AENO:a Novel Reconstruction Method in Conjunction with ADER Schemes for Hyperbolic Equations

In this paper,we present a novel spatial reconstruction scheme,called AENO,that results from a special averaging of the ENO polynomial and its closest neighbour,while retaining the stencil direction decided by the ENO choice.A variant of the scheme,called m-AENO,results from averaging the modified ENO(m-ENO)polynomial and its closest neighbour.The concept is thoroughly assessed for the one-dimensional linear advection equation and for a one-dimensional non-linear hyperbolic system,in conjunction with the fully discrete,high-order ADER approach implemented up to fifth order of accuracy in both space and time.The results,as compared to the conventional ENO,m-ENO and WENO schemes,are very encouraging.Surprisingly,our results show that the L_(1)-errors of the novel AENO approach are the smallest for most cases considered.Crucially,for a chosen error size,AENO turns out to be the most efficient method of all five methods tested.

浅水波方程的高阶保正Well-Balanced ADER间断Galerkin格式

本文针对具有不规则几何形状和非平坦底地形的浅水波方程,引入了保正高阶ADER间断Galerkin方法,该方法能准确地保持静水的稳态。为了满足well-balanced的性质,我们提出了well-balanced的数值通量,并基于分解算法将数值解分解为两部分,构造了一种新的源项近似,并相应地将源项近似分解为两部分。此外,还引入了一个简单的保正限制器,从而在干湿锋面附近提供高效和鲁棒性的模拟。大量的数值实验也表明,所得到的格式s能够准确地捕捉静止稳定状态下湖泊的小扰动,保持水面高度的非负性,同时保持光滑解的真正高阶精度。

非守恒双曲方程组的路径守恒ADER间断Galerkin方法:在浅水方程中的应用

本文提出了求解非守恒双曲型偏微分方程的一种新的路径守恒间断Galerkin (DG)方法。特别地,这里的方法采用了一级ADER (在空间和时间的任意导数)方法来实现时间离散化。此外,该方法采用微分变换(DT)过程而不是Cauchy-Kowalewski (C-K)过程来实现局部时间演化。与经典的ADER方法相比,该方法不需要求解内部单元的广义黎曼问题。与RKDG (Runge-Kutta DG)方法相比,该方法不需要中间步骤,因此需要较少的计算机存储空间。简而言之,当前的方法是一步一步完全离散的。而且,该方法在空间和时间上都容易获得高阶精度。浅水方程的数值结果表明,该方法具有较高的阶精度,对间断解具有较好的分辨率。

鲍曼不动杆菌主动外排系统adeR基因分布及耐药性分析

目的通过检测外排泵基因adeR在鲍曼不动杆菌中的分布及对临床常用抗菌药物的药敏情况,初步探讨外排泵对鲍曼不动杆菌耐药性的影响。方法采用聚合酶链反应(PCR)检测84株鲍曼不动杆菌外排泵基因adeR的分布情况,并根据PCR结果将菌株分为adeR基因阳性组和adeR基因阴性组,比较两组鲍曼不动杆菌对阿米卡星、头孢吡肟、左氧氟沙星和亚胺培南的耐药率。结果 PCR结果显示,收集的鲍曼不动杆菌adeR基因阳性率为70.24%(59/84);adeR基因阳性组对阿米卡星、头孢吡肟、左氧氟沙星和亚胺培南的耐药率分别为83.93%、90.74%、84.75%和67.80%;adeR基因阴性组对各抗菌药物的耐药率分别为58.33%、73.91%、56.00%和44.00%;两组间耐药率比较,差异有统计学意义(P<0.05)。结论外排泵基因adeR在该地区鲍曼不动杆菌中的检出率较高,与临床常用抗菌药物耐药情况高度相关,提示外排系统是该地区鲍曼不动杆菌多重耐药的重要原因之一。

鲍曼不动杆菌RND主动外排泵的表达与耐药性的关系

目的检测鲍曼不动杆菌耐药结节分化家族(RND)外排系统的分布,探索其表达与耐药性的关系。方法对南昌大学第一附属医院临床标本分离的59株多重耐药鲍曼不动杆菌进行细菌的鉴定与药敏分析,采用PCR技术检测鲍曼不动杆菌中RND主动外排系统的分布情况,比较不同耐药表型的鲍曼不动杆菌间外排泵基因的表达情况,分析其表达量与耐药的关系,并对RND外排系统的扩增产物进行测序。结果鲍曼不动杆菌对氨苄西林/舒巴坦、亚胺培南、庆大霉素、环丙沙星、左氧氟沙星耐药率高达93.2%、94.9%、88.1%、96.6%、52.5%。59株鲍曼不动杆菌经外排泵及整合子基因PCR扩增检测,adeR、adeS、adeB、adeJ、adeG基因的携带率分别为81.4%、91.5%、93.2%、100.0%、61.0%。不同菌株外排泵基因的表达均不相同,其中庆大霉素、亚胺培南、氨苄西林/舒巴坦耐药组与非耐药组鲍曼不动杆菌adeB、adeJ基因的表达量相比,差异均有统计学意义(均P<0.05)。adeABC外排泵的调控基因adeR、adeS的碱基序列未出现基因突变或插入序列。结论 RND外排系统在鲍曼不动杆菌中普遍存在,RND外排系统中adeB、adeJ基因的表达水平升高与细菌对庆大霉素、亚胺培南、氨苄西林/舒巴坦的耐药性有关。

局部时间步长间断有限元方法求解三维欧拉方程

使用间断有限元方法求解三维流体力学方程.空间剖分采用非结构四面体网格,为了克服显格式在单元网格尺寸差别较大时计算效率低下的问题,在格式中采用局部时间步长技术(LTS),即控制方程在空间、时间上积分得到一种单步格式,既可以局部计算每个单元又避免了Runge-Kutta高精度格式处理三维问题时存储量过大的问题.为了提高流体力学方程计算精度,在计算单元边界的数值流通量时使用任意高阶精度方法(ADER).数值算例表明格式稳定有效.

Application of ADER Scheme in MHD Simulation

The Arbitrary accuracy Derivatives Riemann problem method(ADER) scheme is a new high order numerical scheme based on the concept of finite volume integration,and it is very easy to be extended up to any order of space and time accuracy by using a Taylor time expansion at the cell interface position.So far the approach has been applied successfully to flow mechanics problems.Our objective here is to carry out the extension of multidimensional ADER schemes to multidimensional MHD systems of conservation laws by calculating several MHD problems in one and two dimensions: (ⅰ) Brio-Wu shock tube problem,(ⅱ) Dai-Woodward shock tube problem,(ⅲ) Orszag-Tang MHD vortex problem.The numerical results prove that the ADER scheme possesses the ability to solve MHD problem,remains high order accuracy both in space and time,keeps precise in capturing the shock.Meanwhile,the compared tests show that the ADER scheme can restrain the oscillation and obtain the high order non-oscillatory result.

ADER Methods for Hyperbolic Equations with a Time-Reconstruction Solver for the Generalized Riemann Problem: the Scalar Case

The ADER approach to solve hyperbolic equations to very high order of accuracy has seen explosive developments in the last few years,including both methodological aspects as well as very ambitious applications.In spite of methodological progress,the issues of efficiency and ease of implementation of the solution of the associated generalized Riemann problem(GRP)remain the centre of attention in the ADER approach.In the original formulation of ADER schemes,the proposed solution procedure for the GRP was based on(i)Taylor series expansion of the solution in time right at the element interface,(ii)subsequent application of the Cauchy-Kowalewskaya procedure to convert time derivatives to functionals of space derivatives,and(iii)solution of classical Riemann problems for high-order spatial derivatives to complete the Taylor series expansion.For realistic problems the Cauchy-Kowalewskaya procedure requires the use of symbolic manipulators and being rather cumbersome its replacement or simplification is highly desirable.In this paper we propose a new class of solvers for the GRP that avoid the Cauchy-Kowalewskaya procedure and result in simpler ADER schemes.This is achieved by exploiting the history of the numerical solution that makes it possible to devise a time-reconstruction procedure at the element interface.Still relying on a time Taylor series expansion of the solution at the interface,the time derivatives are then easily calculated from the time-reconstruction polynomial.The resulting schemes are called ADER-TR.A thorough study of the linear stability properties of the linear version of the schemes is carried out using the von Neumann method,thus deducing linear stability regions.Also,via careful numerical experiments,we deduce stability regions for the corresponding non-linear schemes.Numerical examples using the present simplified schemes of fifth and seventh order of accuracy in space and time show that these compare favourably with conventional ADER methods.This paper is restricted to the one-dimensional scalar case with source term,but preliminary results for the one-dimensional Euler equations indicate that the time-reconstruction approach offers significant advantages not only in terms of ease of implementation but also in terms of efficiency for the high-order range schemes.

An Approximate Riemann Solver for Advection-Diffusion Based on the Generalized Riemann Problem

We construct an approximate Riemann solver for scalar advection-diffusion equations with piecewise polynomial initial data.The objective is to handle advection and diffusion simultaneously to reduce the inherent numerical diffusion produced by the usual advection flux calculations.The approximate solution is based on the weak formulation of the Riemann problem and is solved within a space-time discontinuous Galerkin approach with two subregions.The novel generalized Riemann solver produces piecewise polynomial solutions of the Riemann problem.In conjunction with a recovery polynomial,the Riemann solver is then applied to define the numerical flux within a finite volume method.Numerical results for a piecewise linear and a piecewise parabolic approximation are shown.These results indicate a reduction in numerical dissipation compared with the conventional separated flux calculation of advection and diffusion.Also,it is shown that using the proposed solver only in the vicinity of discontinuities gives way to an accurate and efficient finite volume scheme.

双曲守恒律方程的高精度ADER间断Galerkin方法

本文提出了一种全新的间断Galerkin (DG)方法,该方法使用单级ADER (任意时–空导数)方式进行时间离散。该方法利用微分变换步骤递归地将解的时–空展开系数通过低阶空间展开系数来表示,能够在空间和时间上达到任意高阶精度。与传统有限体积ADER格式相比较,该方法避免了在单元界面处求解广义Riemann问题。与多级Runge-Kutta DG (RKDG)方法相比较,由于不存在中间级,本方法需要较少的计算机内存。综上所述,所得到的方法是单步的、单级的、全离散的。最后,经典数值算例验证了该方法的良好性能:高精度、高分辨率、高效率。

鲍曼不动杆菌双组份系统调控AdeABC外排泵表达的研究

鲍曼不动杆菌(Acinetobacter baumannii,AB)是一种革兰阴性菌(Gram negative bacterium),是引发院内感染的主要致病菌之一。AB耐药机制复杂,其中AdeABC外排泵是AB的主要耐药机制之一。双组份系统(two component system, TCS)是AB的信号转导系统,TCS AdeRS和TCS BaeSR可以调控AdeABC外排泵表达,有很大潜力成为AB的抗菌药物靶点。现就TCS对AdeABC外排泵的调控机制及TCS抑制剂的研究进展作一概述。

High Order ADER-IPDG Methods for the Unsteady Advection-Diffusion Equation

We present a high-order Galerkin method in both space and time for the 1D unsteady linear advection-diffusion equation. Three Interior Penalty Discontinuous Galerkin (IPDG) schemes are detailed for the space discretization, while the time integration is performed at the same order of accuracy thanks to an Arbitrary high order DERivatives (ADER) method. The orders of convergence of the three ADER-IPDG methods are carefully examined through numerical illustrations, showing that the approach is consistent, accurate, and efficient. The numerical results indicate that the symmetric version of IPDG is typically more accurate and more efficient compared to the other approaches.

鲍曼不动杆菌临床株多重药物外排泵AdeABC的研究

目的研究鲍曼不动杆菌（Acinetobaeter baumannii）临床株外排泵AdeABC的表达与耐药的关系及表达调控。方法微量肉汤稀释法检测鲍曼不动杆菌临床株对抗菌药物的敏感性及泵抑制剂作用，RT—PCR检测泵基因adeB的mRNA表达水平，PCR扩增泵调控基因adeRS并测序分析。结果30株多重耐药的鲍曼不动杆菌临床株及5株敏感株均存在泵结构基因片段adeB和调控基因adeRS，随机选取15株多重耐药株中均检测到adeB的mRNA表达，而在5株敏感株中无表达。测定2株多重耐药株调控基因adeRS序列均出现基因突变，发生氨基酸替代及缺失。结论鲍曼不动杆菌临床株外排泵AdeABC的表达可能与耐药性有关，在多重耐药株中存在着调控基因adeRS的基因序列变化。

西安地区鲍氏不动杆菌耐药程度与主动外排作用的相关性研究

目的研究西安地区鲍氏不动杆菌耐药程度与主动外排作用的相关性,明确主动外排作用是鲍氏不动杆菌多药耐药的重要原因之一。方法应用K-B法进行体外药敏试验,采用羰基氰氯苯腙(CCCP)抑制试验进行外排表型检测,观察在含20μg/mlCCCP条件下152株鲍氏不动杆菌对5种抗菌药物MIC值的变化;用PCR法检测多药耐药菌adeABC外排系统的外排基因adeB和调节基因adeR、adeS。结果 CCCP抑制试验:阿米卡星、头孢他啶、环丙沙星、亚胺培南和氯霉素为底物,分别有89、64、70、46和62株符合外排阳性的标准;PCR检测多药耐药鲍氏不动杆菌基因adeB、adeR、adeS的检出率分别为74.32%、71.62%、68.92%,敏感菌株中检出率分别为16.67%、16.67%、16.67%。结论鲍氏不动杆菌中的确存在对抗菌药物的主动外排作用,主动外排作用是鲍氏不动杆菌多药耐药的重要原因之一。

替加环素不敏感鲍曼不动杆菌的分子流行病学及耐药机制

为探讨替加环素不敏感鲍曼不动杆菌Acinetobacter baumannii的耐药机制,为院内感染控制及临床合理用药提供理论依据,采用琼脂稀释法和微量肉汤稀释法检测全国多中心12个城市20家医院临床分离的94株非重复的替加环素不敏感鲍曼不动杆菌的最低抑菌浓度(Minimum inhibitory concentration,MIC),应用多位点序列分型(Multilocus sequence typing,MLST)技术进行分子流行病学研究,应用eBURST软件对MLST结果进行分析;用PCR和测序技术分析常见耐药基因(bla_(OXA-40-like)、bla_(OXA-58-like)、bla_(OXA-23-like)、bla_(OXA-51-like)、bla_(NDM-1)),与替加环素耐药相关的外排泵调控基因adeR和adeS的突变位点、trm的突变位点。经检测94株鲍曼不动杆菌除对多粘菌素B 100%敏感、对米诺环素敏感率25.5%外,其他抗菌药物的敏感率均低于3.5%,亚胺培南和美罗培南敏感率均只有1.1%。MLST分型得到12种ST分型,以ST195(45株,47.9%)、ST208(19株,20.2%)和ST457(10株,10.6%)为主,eBURST分析发现其中8个ST型均属于克隆复合体92(Clonal Complex 92,CC92);99%菌株bla_(OXA-23-like)型碳青霉烯酶基因阳性;均未扩增出bla_(NDM-1)基因;外排泵调控基因adeR和adeS的检出率分别是73.4%和91.5%,Asp26Asn和Ala97Glu分别为adeR和adeS的高频突变位点;在12株鲍曼不动杆菌中检测到了adeS基因的ISAba1,以北部地区为主;trm基因均在第240位核苷酸发生缺失突变。综上所述,替加环素不敏感鲍曼不动杆菌对除多粘菌素B外的大多数抗菌药物具有很高的耐药性,AdeABC外排泵上游的双组分调控系统adeR和adeS的缺失和突变,trm缺失突变是导致鲍曼不动杆菌对替加环素敏感性降低的主要原因。

AN EFFICIENT ADER DISCONTINUOUS GALERKIN SCHEME FOR DIRECTLY SOLVING HAMILTON-JACOBI EQUATION

This paper proposes an efficient ADER(Arbitrary DERivatives in space and time)discontinuous Galerkin(DG)scheme to directly solve the Hamilton-Jacobi equation.Unlike multi-stage Runge-Kutta methods used in the Runge-Kutta DG(RKDG)schemes,the ADER scheme is one-stage in time discretization,which is desirable in many applications.The ADER scheme used here relies on a local continuous spacetime Galerkin predictor instead of the usual Cauchy-Kovalewski procedure to achieve high order accuracy both in space and time.In such predictor step,a local Cauchy problem in each cell is solved based on a weak formulation of the original equations in spacetime.The resulting spacetime representation of the numerical solution provides the temporal accuracy that matches the spatial accuracy of the underlying DG solution.The scheme is formulated in the modal space and the volume integral and the numerical fluxes at the cell interfaces can be explicitly written.The explicit formulae of the scheme at third order is provided on two-dimensional structured meshes.The computational complexity of the ADER-DG scheme is compared to that of the RKDG scheme.Numerical experiments are also provided to demonstrate the accuracy and efficiency of our scheme.

High Order Accurate Direct Arbitrary-Lagrangian-Eulerian ADER-MOOD Finite Volume Schemes for Non-Conservative Hyperbolic Systems with Stiff Source Terms

In this paper we present a 2D/3D high order accurate finite volume scheme in the context of direct Arbitrary-Lagrangian-Eulerian algorithms for general hyperbolic systems of partial differential equations with non-conservative products and stiff source terms.This scheme is constructed with a single stencil polynomial reconstruction operator,a one-step space-time ADER integration which is suitably designed for dealing even with stiff sources,a nodal solver with relaxation to determine the mesh motion,a path-conservative integration technique for the treatment of non-conservative products and an a posteriori stabilization procedure derived from the so-called Multidimensional Optimal Order Detection(MOOD)paradigm.In this work we consider the seven equation Baer-Nunziato model of compressible multi-phase flows as a representative model involving non-conservative products as well as relaxation source terms which are allowed to become stiff.The new scheme is validated against a set of test cases on 2D/3D unstructured moving meshes on parallel machines and the high order of accuracy achieved by the method is demonstrated by performing a numerical convergence study.Classical Riemann problems and explosion problems with exact solutions are simulated in 2D and 3D.The overall numerical code is also profiled to provide an estimate of the computational cost required by each component of the whole algorithm.

A New Family of High Order Unstructured MOOD and ADER Finite Volume Schemes for Multidimensional Systems of Hyperbolic Conservation Laws

In this paper,we investigate the coupling of the Multi-dimensional Optimal Order Detection(MOOD)method and the Arbitrary high order DERivatives(ADER)approach in order to design a new high order accurate,robust and computationally efficient Finite Volume(FV)scheme dedicated to solve nonlinear systems of hyperbolic conservation laws on unstructured triangular and tetrahedral meshes in two and three space dimensions,respectively.The Multi-dimensional Optimal Order Detection(MOOD)method for 2D and 3D geometries has been introduced in a recent series of papers for mixed unstructured meshes.It is an arbitrary high-order accurate Finite Volume scheme in space,using polynomial reconstructions with a posteriori detection and polynomial degree decrementing processes to deal with shock waves and other discontinuities.In the following work,the time discretization is performed with an elegant and efficient one-step ADER procedure.Doing so,we retain the good properties of the MOOD scheme,that is to say the optimal high-order of accuracy is reached on smooth solutions,while spurious oscillations near singularities are prevented.The ADER technique permits not only to reduce the cost of the overall scheme as shown on a set of numerical tests in 2D and 3D,but it also increases the stability of the overall scheme.A systematic comparison between classical unstructured ADER-WENO schemes and the new ADER-MOOD approach has been carried out for high-order schemes in space and time in terms of cost,robustness,accuracy and efficiency.The main finding of this paper is that the combination of ADER with MOOD generally outperforms the one of ADER and WENO either because at given accuracy MOOD is less expensive(memory and/or CPU time),or because it is more accurate for a given grid resolution.A large suite of classical numerical test problems has been solved on unstructured meshes for three challenging multi-dimensional systems of conservation laws:the Euler equations of compressible gas dynamics,the classical equations of ideal magneto-Hydrodynamics(MHD)and finally the relativistic MHD equations(RMHD),which constitutes a particularly challenging nonlinear system of hyperbolic partial differential equation.All tests are run on genuinely unstructured grids composed of simplex elements.