting front during the infiltration process have been substantially overcome by the new method. Numerical experiments for an one-dimensional infiltration problem are presented to compare the SAG method to the modified Picard method using a fixed grid. Results show that accuracy of a SAG solution using 41 nodes is comparable with the solution of the fixed grid method using 201 nodes, while it requires only 50% of the CPU time. The global mass balance and the convergence of SAG solutions are strongly affected by the time step size (Δt) and the weighting parameter (${\gamma}$) used for generating solution-adaptive grids. Thus, the method requires automated readjustment of Δt and ${\gamma}$ to yield mass-conservative and convergent solutions, although it may increase computational costs. The method can be effective especially for simulating unsaturated flow and other transport problems involving the propagation of a sharp-front.