We consider the problem of modeling flow through naturally fractured porous media. In this type of media, various physical phenomena occur on disparate length scales, so it is difficult to properly average their effec...
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We consider the problem of modeling flow through naturally fractured porous media. In this type of media, various physical phenomena occur on disparate length scales, so it is difficult to properly average their effects. In particular, gravitational forces pose special problems. In this paper we develop a general understanding of how to incorporate gravitational forces into the dual-porosity concept. We accomplish this through the mathematical technique of formal two-scale homogenization. This technique enables us to average the single-porosity, Darcy equations that govern the flow on the finest (fracture thickness) scale. The resulting homogenized equations are of dual-porosity type. We consider three flow situations, the flow of a single component in a single phase, the flow of two fluid components in two completely immiscible phases, and the completely miscible flow of two components.
An FFT method is described for the solution of Poisson's equation over a rectangular region with Robbins boundary conditions on either one or two sides of the region, together with suitable conditions on the rest ...
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An FFT method is described for the solution of Poisson's equation over a rectangular region with Robbins boundary conditions on either one or two sides of the region, together with suitable conditions on the rest of the boundary. In contrast to earlier applications of the FFT technique, the equations for the Fourier harmonic amplitudes do not decouple into simpler independent systems and an effective iterative scheme is developed for the solution of these equations. A theoretical convergence analysis is shown generally to support the results obtained from practical computation. For the test problems considered the method is found to take between 3 and 4 times the execution time for problems soluble directly by the FFT technique.
[1] has proved that the dissipative Zakharov system has an ε2-weak compact attractor. In this paper, we further show that the dissipative Langmuir waves in plasmas admit an inertial fractal set of (ε2,ε1)-type. We ...
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[1] has proved that the dissipative Zakharov system has an ε2-weak compact attractor. In this paper, we further show that the dissipative Langmuir waves in plasmas admit an inertial fractal set of (ε2,ε1)-type. We also make the estimates on its fractal dimension and exponential attraction.
Some convergence results are given for A(a)-stable linear multistep methods applied to two classes of two-parameter singular perturbation problems, which extend the existing relevant results about one-parameter proble...
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Some convergence results are given for A(a)-stable linear multistep methods applied to two classes of two-parameter singular perturbation problems, which extend the existing relevant results about one-parameter problems by Lubich~[1]. Some numerical examples confirm our results.
The open-shell single-reference many-body perturbation theory (MBPT) method for electron correlation calculation has been implemented up to the third order. The inclusion of bubble as well as non-bubble diagrams allow...
The open-shell single-reference many-body perturbation theory (MBPT) method for electron correlation calculation has been implemented up to the third order. The inclusion of bubble as well as non-bubble diagrams allows the unrestricted Hartree-Fock (UHF) reference with the UHF as well as the restricted Hartree-Fock (RHF) optimized orbitals. The program has been implemented in C language for its efficiency and flexibility. Given the input requirements and physical resource limitations, dynamic memory allocation capability of C allows optimal use of physical memory automatically. Input data are taken from the standard input stream in text/ASCII for-m for generality;allowing interoperation with programs in other languages and piping for minimizing disk space requirements. If the correct input is provided by the appropriate SCF program and prefilter, user involvement in the calculation is minimal. Various command line options are provided to monitor the program progress through timings, memory allocation and deallocation as well as file and disk size tracing. The appropriate environment variables under UNIX operating system allow flexible reassignment of temporary files to different directories and/or disks without program recompilation.
We prove the existence of solutions of the static Landau-Lifshitz equation with multi- direct effective field and with Dirichlet boundary condition,and establish the stability of the solution of Landau-Lifshitz equati...
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We prove the existence of solutions of the static Landau-Lifshitz equation with multi- direct effective field and with Dirichlet boundary condition,and establish the stability of the solution of Landau-Lifshitz equation with respect to time.
This study investigates numerically the coupling effect on the evolution of Richtmyer-Meshkov instability at double heavy square *** scenarios are considered,each with varying initial separations S/L(where L demotes t...
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This study investigates numerically the coupling effect on the evolution of Richtmyer-Meshkov instability at double heavy square *** scenarios are considered,each with varying initial separations S/L(where L demotes the side length of the square)ranging from 0.125 to *** are filled with SF6gas,and are enclosed by *** simulations of shock-induced multispecies flow are performed by solving the two-dimensional compressible Euler equations with a higher-order explicit modal discontinuous Galerkin *** simulations demonstrate that the flow morphology resulting from the coupling effect is highly dependent on the separation between two *** the separation is large,the squares experience a weaker coupling effect and evolve ***,as the separation reduces,the coupling effect manifests earlier in the interaction and becomes more *** a result,this phenomenon greatly intensifies the motion of inner upstream/downstream vortex rings towards the symmetry axis,leading to the emergence of multiple jets such as the twisted downward,upward,and coupled jets.A thorough exploration of the coupling effect of double squares is conducted by analyzing the vorticity ***,a significant quantity of vorticity is produced along the squares interface for smaller ***,these coupling effects result in various interface features(upstream/downstream movement,and height/width evolution),and temporal variations of various spatially integrated ***,the analysis of the flow structure also considers the interaction between two more flow parameters,the Mach and Atwood numbers,in order to evaluate the coupling effects.
We systematically investigate the influence of atomic potentials on the above-threshold ionization （ATI） spectra in one-dimensional （1D） cases and compare them with the three-dimensional （3D） case by numerically...
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We systematically investigate the influence of atomic potentials on the above-threshold ionization （ATI） spectra in one-dimensional （1D） cases and compare them with the three-dimensional （3D） case by numerically solving the time-dependent Schrrdinger equation. It is found that the direct ionization plateau and the rescattering plateau of the ATI spectrum in the 3D case can be well reproduced by the 1D ATI spectra calculated from the supersolid-core potential and the soft-core potential, respectively. By analyzing the factors that affect the yield of the ATI spectrum, we propose a modified-potential with which we can reproduce the overall 3D ATI spectrum. In addition, the influence of the incident laser intensities and frequencies on the ATI spectra calculated from the proposed modified potential is studied.
Switching properties of the time-optimal control are obtained for a linear time-invariant system for which the state matrix has all its eigenvalues real, the controlusatisfies the constraint |u| ≤ 1 and the...
Switching properties of the time-optimal control are obtained for a linear time-invariant system for which the state matrix has all its eigenvalues real, the controlusatisfies the constraint |u| ≤ 1 and the state vectorxthe constraint |a´x| ≤K,abeing a constant vector associated with an eigenspace ofA. These switching properties are extensions of the property that, when no state constraints are present,uhas at mostn− 1 switches between the values + 1 and − 1.
We perform deep variational free energy calculations to investigate the dense hydrogen system at 1200 K and high pressures. In this computational framework, neural networks are used to model the free energy through th...
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