摘要：
Due to its high resolution for discontinuities and high efficiency, the HLLEM scheme is a popular numerical method to calculate the conservative hyperbolic systems. When capturing multidimensional strong shock waves, however, it will encounter different forms of numerical oscillations, such as the odd-even decoupling and carbuncle phenomenon, which is a great hindrance to its application in hypersonic flow problems. In this paper the numerical shock instability of the HLLEM scheme is investigated from a mathematical perspective and a corresponding cure is proposed. A special linearized small perturbation analysis shows that perturbations evolved in the streamwise direction will be attenuated while the density and shear velocity perturbations evolved in the transverse direction will not be attenuated and thus induce the occurrence of instability. In order to suppress the numerical oscillation in capturing strong shock waves, a function based on the pressure ratio at the cell interface is defined to control the dissipation of the HLLEM flux. And a BVD (boundary variation diminishing) algorithm is implemented to pick the smallest density jump from all combinations among reconstructed density values to reduce the numerical dissipation, thus the contact resolving capability of the HLLEM scheme is further improved. The higher resolution for contact discontinuities and better stability for shock waves brought by the current strategies are demonstrated through solving a series of one- and two-dimensional benchmark test problems. (C) 2022 Elsevier Inc. All rights reserved.
期刊：
Fuzzy Sets and Systems,2022年426:27-45 ISSN：0165-0114
通讯作者：
Li, Long
作者机构：
[Li, Long] Hengyang Normal Univ, Coll Math & Stat, Hengyang, Hunan, Peoples R China.;[Long, Zuqiang] Hengyang Normal Univ, Coll Phys & Elect Engn, Hengyang, Hunan, Peoples R China.;[Ying, Hao] Wayne State Univ, Dept Elect & Comp Engn, Detroit, MI 48202 USA.;[Qiao, Zhijun] Univ Texas Rio Grande Valley, Dept Math, Edinburg, TX 78539 USA.
通讯机构：
[Li, Long] H;Hengyang Normal Univ, Coll Math & Stat, Hengyang, Hunan, Peoples R China.
期刊：
Journal of Functional Analysis,2022年282(1):109254 ISSN：0022-1236
通讯作者：
Chen, Shaolin
作者机构：
[Chen, Shaolin] Hengyang Normal Univ, Coll Math & Stat, Hengyang 421008, Hunan, Peoples R China.;[Hamada, Hidetaka] Kyushu Sangyo Univ, Fac Sci & Engn, Higashi Ku, 3-1 Matsukadai 2 Chome, Fukuoka 8138503, Japan.
通讯机构：
[Chen, Shaolin] H;Hengyang Normal Univ, Coll Math & Stat, Hengyang 421008, Hunan, Peoples R China.
关键词：
Bohr phenomenon;Harmonic function;Pluriharmonic function;Schwarz-Pick type lemma of arbitrary order;Sharp Schwarz-Pick type estimate
摘要：
The purpose of this paper is to study the Schwarz-Pick type inequalities for harmonic or pluriharmonic functions. By analogy with the generalized Khavinson conjecture, we first give some sharp estimates of the norm of harmonic functions from the Euclidean unit ball in R-n into the unit ball of the real Minkowski space. Next, we give several sharp Schwarz-Pick type inequalities for pluriharmonic functions from the Euclidean unit ball in C-n or from the unit polydisc in C-n into the unit ball of the Minkowski space. Furthermore, we establish some sharp coefficient type Schwarz-Pick inequalities for pluriharmonic functions defined in the Minkowski space. Finally, we use the obtained Schwarz-Pick type inequalities to discuss the Lipschitz continuity, the Schwarz-Pick type lemmas of arbitrary order and the Bohr phenomenon of harmonic or pluriharmonic functions. (C) 2021 Elsevier Inc. All rights reserved.
期刊：
Journal of Applied Mathematics and Computing,2022年68(5):3473-3490 ISSN：1598-5865
通讯作者：
Wang, Keyan
作者机构：
[Wang, Keyan] Hengyang Normal Univ, Sch Math & Stat, Hengyang 421008, Hunan, Peoples R China.
通讯机构：
[Wang, Keyan] H;Hengyang Normal Univ, Sch Math & Stat, Hengyang 421008, Hunan, Peoples R China.
关键词：
Parabolic integro-differential equations;Finite element method;Two-grid method;Error estimate
摘要：
In this paper, we study the unconditional convergence and error estimates of a two-grid finite element method for the semilinear parabolic integro-differential equations. By using a temporal-spatial error splitting technique, optimal
$$L^p$$
and
$$H^1$$
error estimates of the finite element method can be obtained. Moreover, to deal with the semilinearity of the model, we use the two-grid method. Optimal error estimates in
$$L^2$$
and
$$H^1$$
-norms of two-grid solution are derived without any time-step size conditions. Finally, some numerical results are provided to confirm the theoretical analysis, and show the efficiency of the proposed method.
摘要：
In this paper, we consider gradient estimates for positive solutions to the following equation Delta vu + au(p) log u = 0 on complete noncompact Riemannian manifold with k-dimensional Bakry- mery Ricci curvature bounded from below. Using the Bochner formula and the Cauchy inequality, we obtain upper bounds of vertical bar del u vertical bar with respect to the lower bound of the Bakry- mery Ricci curvature.
作者机构：
[Tan, Yanliang; Lin, Fen; Hu, Tao; Yuan, Hongzhi; Mo, Yixiang; Fan, Zhongkai] Hengyang Normal Univ, Coll Phys & Elect Engn, Huangbai Rd 165, Hengyang 421008, Hunan, Peoples R China.;[Xie, Lin] Hengyang Normal Univ, Coll Math & Stat, Huangbai Rd 165, Hengyang 421008, Hunan, Peoples R China.
通讯机构：
[Yanliang Tan] C;College of Physics and Electronic Engineering , Hengyang Normal University, Huangbai Road 165#, Hengyang, Hunan Province 421008 , China
摘要：
As Rn-222 decays, an alpha particle is emitted and the residual polonium nucleus recoils in the opposite direction. At the end of the recoil path, 88% of the polonium atoms have a positive charge and 12% are neutral. The electric potential distribution in the 60 ml hemispherical internal cell of the radon monitor based on electrostatic collection is studied for reducing the combined probability of the positively charged Po-218 and the OH− produced by the ionization of water vapour in the air. The COMSOL software is used to simulate the electric potential distribution in the internal cell of the radon monitor based on the electrostatic collection method at 27°C, a pressure of 0.1 Mpa. For improving the collection efficiency of Po-218 ions, the average collection time along vertical and oblique lines is calculated when the upper surface of the internal cell is plastic, uncharged metal and charged metal, respectively. Assuming that the gas in the internal cell is uniformly distributed, the results show that if the upper surface of the hemispherical internal cell is plastic or uncharged metal, the electric potential formed in the internal cell is more uniform, and it is beneficial to reduce the total collection time of the positively charged Po-218 ions, thereby improving collection efficiency. The simulation results can be used as an effective reference for optimizing the design of the internal cell structure of the radon monitor based on electrostatic collection method.
