A discontinuous Galerkin immersed boundary solver for compressible flows: Adaptive local time stepping for artificial viscosity–based shock-capturing on cut cells

We present a higher-order cut cell immersed boundary method (IBM) for the simulation of high Mach number flows. As a novelty on a cut cell grid, we evaluate an adaptive local time stepping (LTS) scheme in combination with an artificial viscosity–based shock-capturing approach. The cut cell grid is optimized by a nonintrusive cell agglomeration strategy in order to avoid problems with small or ill-shaped cut cells. Our approach is based on a discontinuous Galerkin discretization of the compressible Euler equations, where the immersed boundary is implicitly defined by the zero isocontour of a level set function. In flow configurations with high Mach numbers, a numerical shock-capturing mechanism is crucial in order to prevent unphysical oscillations of the polynomial approximation in the vicinity of shocks. We achieve this by means of a viscous smoothing where the artificial viscosity follows from a modal decay sensor that has been adapted to the IBM. The problem of the severe time step restriction caused by the additional second-order diffusive term and small nonagglomerated cut cells is addressed by using an adaptive LTS algorithm. The robustness, stability, and accuracy of our approach are verified for several common test cases. Moreover, the results show that our approach lowers the computational costs drastically, especially for unsteady IBM problems with complex geometries.     

Revealing Phosphorus Nitrides up to the Megabar Regime: Synthesis of α′-P3N5, δ-P3N5 and PN2

Non-metal nitrides are an exciting field of chemistry, featuring a significant number of compounds that can possess outstanding material properties. These properties mainly rely on maximizing the number of strong covalent bonds, with crosslinked XN₆ octahedra frameworks being particularly attractive. In this study, the phosphorus–nitrogen system was studied up to 137 GPa in laser-heated diamond anvil cells, and three previously unobserved phases were synthesized and characterized by single-crystal X-ray diffraction, Raman spectroscopy measurements and density functional theory calculations. δ-P₃N₅ and PN₂ were found to form at 72 and 134 GPa, respectively, and both feature dense 3D networks of the so far elusive PN₆ units. The two compounds are ultra-incompressible, having a bulk modulus of K₀=322 GPa for δ-P₃N₅ and 339 GPa for PN₂. Upon decompression below 7 GPa, δ-P₃N₅ undergoes a transformation into a novel α′-P₃N₅ solid, stable at ambient conditions, that has a unique structure type based on PN₄ tetrahedra. The formation of α′-P₃N₅ underlines that a phase space otherwise inaccessible can be explored through materials formed under high pressure.     

Experimental and Computational Studies of Anti‐Bredt Amidinium Salts

Experimental and computational investigations of anti‐Bredt amidinium salts are presented. Calculations show that the pyramidalization of an amino group can significantly destabilize the formal carbocation center of amidiniums, due to the decreased π donation. In some cases, the unfavorable ‐I effect of nitrogen surpasses its beneficial +M effect, and amidiniums become less stable than iminiums. It is shown that although 1‐aza‐3‐azonia[3.3.1]bicyclo‐non‐2‐enes can be isolated, they feature a nonclassical reactivity, which is more typical for iminium than amidinium salts, such as pronounced electrophilicity and azomethineylide instead of carbene formation.