The computational modeling of high-speed flows (e.g. hypersonic) and space plasmas is characterized by a plethora of complex physical phenomena, in particular involving strong oblique shocks, bow shocks and/or shock waves boundary layer interactions. The characterization of those flows requires accurate, robust and advanced numerical techniques. To this end, adaptive mesh algorithms provide an automatic way to improve the quality of the numerical results, by increasing the mesh density where required in order to resolve the most critical physical features. In this work, we propose a r-adaptive algorithm that consists in repositioning mesh nodes as resulting from the solution of a physics-driven pseudo-elastic system of equations. The developed mesh refinement techniques are based upon spring networks deriving from linear, semi-torsional and ortho-semi- torsional analogies, but driven by a combination of local physical and geometrical properties depending on a user-defined monitoring flow variable. Furthermore, a mesh quality indicator is developed within this work in order to grade and investigate the quality of an adapted mesh. Finally, a refinement stop indicator is proposed and demonstrated in order to further automatize the resulting adaptive simulation. All new physics-based mesh motion algorithms are illustrated through multiple examples that emphasize the applicability to different physical models and problems together with the improved quality of the results.
An adaptive Cartesian embedded boundary approach for fluid simulations of two- and three-dimensional low temperature plasma filaments in complex geometries
A P-Adaptive Hybridizable Discontinuous Galerkin Spectral Element Method for Electrostatic Particle-in-Cell Simulations
University of Stuttgart（斯图加特大学）；Institute of Space Systems, University of Stuttgart（斯图加特大学空间研究所）；boltzplatz - numerical plasma dynamics GmbH（boltzplatz 数值等离子体动力学有限公司）
Exploration vs Convergence Speed in Adaptive-bias Enhanced Sampling
在自适应偏置增强采样方法中，向系统添加偏置电势以驱动亚稳态之间的转变。偏置电位是几个集体变量的函数，并根据底层自由能表面逐渐修改。我们表明，当集体变量是次优的，有一个探索收敛的权衡，必须选择一个快速收敛的偏见，这将导致更少的过渡，或较慢收敛的偏见，可以更有效地探索相空间，但可能需要更长的时间来产生一个准确的自由能估计。最近提出的On-the-fly Probability Enhanced Sampling（OPES）方法专注于快速收敛，但也有快速探索的情况。出于这个原因，我们引入了一个新的变种的OPES方法，专注于快速逃离亚稳态，在收敛速度的代价。我们说明了这种方法的好处原型系统，并表明它优于流行的元自适应方法。
