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Abstract.A new triangular mesh adaptivity algorithm for elliptic PDEs that combines a posteriori error estimation with centroidal Voronoi-Delaunay tessellations of domains in two dimensions is proposed and tested. The ability of the first ingredient to detect local regions of large error and the ability of the second ingredient to generate superior unstructured grids result in a mesh adaptivity algorithm that has several very desirable features, including the following. Errors are very well equidistributed over the triangles; at all levels of refinement, the triangles remain very well shaped, even if the grid size at any particular refinement level, when viewed globally, varies by several orders of magnitude; and the convergence rates achieved are the best obtainable using piecewise linear finite elements. This methodology can be easily extended to higher-order finite element approximations or mixed finite element formulations although only the linear approximation is considered in this paper.

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A two-dimensional sand tank experiment was designed to explore the mechanism of water distribution and silt clogging of Yellow River water whilst replenishing groundwater in ‘open window’ reach of the piedmont river and strong seepage area consisting of a gravel and karst layer from top to bottom. Water released through the reach was divided into surface, pore and fracture karst water, of which karst water was an effective recharge from the surface water. A reasonable released water plan is necessary in recharging to avoid invalid recharge. The karst water accounted for 60–70% of the amount of water released before clogging, and this value was reduced to approximately 10–20% whilst a thin clay layer formed from suspended particles on the surface layer of the medium after clogging. The removal rate of suspended solids along vertical and lateral directions in the medium can reach over 96%. The retained amount of suspended particles was mainly distributed on the surface and upper layer region of the medium. A rubber dam can improve effective infiltration whilst promoting suspended solid deposition in the medium. The fitting degree of the numerical simulation and measured results was above 0.9, which proves the reliability of the sand tank model results.

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