A High Order Bound Preserving Finite Difference Linear Scheme for Incompressible Flows

We propose a high order finite difference linear scheme combined with a high order bound preserving maximum-principle-preserving (MPP) flux limiter to solve the incompressible flow system. For such problem with highly oscillatory structure but not strong shocks, our approach seems to be less dissipative and much less costly than a WENO type scheme, and has high resolution due to a Hermite reconstruction. Spurious numerical oscillations can be controlled by the weak MPP flux limiter. Numerical tests are performed for the Vlasov-Poisson system, the 2D guiding-center model and the incompressible Euler system. The comparison between the linear and WENO type schemes, with and without the MPP flux limiter, will demonstrate the good performance of our proposed approach.     

A Priori Subcell Limiting Approach for the FR/CPR Method on Unstructured Meshes

A priori subcell limiting approach is developed for high-order flux reconstruction/correction procedure via reconstruction (FR/CPR) methods on two-dimensional unstructured quadrilateral meshes. Firstly, a modified indicator based on modal energy coefficients is proposed to detect troubled cells, where discontinuities exist. Then, troubled cells are decomposed into nonuniform subcells and each subcell has one solution point. A second-order finite difference shock-capturing scheme based on nonuniform nonlinear weighted (NNW) interpolation is constructed to perform the calculation on troubled cells while smooth cells are calculated by the CPR method. Numerical investigations show that the proposed subcell limiting strategy on unstructured quadrilateral meshes is robust in shock-capturing.     

角膜电刺激对糖尿病大鼠前部缺血性视神经病变模型的影响

观察并评估角膜电刺激对糖尿病大鼠前部缺血性视神经病变（AION）模型的影响。方法：实验 研究。健康雄性Sparague-Dawley大鼠40只，随机分组后抽出8只作为正常大鼠组。余下32只先予 以链脲佐菌素腹腔注射建立糖尿病大鼠模型，将造模成功的大鼠随机抽出8只作为糖尿病组，余下 24只糖尿病大鼠采用孟加拉玫瑰红联合532 nm激光方法建立AION大鼠模型。将24只造模成功的 AION大鼠随机分成3组，每组8只，分别为AION模型组，不予任何处理；电刺激组，予以角膜电刺 激（刺激参数为：电流1 mA，频率20 Hz，波宽1 ms/phase，刺激时间1 h，隔日1次，刺激2周）；假电 刺激组，电极安放位置与电刺激组相同，仅不接通电源。2周后5组大鼠进行眼底照相、光学相干断 层扫描和视觉诱发电位，然后处死，行视网膜及视神经冰冻切片，苏木精伊红染色观察。数据采用 单因素方差分析和LSD-t检验进行分析。结果：正常大鼠组视盘上半部视网膜厚度为（211±13）μm， 糖尿病大鼠组为（206±16）μm，AION模型组为（240±54）μm，假电刺激组为（216±11）μm，电刺 激组为（198±4）μm，5组视盘上半部视网膜厚度差异有统计学意义（F=2.854，P=0.038）。其中AION 模型组视盘上半部视网膜厚度高于正常组、糖尿病组、电刺激组，差异均有统计学意义（P<0.05）； 正常组与糖尿病组差异无统计学意义，AION模型组与假电刺激组未见明显差异。视觉诱发电位示 AION模型组N1潜伏期较电刺激组延长，差异有统计学意义（t=4.1，P<0.001）；AION模型组P1潜伏 期较正常组、糖尿病组、假电刺激组、电刺激组延长，差异均有统计学意义（t=4.1、2.5、2.6、3.2， P<0.05）；电刺激组N1-P1波幅大于假电刺激组，差异有统计学意义（t=4.0，P<0.001）。结论：角膜电 刺激能促进糖尿病大鼠前部缺血性视神经病变模型肿胀的视盘变薄，加速视盘水肿的消退，同时在 一定程度上改善视功能。