In this paper, we consider the Buckley-Leverett model for space-dimensional problems of two-phase filtration of incompressible fluids based on gravity and without capillary forces. An advanced modified alternating tri...
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ISBN:
(纸本)9781509012695
In this paper, we consider the Buckley-Leverett model for space-dimensional problems of two-phase filtration of incompressible fluids based on gravity and without capillary forces. An advanced modified alternating triangular iterative method (MATM) that takes into account the availability of sources (sinks) in a relatively small number of nodes characterised by generalised delta-shaped functions is applied for a discrete model that approximates the boundary-initial task of filtration. We investigate the numerical solution of computationally time-consuming tasks in the reservoir with significant heterogeneity of permeability, which changes by four orders of magnitude within the reservoir and has a significant advantage to achieve a given accuracy within the number of iterations. In order to develop a coherent version of the advanced MATM, a parallel algorithm of its numerical implementation, based on decomposition in two spatial directions, is implemented on a multi-processor system with shared memory containing 2048 cores and a peak performance of 18.8 teraflops. Compared with a traditional implementation, a significant efficiency boost is demonstrated leading to a tenfold reduction of the the simulation process.
A modification of the multigrid method for the solution of linear algebraic equation systems with a strongly nonsymmetric matrix obtained after difference approximation of the convection-diffusion equation with domina...
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A modification of the multigrid method for the solution of linear algebraic equation systems with a strongly nonsymmetric matrix obtained after difference approximation of the convection-diffusion equation with dominant convection is proposed. Specially created triangular iterative methods have been used as the smoothers of the multigrid method. Some theoretical and numerical results are presented. (c) 2008 Elsevier B.V. All rights reserved.
In this paper, we consider the Buckley-Leverett model for space-dimensional problems of two-phase filtration of incompressible fluids based on gravity and without capillary forces. An advanced modified alternating tri...
详细信息
ISBN:
(纸本)9781509012701
In this paper, we consider the Buckley-Leverett model for space-dimensional problems of two-phase filtration of incompressible fluids based on gravity and without capillary forces. An advanced modified alternating triangular iterative method (MATM) that takes into account the availability of sources (sinks) in a relatively small number of nodes characterised by generalised delta-shaped functions is applied for a discrete model that approximates the boundary-initial task of filtration. We investigate the numerical solution of computationally time-consuming tasks in the reservoir with significant heterogeneity of permeability, which changes by four orders of magnitude within the reservoir and has a significant advantage to achieve a given accuracy within the number of iterations. In order to develop a coherent version of the advanced MATM, a parallel algorithm of its numerical implementation, based on decomposition in two spatial directions, is implemented on a multi-processor system with shared memory containing 2048 cores and a peak performance of 18.8 teraflops. Compared with a traditional implementation, a significant efficiency boost is demonstrated leading to a tenfold reduction of the simulation process.
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