A new method for conditioning stochastic groundwater flow models in fractured media

Many geological formations consist of crystalline rocks that have very low matrix permeability but allow flow through an interconnected network of fractures. Understanding the flow of groundwater through such rocks is important in considering disposal of radioactive waste in underground repositories. A specific area of interest is the conditioning of fracture transmissivities on measured values of pressure in these formations. This is the process where the values of fracture transmissivities in a model are adjusted to obtain a good fit of the calculated pressures to measured pressure values. While there are existing methods to condition transmissivity fields on transmissivity, pressure and flow measurements for a continuous porous medium there is little literature on conditioning fracture networks. Conditioning fracture transmissivities on pressure or flow values is a complex problem because the measurements are not linearly related to the fracture transmissivities and they are also dependent on all the fracture transmissivities in the network. We present a new method for conditioning fracture transmissivities on measured pressure values based on the calculation of certain basis vectors; each basis vector represents the change to the log transmissivity of the fractures in the network that results in a unit increase in the pressure at one measurement point whilst keeping the pressure at the remaining measurement points constant. The fracture transmissivities are updated by adding a linear combination of basis vectors and coefficients, where the coefficients are obtained by minimizing an error function. A mathematical summary of the method is given. This algorithm is implemented in the existing finite element code ConnectFlow developed and marketed by Serco Technical Services, which models groundwater flow in a fracture network. Results of the conditioning are shown for a number of simple test problems as well as for a realistic large scale test case.

Amphetamine increases blood pressure and heart rate but has no effect on motor recovery or cerebral haemodynamics in ischaemic stroke: a randomized controlled trial (ISRCTN 36285333)

Amphetamine enhances recovery after experimental ischaemia and has shown promise in small clinical trials when combined with motor or sensory stimulation. Amphetamine, a sympathomimetic, might have haemodynamic effects in stroke patients, although limited data have been published. Subjects were recruited 3-30 days post ischaemic stroke into a phase II randomised (1:1), double blind, placebo-controlled trial. Subjects received dexamphetamine (5mg initially, then 10mg for 10 subsequent doses with 3 or 4 day separations) or placebo in addition to inpatient physiotherapy. Recovery was assessed by motor scales (Fugl-Meyer, FM), and functional scales (Barthel index, BI and modified Rankin score, mRS). Peripheral blood pressure (BP), central haemodynamics and middle cerebral artery blood flow velocity were assessed before, and 90 minutes after, the first 2 doses. 33 subjects were recruited, age 33-88 (mean 71) years, males 52%, 4-30 (median 15) days post stroke to inclusion. 16 patients were randomised to placebo and 17 amphetamine. Amphetamine did not improve motor function at 90 days; mean (standard deviation) FM 37.6 (27.6) vs. control 35.2 (27.8) (p=0.81). Functional outcome (BI, mRS) did not differ between treatment groups. Peripheral and central systolic BP, and heart rate, were 11.2 mmHg (p=0.03), 9.5 mmHg (p=0.04) and 7 beats/minute (p=0.02) higher respectively with amphetamine, compared with control. A non-significant reduction in myocardial perfusion (Buckberg Index) was seen with amphetamine. Other cardiac and cerebral haemodynamics were unaffected. Amphetamine did not improve motor impairment or function after ischaemic stroke but did significantly increase BP and heart rate without altering cerebral haemodynamics.

Sloshing and slamming oscillations in collapsible channel flow

We consider laminar high-Reynolds-number flow through a finite-length planar channel, where a portion of one wall is replaced by a thin massless elastic membrane that is held under longitudinal tension T and subject to an external pressure distribution. The flow is driven by a fixed pressure drop along the full length of the channel. We investigate the global stability of two-dimensional Poiseuille flow using a method of matched local eigenfunction expansions, which is compared to direct numerical simulations. We trace the neutral stability curve of the primary oscillatory instability of the system, illustrating a transition from high-frequency ‘sloshing’ oscillations at high T to vigorous ‘slamming’ motion at low T . Small-amplitude sloshing at high T can be captured using a low-order eigenmode truncation involving four surface-based modes in the compliant segment of the channel coupled to Womersley flow in the rigid segments. At lower tensions, we show that hydrodynamic modes contribute increasingly to the global instability and we demonstrate a change in the mechanism of energy transfer from the mean flow, with viscous effects being destabilising. Simulations of finite-amplitude oscillations at low T reveal a generic slamming motion, in which the the flexible membrane is drawn close to the opposite rigid wall before rapidly recovering. A simple model is used to demonstrate how fluid inertia in the downstream rigid channel segment, coupled to membrane curvature downstream of the moving constriction, together control slamming dynamics.

Adaptivity and a posteriori error control for bifurcation problems II: Incompressible fluid flow in open systems with Z_2 symmetry

In this article we consider the a posteriori error estimation and adaptive mesh refinement of discontinuous Galerkin finite element approximations of the bifurcation problem associated with the steady incompressible Navier-Stokes equations. Particular attention is given to the reliable error estimation of the critical Reynolds number at which a steady pitchfork or Hopf bifurcation occurs when the underlying physical system possesses reflectional or Z_2 symmetry. Here, computable a posteriori error bounds are derived based on employing the generalization of the standard Dual-Weighted-Residual approach, originally developed for the estimation of target functionals of the solution, to bifurcation problems. Numerical experiments highlighting the practical performance of the proposed a posteriori error indicator on adaptively refined computational meshes are presented.