Numerical simulation of pollutant transport in fractured vuggy porous karstic aquifers.
Numerical Solution of Steady-State Porous Flow Free Boundary Problems.
Numerical solution of the Kiessl model
The Kiessl model of moisture and heat transfer in generally nonhomogeneous porous materials is analyzed. A weak formulation of the problem of propagation of the state parameters of this model, which are so-called moisture potential and temperature, is derived. An application of the method of discretization in time leads to a system of boundary-value problems for coupled pairs of nonlinear second order ODE’s. Some existence and regularity results for these problems are proved and an efficient numerical...
Numerical studies of groundwater flow problems with a singularity
The paper studies mesh dependent numerical solution of groundwater problems with singularities, caused by boreholes represented as points, instead of a real radius. We show on examples, that the numerical solution of the borehole pumping problem with point source (singularity) can be related to the exact solution of a regular problem with adapted geometry of a finite borehole radius. The radius providing the fit is roughly proportional to the mesh step. Next we define a problem of fracture-rock...
On a boundary value problem for an equation of the type of non-stationary filtration
On a free boundary value problem connected with a non steady filtration phenomenon
On a seawater intrusion problem.
On a variational method for solving hydrodynamical free boundary problems.
On modelling the drying of porous materials: Analytical solutions to coupled partial differential equations governing heat and moisture transfer.
On oblique waves forcing by a porous cylindrical wall.
On steady MHD thermally radiating and reacting thermosolutal viscous flow through a channel with porous medium.
On the behavior of the interface separating fresh and salt groundwater in a heterogeneous coastal aquifer.
On the boundary conditions at the contact interface between a porous medium and a free fluid
On the boundary value problem arising in the radially symmetrical filtration of fluid
On the Charney Conjecture of Data Assimilation Employing Temperature Measurements Alone: The Paradigm of 3D Planetary Geostrophic Model
Analyzing the validity and success of a data assimilation algorithmwhen some state variable observations are not available is an important problem in meteorology and engineering. We present an improved data assimilation algorithm for recovering the exact full reference solution (i.e. the velocity and temperature) of the 3D Planetary Geostrophic model, at an exponential rate in time, by employing coarse spatial mesh observations of the temperature alone. This provides, in the case of this paradigm,...
On the dam problem with boundary leaky condition
On the existence and uniqueness of non-negative solutions of a certain non-linear convolution equation
On the existence of shock propagation in a flow through deformable porous media
We consider a one-dimensional incompressible flow through a porous medium undergoing deformations such that the porosity and the hydraulic conductivity can be considered to be functions of the flux intensity. The medium is initially dry and we neglect capillarity, so that a sharp wetting front proceeds into the medium. We consider the open problem of the continuation of the solution in the case of onset of singularities, which can be interpreted as a local collapse of the medium, in the general...
On the existence of the weak solution of a boundary value problem arising in the theory of water percolation
On the global existence for the Muskat problem
The Muskat problem models the dynamics of the interface between two incompressible immiscible fluids with different constant densities. In this work we prove three results. First we prove an maximum principle, in the form of a new “log” conservation law which is satisfied by the equation (1) for the interface. Our second result is a proof of global existence for unique strong solutions if the initial data is smaller than an explicitly computable constant, for instance . Previous results of this...