A Phosphine‐Coordinated Boron‐Centered Gomberg‐Type Radical

The P‐coordinated boryl radical [Ph₂P(naphthyl)BMes]^. (Mes=mesityl) was prepared by (electro)chemical reduction of the corresponding borenium salt or bromoborane. Electron paramagnetic resonance (EPR) analysis in solution and DFT calculations indicate large spin density on boron (60–70 %) and strong P–B interactions (P→B σ donation and B→P negative hyperconjugation). The radical is persistent in solution and participates in a Gomberg‐type dimerization process. The associated quinoid‐type dimer has been characterized by single‐crystal X‐ray diffraction.     

Development and validation of a SUPG finite element scheme for the compressible Navier–Stokes equations using a modified inviscid flux discretization

This paper considers the streamline‐upwind Petrov–Galerkin (SUPG) method applied to the unsteady compressible Navier–Stokes equations in conservation‐variable form. The spatial discretization, including a modified approach for interpolating the inviscid flux terms in the SUPG finite element formulation, and the second‐order accurate time discretization are presented. The numerical method is discussed in detail. The performance of the algorithm is then investigated by considering inviscid flow past a circular cylinder. Validation of the finite element formulation via comparisons with experimental data for high‐Mach number perfect gas laminar flows is presented, with a specific focus on comparisons with experimentally measured skin friction and convective heat transfer on a 15° compression ramp. Copyright © 2007 John Wiley & Sons, Ltd.     

Stream function solution of Navier-Stokes problems with inter-element penalties

In this note, we apply a finite element stream function formulation with inter-element penalties to the Navier-Stokes equations. The approach is an extension of a technique previously introduced for Stokes, flow. The solution is obtained by iterative linearization using successive approximation, and results for a standard numerical test case are given.