On the upstream mobility scheme for two-phase flow in porous media

When neglecting capillarity, two-phase incompressible flow in porous media is modelled as a scalar nonlinear hyperbolic conservation law. A change in the rock type results in a change of the flux function. Discretizing in one-dimensional with a finite volume method, we investigate two numerical fluxes, an extension of the Godunov flux and the upstream mobility flux, the latter being widely used in hydrogeology and petroleum engineering. Then, in the case of a changing rock type, one can give examples when the upstream mobility flux does not give the right answer.Comment: A preprint to be published in Computational Geoscience

A theory of L1L^1-dissipative solvers for scalar conservation laws with discontinuous flux

We propose a general framework for the study of $L^1$ contractive semigroups of solutions to conservation laws with discontinuous flux. Developing the ideas of a number of preceding works we claim that the whole admissibility issue is reduced to the selection of a family of "elementary solutions", which are certain piecewise constant stationary weak solutions. We refer to such a family as a "germ". It is well known that (CL) admits many different $L^1$ contractive semigroups, some of which reflects different physical applications. We revisit a number of the existing admissibility (or entropy) conditions and identify the germs that underly these conditions. We devote specific attention to the anishing viscosity" germ, which is a way to express the "$\Gamma$-condition" of Diehl. For any given germ, we formulate "germ-based" admissibility conditions in the form of a trace condition on the flux discontinuity line $x=0$ (in the spirit of Vol'pert) and in the form of a family of global entropy inequalities (following Kruzhkov and Carrillo). We characterize those germs that lead to the $L^1$-contraction property for the associated admissible solutions. Our approach offers a streamlined and unifying perspective on many of the known entropy conditions, making it possible to recover earlier uniqueness results under weaker conditions than before, and to provide new results for other less studied problems. Several strategies for proving the existence of admissible solutions are discussed, and existence results are given for fluxes satisfying some additional conditions. These are based on convergence results either for the vanishing viscosity method (with standard viscosity or with specific viscosities "adapted" to the choice of a germ), or for specific germ-adapted finite volume schemes

Hyperventilation syndrome: clinical, ventilatory, and personality characteristics as observed in neurological practice.

The symptoms of the hyperventilation syndrome (HVS) are sometimes diffuse, and HVS may resemble other clinical conditions. A diagnosis of HVS was made in 25 patients referred for neurological assessment because of atypical, shortlasting, episodic complaints. The referral diagnoses varied within a wide range. A need for more indepth knowledge about this group of patients thus arose. During a provocation test with forced respiration, all patients reported symptoms similar to those during attacks. Eight patients described numbness or paraesthesias with unilateral predominance. End-tidal pCO2 levels were monitored prior to and during a forced hyperventilation test. Compared with controls, the patients had significantly decreased end-tidal pCO2 even during symptom free periods. After hyperventilation, hypocapnia followed a protracted course in the patient group. Sensory symptoms may be asymmetric and mimic focal cerebral disease. Strained respiration may be denied during spontaneous attacks. Personality characteristics were evaluated with the Minnesota Multiphasic Personality Inventory (MMPI). A mean group profile very similar to profiles reported on "pseudoepileptic" patients was found. The profile indicates a neurotic pattern where patients tend to respond to psychological stress with somatic symptoms