On the Divergence-Free Condition in Godunov-Type Schemes for Ideal Magnetohydrodynamics: the Upwind Constrained Transport Method

We present a general framework to design Godunov-type schemes for multidimensional ideal magnetohydrodynamic (MHD) systems, having the divergence-free relation and the related properties of the magnetic field B as built-in conditions. Our approach mostly relies on the 'Constrained Transport' (CT) discretization technique for the magnetic field components, originally developed for the linear induction equation, which assures div(B)=0 and its preservation in time to within machine accuracy in a finite-volume setting. We show that the CT formalism, when fully exploited, can be used as a general guideline to design the reconstruction procedures of the B vector field, to adapt standard upwind procedures for the momentum and energy equations, avoiding the onset of numerical monopoles of O(1) size, and to formulate approximate Riemann solvers for the induction equation. This general framework will be named here 'Upwind Constrained Transport' (UCT). To demonstrate the versatility of our method, we apply it to a variety of schemes, which are finally validated numerically and compared: a novel implementation for the MHD case of the second order Roe-type positive scheme by Liu and Lax (J. Comp. Fluid Dynam. 5, 133, 1996), and both the second and third order versions of a central-type MHD scheme presented by Londrillo and Del Zanna (Astrophys. J. 530, 508, 2000), where the basic UCT strategies have been first outlined

A high order compact scheme for hypersonic aerothermodynamics

A novel high order compact scheme for solving the compressible Navier-Stokes equations has been developed. The scheme is an extension of a method originally proposed for solving the Euler equations, and combines several techniques for the solution of compressible flowfields, such as upwinding, limiting and flux vector splitting, with the excellent properties of high order compact schemes. Extending the method to the Navier-Stokes equations is achieved via a Kinetic Flux Vector Splitting technique, which represents an unusual and attractive way to include viscous effects. This approach offers a more accurate and less computationally expensive technique than discretizations based on more conventional operator splitting. The Euler solver has been validated against several inviscid test cases, and results for several viscous test cases are also presented. The results confirm that the method is stable, accurate and has excellent shock-capturing capabilities for both viscous and inviscid flows

Reallocating resources to focused factories: a case study in chemotherapy

This study investigates the expected service performance associated with a proposal to reallocate resources from a centralized chemotherapy department to a breast cancer focused factory. Using a slotted queueing model we show that a decrease in performance is expected and calculate the amount of additional resources required to offset these losses. The model relies solely on typical outpatient scheduling system data, making the methodology easy to replicate in other outpatient clinic settings. Finally, the paper highlights important factors to consider when assigning capacity to focused factories. These considerations are generally relevant to other resource allocation decisions

Myofibrillar Protein Status of the Gastrocnemius in Male Rats: Effect of Mild Undernutrition

The aim of this work was the determination of the myofibrillar protein profiles in the fed and the mildly underfed rat. Sixteen male rats were divided into 2 groups: CR (control) fed ad libitum and MR (mildly undernourished) fed 75% of energetic maintenance needs. The animals were sacrificed at day 23 and the gastrocnemius muscle was taken for myofibrillar protein characterisation. The myofibrillar protein profiles were found to be very similar in the two groups revealing the lack of preferred catabolism of myofibrillar proteins and consequently that the muscle structure is maintained even in situations of mild undernutrition

Reallocating resources to focused factories: a case study in chemotherapy

This study investigates the expected service performance associated with a proposal to reallocate resources from a centralized chemotherapy department to a breast cancer focused factory. Using a slotted queueing model we show that a decrease in performance is expected and calculate the amount of additional resources required to offset these losses. The model relies solely on typical outpatient scheduling system data, making the methodology easy to replicate in other outpatient clinic settings. Finally, the paper highlights important factors to consider when assigning capacity to focused factories. These considerations are generally relevant to other resource allocation decisions

High Order Upwind Schemes for Multidimensional Magnetohydrodynamics

A general method for constructing high order upwind schemes for multidimensional magnetohydrodynamics (MHD), having as a main built-in condition the divergence-free constraint \divb=0 for the magnetic field vector \bb, is proposed. The suggested procedure is based on {\em consistency} arguments, by taking into account the specific operator structure of MHD equations with respect to the reference Euler equations of gas-dynamics. This approach leads in a natural way to a staggered representation of the \bb field numerical data where the divergence-free condition in the cell-averaged form, corresponding to second order accurate numerical derivatives, is exactly fulfilled. To extend this property to higher order schemes, we then give general prescriptions to satisfy a $(r+1)^{th}$ order accurate \divb=0 relation for any numerical \bb field having a $r^{th}$ order interpolation accuracy. Consistency arguments lead also to a proper formulation of the upwind procedures needed to integrate the induction equations, assuring the exact conservation in time of the divergence-free condition and the related continuity properties for the \bb vector components. As an application, a third order code to simulate multidimensional MHD flows of astrophysical interest is developed using ENO-based reconstruction algorithms. Several test problems to illustrate and validate the proposed approach are finally presented.Comment: 34 pages, including 14 figure