Kwang Y. Kim

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We construct and analyze a mixed finite volume method on quadrilateral grids for elliptic problems written as a system of two first order PDEs in the state variable (e.g., pressure) and its flux (e.g., Darcy velocity). An important point is that no staggered grids or covolumes are used to stabilize the system. Only a single primary grid system is adopted,(More)
We consider covolume methods for the mixed formulations of quasi-linear secondorder elliptic problems. Covolume methods for the mixed formulations of linear elliptic problem was first considered by Russell [Rigorous Block-Centered Discretizations on Irregular Grids: Improved Simulation of Complex Reservoir Systems, Tech. report 3, Project Report, Reservoir(More)
We present a general framework for constructing and analyzing finite volume methods applied to the mixed formulation of second-order elliptic problems on quadrilateral grids. The control volumes, or covolumes, in the grids overlap. An overlapping finite volume method of this type was first introduced by Russell in [T. F. Russell, Tech. report 3, Reservoir(More)
A flux recovery technique is introduced and analyzed for the computed solution of the primal hybrid finite element method for second-order elliptic problems. The recovery is carried out over a single element at a time while ensuring the continuity of the flux across the interelement edges and the validity of the discrete conservation law at the element(More)
In this paper we introduce and analyze new mixed finite volume methods for second order elliptic problems which are based on H(div)-conforming approximations for the vector variable and discontinuous approximations for the scalar variable. The discretization is fulfilled by combining the ideas of the traditional finite volume box method and the local(More)
This study presents experimental results on evaporation and drainage in both wettable and water-repellent sands whose surface wettability was artificially modified by silanization. The 2D optical and 3D X-ray computed tomographic imaging was performed during evaporation and the water retention during cyclic drainage and infiltration was measured to assess(More)
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