This paper presents a new strategy to deal with the excessive diffusion that standard finite volume methods for compressible Euler equations display in the limit of low Mach number. The strategy can be understood as using centered discretizations for the acoustic part of the Euler equations and stabilizing them with a leap-frog-type ("sequential explicit") time integration, a fully explicit method. This time integration takes inspiration from time-explicit staggered grid numerical methods. In this way, advantages of staggered methods carry over to collocated methods. The paper provides a number of new collocated schemes for linear acoustic/Maxwell equations that are inspired by the Yee scheme. They are then extended to an all-speed method for the full Euler equations on Cartesian grids. By taking the opposite view and taking inspiration from collocated methods, the paper also suggests a new way of staggering the variables which increases the stability as compared to the traditional Yee scheme.
High-performance computing for the BGK model of the Boltzmann equation with a meshfree Arbitrary Lagrangian-Eulerian method
Indian Institute of Technology Tirupati（印度理工学院蒂鲁帕蒂分校）；RPTU Kaiserslautern-Landau（莱茵兰-普法尔茨技术大学凯泽斯劳滕-兰道校区）；SRM Institute of Science and Technology（SRM科学与技术研究所）
Conjugate-symplecticity properties of Euler--Maclaurin methods and their implementation on the Infinity Computer
Università degli Studi di Bari Aldo Moro（巴里阿尔多·莫罗大学）；Università della Calabria（卡拉布里亚大学）；Lobachevsky State University of Nizhni Novgorod（下诺夫哥罗德洛巴切夫斯基州立大学）
Adaptive pseudo-time methods for the Poisson-Boltzmann equation with Eulerian solvent excluded surface
这一工作进一步改进了溶剂化生物分子静电分析中泊松-玻尔兹曼方程（PBE）的伪瞬态方法。已知非线性PBE的数值解涉及许多困难，例如指数非线性项、源项的强奇异性以及复杂的介电界面。近年来，在[S. Ahmed Ullah和S. Zhao，应用数学和计算，380，125267，（2020）]，通过分析处理非线性和奇异源。GFM界面处理不仅捕捉了正则化势及其通量在分子表面的不连续性，而且保证了时间积分的稳定性和效率。然而，基于MSMS包的分子表面定义已知在某些情况下会引起不稳定性，并且非平凡的拉格朗日到欧拉转换对于GFM有限差分离散化是必不可少的。在本文中，一个欧拉溶剂排除表面（ESES）的实现，以取代MSMS定义的介电界面。静电分析表明，ESES自由能比MSMS更准确，同时没有不稳定性问题。此外，这项工作探索，首次在PBE文献，自适应时间积分技术的伪瞬态模拟。一个主要的发现是，时间增量$Δt$应该随着时间的增加而变小，以保持时间精度。这与稳态收敛的一般做法相反，并且被认为是由于PBE非线性及其时间分裂处理。有效的自适应计划已被构造，使伪时间GFM方法变得比常数$Δt$更有效。
