In this article, we briefly review the random choice method (RCM) and ADER methods for solving one and two-dimensional hyperbolic conservation laws. The main advantage of RCM is that it computes ...discontinuities with infinite resolution. In this method, the original problem is reduced to a set of local Riemann problems (RPs). The exact solutions of these RPs are used to form the solution of the original problem. However, RCM has the following disadvantages: (1) one should solve the RP exactly, however, the exact solutions are usually complex and unavailable for many problems. (2) The accuracy of the smooth region of the flow is poor. ADER methods are explicit, one-step schemes with a very high order of accuracy in time and space. They depend on the solution of the generalized RP (GRP) exactly. In Zahran (J Math Anal Appl 346:120–140, 2008), an improved version of ADER methods (central ADER) was introduced where the RPs were solved numerically and used central fluxes, instead of upwind fluxes. The improved central ADER schemes are more accurate, faster, simple to implement, RP solver free, and need less computer memory. To fade the drawbacks of the above schemes and keep their advantages, we propose, in this paper, an improved version of the RCM. We merge the central ADER technique with the RCM. The resulting scheme is called Central RCM (CRCM). The improvements are listed as follows: we use the WENO reconstruction for the initial data instead of constant reconstruction in RCM, we solve the RPs numerically by using central finite difference schemes and use random sampling to update the solution, as the original RCM. Here we use the staggered and non-staggered RCM. To enhance the accuracy of the new methods, we use a third-order TVD flux (Zahran in Bull Belg Math Soc Simon Stevin 14:259–275, 2007), instead of a first-order flux. Compared with the original RCM and the central ADER, the new methods combine the advantages of RCM, ADER, and central finite difference methods as follows: more accurate, very simple to implement, need less computer memory, and RP solver free. Moreover, the new methods capture the discontinuities with infinite resolution and improve the accuracy of the smooth parts. The new methods have less CPU time than the central ADER methods, this is due to less flux evaluation in CRCM. An extension of the schemes to general systems of nonlinear hyperbolic conservation laws in one and two dimensions is presented. We present several numerical examples for one and two-dimensional problems. The results confirm that the presented schemes are superior to the original RCM, ADER, and central ADER schemes.
•A new seventh Hermite WENO scheme for solving hyperbolic conservation laws.•The major advantage of HWENO scheme is its compactness in the reconstruction.•It uses the central upwind flux presented by ...Kurganov which is simple, universal and efficient.•For time integration, we use (ℓSSPRK 7) for linear problems and SSPRK54 for nonlinear problems.•The advantages: improvement in the accuracy of smooth parts decreases the dissipation near discontinuities and can be used for problems with non-convex fluxes.
In this paper, we construct a new seventh-order Hermite weighted essentially non-oscillatory (HWENO7) scheme, for solving one and two dimensional hyperbolic conservation laws, by extending the fifth order HWENO introduced in Qiu J, Shu C-W. J Comput Phys 2003;193:115–135. The idea of the reconstruction in the HWENO schemes comes from the original WENO schemes, however both function and its derivative values are evolved in time and used in the reconstruction, while only the function values are evolved and used in the original WENO schemes. The major advantage of HWENO schemes is its compactness in the reconstruction. For example, seven points are needed in the stencil for a seventh order WENO reconstruction, while only five points are needed for HWENO7 reconstruction. We use the central-upwind flux Kurganov A, Noelle S, Petrova G, SIAM J Sci Comp 2001;23:707–740 which is simple, universal and efficient. The numerical solution is advanced in time by the seventh order linear strong-stability-preserving Runge–Kutta (ℓSSPRK) scheme for linear problems and the fourth order SSPRK(5,4) for nonlinear problems. The resulting scheme improves the convergence and accuracy of smooth parts of solution as well as decrease the dissipation near discontinuities. This is especially for long time evolution problems. Numerical experiments of the new scheme for one and two dimensional problems are reported. The results demonstrate that the proposed scheme is superior to the original HWENO and classical WENO schemes.
Shale reservoirs are characterized by very low permeability in the scale of nano-Darcy. This is due to the nanometer scale of pores and throats in shale reservoirs, which causes a difference in flow ...behavior from conventional reservoirs. Slip flow is considered to be one of the main flow regimes affecting the flow behavior in shale gas reservoirs and has been widely studied in the literature. However, the important mechanism of gas desorption or adsorption that happens in shale reservoirs has not been investigated thoroughly in the literature. This paper aims to study slip flow together with gas desorption in shale gas reservoirs using pore network modeling. To do so, the compressible Stokes equation with proper boundary conditions was applied to model gas flow in a pore network that properly represents the pore size distribution of typical shale reservoirs. A pore network model was created using the digitized image of a thin section of a Berea sandstone and scaled down to represent the pore size range of shale reservoirs. Based on the size of pores in the network and the pore pressure applied, the Knudsen number which controls the flow regimes was within the slip flow regime range. Compressible Stokes equation with proper boundary conditions at the pore’s walls was applied to model the gas flow. The desorption mechanism was also included through a boundary condition by deriving a velocity term using Langmuir-type isotherm. It was observed that when the slip flow was activated together with desorption in the model, their contributions were not summative. That, is the slippage effect limited the desorption mechanism through a reduction of pressure drop. Eagle Ford and Barnett shale samples were investigated in this study when the measured adsorption isotherm data from the literature were used. Barnett sample showed larger contribution of gas desorption toward gas recovery as compared to Eagle Ford sample. This paper has produced a pore network model to further understand the gas desorption and the slip flow effects in recovery of shale gas reservoirs.
In this article, we propose a new ninth‐order central Hermite weighted essentially nonoscillatory (HWENO) scheme, for solving hyperbolic conservation laws. The new scheme consists of the following: ...ninth‐order reconstruction using only five points stencil; to calculate the linear weights we used the central WENO (CWENO) technique and for nonlinear weights we used a new weighting technique. The numerical solution is advanced in time by using the ninth‐order linear strong‐stability‐preserving Runge–Kutta (ℓSSPRK) scheme and for computing the numerical flux, we used the central‐upwind flux which is efficient, simple and can be used for nonconex fluxes problems. The resulting scheme is ninth order in both smooth regions and at critical points with very small numerical dissipation near discontinuities, this is due to using new smoothness indicators. Several numerical examples are presented for one‐ and two‐dimensional problems to confirm that the new scheme is superior to the other high‐order WENO schemes.
A new ninth‐order central Hermite weighted essentially nonoscillatory (HWENO) scheme is proposed, for conservation laws. It consist of ninth‐order reconstruction using only five points stencil; for linear weights we used CWENO technique and for nonlinear weights we extend the weighting technique presented in References with some modification. The resulting scheme has small numerical dissipation near discontinuities. Several examples are presented for one‐ and two‐dimensional problems to confirm the advantages of the scheme.
Infrared spectra of dealuminated high silica MFI zeolites were measured to elucidate the structure of silanol groups active for conversion of 1-butene to propene. The OH groups were replaced by OD ...groups to have clear vibrational spectra. Two sharp bands and one broad band were observed; isolated silanol at 2746 cm
−1
, terminal silanol at 2725 cm
−1
, and hydrogen-bonded silanols centered at 2570 cm
−1
composed of more than one components. Based on the response of these bands to Na poisoning and pyridine adsorption together with the correlation with catalytic results, we propose that the active sites for propene formation are one of the terminal silanol groups and one of the hydrogen-bonded silanol groups in a silanol nest. The active hydrogen-bonded silanol groups are the one whose O atom is hydrogen-bonded to adjacent two H atoms in the silanol nest.
Graphic Abstract
Study the impact of ultrasound-assessed diaphragmatic impairment (DI) on predicting need for invasive mechanical ventilation (IMV) in acute exacerbation of chronic obstructive pulmonary disease ...(AECOPD) patients treated by non-invasive ventilation (NIV).
A prospective observational study.
Critical Care Units of Alexandria Main University Hospital.
75 adult AECOPD patients of both sexes according to sample size calculation.
Ultrasound was used to measure diaphragmatic thickness (DT), diaphragmatic thickness fraction (DTF) was calculated, and DI was diagnosed when fraction was less than 20%. Patients were treated by NIV. Switching to IMV was done after NIV failure. Primary outcome was value of DI to predict need for IMV after NIV failure. Secondary outcome was impact of DI on fate of patients.
According to fate of NIV, patients were categorized into successful and failed NIV groups. DTF in both groups were ≥33-38% and ≤16-18%. DTF with a cut-off value of <26-29% on both sides was able to predict NIV failure with 96.67% sensitivity and 80-82.22% specificity. Days of MV and ICU stay were significantly lower in the successful NIV group, p < 0.001. 28-day mortality was significantly less encountered in successful NIV group, p = 0.018.
DTF was a good indicator of DI that could predict need for IMV after NIV failure in AECOPD patients with good sensitivity and moderate specificity. MV Days, ICU stay, and 28-day mortality were significantly higher in patients with DI who needed IMV.
Cerebrovascular stroke is one of the most disabling chronic conditions, as it is often associated with devastating long-term neurologic deficits.
A prospective observational study.
Critical Care ...Units of Alexandria Main University Hospital.
60 adult mechanically ventilated stroke patients of both genders according to sample size calculation.
Compare the outcome of early versus late tracheotomy on diaphragmatic function, assessed by ultrasonographic assessment in mechanically ventilated stroke patients.
Patients were randomized blindly into two groups: group I was subjected to early bedside percutaneous tracheotomy within 4 days of ICU stay, while group II was tracheostomized after 14 days. A Sonosite Mindray DP10 2015-08 with a 3-5 MHz linear probe was used to assess the diaphragm daily before and after tracheotomy. Measures taken were diaphragmatic excursion (DE) and diaphragmatic thickness (DT). Primary outcome was impact of early tracheotomy on diaphragmatic ultrasound measurements. Secondary outcomes were days of mechanical ventilation, ICU stay, and 28-day mortality.
After tracheotomy, a significant improvement in DE and DTF in group I was encountered more than group II (p < 0.01). There was a significant decrease in ventilator days, and ICU stay in group I (p < 0.01), without statistical significance in the 28-day mortality (p = 0.612).
Early tracheotomy in mechanically ventilated stroke patients could improve diaphragmatic ultrasound measurements resulting in rapid weaning off mechanical ventilation and less ICU stay without significant effect on 28-day mortality.
Multicenter studies showed that early goal directed therapy (EGDT) did not improve outcome in patients with septic shock compared with undefined usual care. The aim of this study was to evaluate the ...efficacy of a protocolized resuscitation care compared to traditional EGDT in early management of septic shock on short-term mortality.
A randomized controlled trail.
Emergency Department and Critical Care Units of Alexandria main university hospital.
100 adult patients of both genders with septic shock.
All patients received early fluid resuscitation, empirical broad-spectrum antibiotic therapy and mechanical ventilation if indicated. Then, they were randomly assigned into two groups: Early goal directed therapy (EGDT) group (n = 50) and Protocolized resuscitation care (PRC) group (n = 50).
EGDT group showed 20% reduction in need for vasopressor than PRC group with significant difference (p = 0.001). PRC group showed lower mortality rate than EGDT group but with no significant difference (p = 0.405). There were no differences in ICU stay, mechanical ventilation days and duration of vasopressor (p= 0.091, 0.243, 0.372 respectively).
A Protocolized resuscitation care may be beneficial as compared to EGDT in early management of septic shock with a non-significant trend to decrease mortality.
Calcineurin inhibitors (CNI) are the mainstay of immunosuppressant medications in both bone marrow transplants and solid organ transplants. Nephrotoxicity is a well-known adverse effect of this ...group. Type IV renal tubular acidosis is a potentially under-recognized complication. Here we report a case of Omenn syndrome in a patient who underwent a bone marrow transplant and developed type IV renal tubular acidosis while on treatment with cyclosporine.
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