Volume 38, Issue 6

Shale rock, being a common caprock for carbon dioxide reservoirs, is subject to extensive research. One of the topics is breakthrough phenomena during injection of supercritical carbon dioxide in shale, the nature of which is still to be fully understood. In the present paper, a two-phase flow model, which may possibly be used to explain the breakthrough behaviour is examined. Capillary effects and geomechanics are included in the model, and influential model parameters are determined.

The present paper considers numerical properties of two different approaches to discretization of the isoneutral diffusion. The necessity of an alternative treatment of the isoneutral diffusion in a terrain-following climate ocean model as opposed to the more convenient rotated tensor formalism is studied. A new method of the approximation of the isoneutral diffusion based on a non-local computational stencil is formulated. The validity of the non-local discretization of the isoneutral diffusion operator with regard to a terrain-following vertical coordinate in the INMCM ocean model is demonstrated.

The paper provides a detailed description of the numerical implementation of the transport scheme in the Earth’s ionosphere three-dimensional dynamical model of the Institute of Numerical Mathematics (INMIM). The presented version of INM-IM model takes into account the global dynamical processes of ion transport and ambipolar diffusion in the altitude range between 100 and 500 km (corresponding to F region). Based upon the splitting method the model solves the equations of ambipolar diffusion on the first split step and incorporates specifically designed advective transport scheme on the second step. The accuracy of transport scheme implementation in the model has been investigated through analytical solutions. The stability of the numerical algorithm has been demonstrated even for cases when transport velocities approaching extreme values.

We show theoretically and numerically that the lowest non-trivial eigenvector function for a specific eigenproblem has almost constant values in high conductivity channels, which are different in separate channels. Therefore, based on these distinct values, all separate connected clusters of open pores can be identified in digital cores.

The problem of variational assimilation of observational data for the sea thermodynamics model is considered with the aim to reconstruct heat fluxes on the sea surface. The local sensitivity of functionals of the solution to the observational data and input data for heat fluxes is studied in the considered problem and the results of numerical experiments are presented for the Black Sea dynamics model.

We present spatial approximation for shallow water equations on a mesh of multiple rectangular blocks with different resolution in Cartesian geometry. The approximation is based on finite-difference operators that fulfill Summation By Parts (SBP) property – a discrete analogue of integration by parts. The solution continuity conditions between mesh blocks are imposed in a weak form using Simultaneous Approximation Terms (SAT) method.We show that the resulting discrete divergence and gradient operators are anti-conjugate. The important consequences are the discrete analogues for mass and energy conservation laws along with the proof of stability for linearized equations. The numerical shallow water equations model based on the presented spatial approximation is tested using problems with meteorological context. Test results prove high-order accuracy of SBP-SAT discretization. The interfaces between mesh blocks of different resolution produce no significant noise. The local mesh refinement is shown to have positive effect on the solution both locally inside the refined region and globally in the dynamically coupled areas.