Podněty Jana Amose Komenského pro soudobou hudební výchovu

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Numerical Investigation on the Fixed-Stress Splitting Scheme for Biot’s Equations: Optimality of the Tuning Parameter

We study the numerical solution of the quasi-static linear Biot equations solved iteratively by the fixed-stress splitting scheme. In each iteration the mechanical and flow problems are decoupled, where the flow problem is solved by keeping an artificial mean stress fixed. This introduces a numerical tuning parameter which can be optimized. We investigate numerically the optimality of the parameter and compare our results with physically and mathematically motivated values from the literature, which commonly only depend on mechanical material parameters. We demonstrate, that the optimal value of the tuning parameter is also affected by the boundary conditions and material parameters associated to the fluid flow problem suggesting the need for the integration of those in further mathematical analyses optimizing the tuning parameter.acceptedVersio

Multigrid particle-in-cell simulations of plasma microturbulence

A new scheme to accurately retain kinetic electron effects in particle-in-cell (PIC) simulations for the case of electrostatic drift waves is presented. The splitting scheme, which is based on exact separation between adiabatic and on adiabatic electron responses, is shown to yield more accurate linear growth rates than the standard df scheme. The linear and nonlinear elliptic problems that arise in the splitting scheme are solved using a multi-grid solver. The multi-grid particle-in-cell approach offers an attractive path, both from the physics and numerical points of view, to simulate kinetic electron dynamics in global toroidal plasmas

Sensitivity and resolution of tomographic pumping tests in an alluvial aquifer

This is the published version. Copyright American Geophysical Union[1] Various investigators have proposed hydraulic tomography, the simultaneous analysis of responses to multiple well tests, as a means to obtain a high-resolution characterization of aquifer flow properties. This study assesses the information content of drawdown records from a set of tomographic pumping tests in an alluvial aquifer, comparing the parameter sensitivity and resolution associated with transient and steady-shape formulations of the objective function for the parameter estimation problem. The steady-shape approach takes advantage of the rapid establishment of constant gradients within the region surrounding a pumping well, comparing observed drawdown differences within this region with drawdown differences predicted by a steady state model. Both the transient and steady-shape approaches resolve K variations only within a limited distance of the pumping intervals and observation points. Relative to the transient approach, the steady-shape approach reduces the influence of poorly resolved property variations, including K variations outside the region of investigation and storage coefficient variations throughout the model domain

The role of rock joint frictional strength in the containment of fracture propagation

The fracturing phenomenon within the reservoir environment is a complex process that is controlled by several factors and may occur either naturally or by artificial drivers. Even when deliberately induced, the fracturing behaviour is greatly influenced by the subsurface architecture and existing features. The presence of discontinuities such as joints, artificial and naturally occurring faults and interfaces between rock layers and microfractures plays an important role in the fracturing process and has been known to significantly alter the course of fracture growth. In this paper, an important property (joint friction) that governs the shear behaviour of discontinuities is considered. The applied numerical procedure entails the implementation of the discrete element method to enable a more dynamic monitoring of the fracturing process, where the joint frictional property is considered in isolation. Whereas fracture propagation is constrained by joints of low frictional resistance, in non-frictional joints, the unrestricted sliding of the joint plane increases the tendency for reinitiation and proliferation of fractures at other locations. The ability of a frictional joint to suppress fracture growth decreases as the frictional resistance increases; however, this phenomenon exacerbates the influence of other factors including in situ stresses and overburden conditions. The effect of the joint frictional property is not limited to the strength of rock formations; it also impacts on fracturing processes, which could be particularly evident in jointed rock masses or formations with prominent faults and/or discontinuities

Numerical simulation of three-phase coning in petroleum reservoirs

Bibliography: p. 194-202.A study of computer simulation of three-phase flow in petroleum reservoirs with particular reference to coning problems is the topic of the present investigation. The mathematical formulation of flow equations is treated in detail and the implications of physically correct as opposed to conventional boundary conditions are clarified. The proper construction of finite difference approximations is discussed. A new finite difference formulation of the boundary conditions is developed, which satisfies the outlet effect and the condition of compatibility between the flow in the reservoir and in the wellbore. Several mathematical properties of the system of difference equations are proved and the methods for solving the resulting system of algebraic equations are surveyed. The investigation of various methods for handling the nonlinearities shows that Newton's method can be used to obtain a fully implicit solution in few iterations. The stability and truncation errors of Newton's method are compared with the linearized and semi-implicit method on test problems . A new method is proposed for handling the nonlinearity due to accumulation terms. The numerical coning model developed on the basis of these theoretical investigations is highly stable, simulates correctly the boundary effects and has a small time-step sensitivity. These features are demonstrated on test problems of two-phase coning and three-phase coning with gas percolation. The investigation of the fea sibility of Newton's iteration shows that best results are obtained if only one iteration per time step is performed and smaller time steps are selected, instead of performing several Newton's iterations with extremely large time steps. The numerical model is used to study the influence of some variables on coning, including capillary pressure and wettability, and to investigate some possibilities of controlling coning