Abstract. Algebraic Reconstruction Techniques (ART), on their both successive or simultaneous formulation, have been developed since early 70's as efficient "row action methods" for solving the image reconstruction problem in Computerized Tomography. In this respect, two important development directions were concerned with, firstly their extension to the inconsistent case of the reconstruction problem, and secondly with their combination with constraining strategies, imposed by the particularities of the reconstructed image. In the first part of our paper we introduce extending and constraining procedures for a general iterative method of ART type and we propose a set of sufficient assumptions that ensure the convergence of the corresponding algorithms. As an application of this approach, we prove that Cimmino's simultaneous reflections method satisfies this set of assumptions, and we derive extended and constrained versions for it. Numerical experiments with all these versions are presented on a head phantom widely used in the image reconstruction literature. We also considered hard thresholding constraining used in sparse approximation problems and applied it successfully to a 3D particle image reconstruction problem.
Picard and Newton iterations are widely used to solve numerically the nonlinear Richards' equation (RE) governing water flow in unsaturated porous media. When solving RE in two space dimensions, direct methods applied to the linearized problem in the Newton/Picard iterations are inefficient. The numerical solving of RE in 2D with a nonlinear multigrid (MG) method that avoids Picard/Newton iterations is the focus of this work. The numerical approach is based on an implicit, second-order accurate time discretization combined with a second-order accurate finite difference spatial discretization. The test problems simulate infiltration of water in 2D unsaturated soils with hydraulic properties described by Broadbridge-White and van Genuchten-Mualem models. The numerical results show that nonlinear MG deserves to be taken into consideration for numerical solving of RE.
The need of accurate and efficient numerical schemes to solve Richards' equation is well recognized. This study is carried out to examine the numerical performances of the nonlinear multigrid method for numerical solving of the two-dimensional Richards' equation modeling water flow in variably saturated porous media. The numerical approach is based on an implicit, second-order accurate time discretization combined with a vertex centered finite volume method for spatial discretization. The test problems simulate infiltration of water in 2D saturated-unsaturated soils with hydraulic properties described by van Genuchten-Mualem models. The numerical results obtained are compared with those provided by the modified Picard-preconditioned conjugated gradient (Krylov subspace) approach.
Methane is one of the most common gaseous fuels that also exist in nature as the main part of the natural gas, the flammable part of biogas or as part of the reaction products from biomass pyrolysis. In this respect, the biogas and biomass installations are always subjected to explosion hazards due to methane. Simple methods for evaluating the explosion hazards are of great importance, at least in the preliminary stage. The paper describes such a method based on an elementary analysis of the cubic law of pressure rise during the early stages of flame propagation in a symmetrical cylindrical vessel of small volume (0.17 L). The pressure–time curves for lean, stoichiometric and rich methane–air mixtures were recorded and analyzed. From the early stages of pressure–time history, when the pressure increase is equal to or less than the initial pressure, normal burning velocities were evaluated and discussed. Qualitative experiments were performed in the presence of a radioactive source of 60Co in order to highlight its influence over the explosivity parameters, such as minimum ignition energy, maximum rate of pressure rise, maximum explosion pressure and normal burning velocity. The results are in agreement with the literature data.
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