R-parameter: A local truncation error based adaptive framework for finite volume compressible flow solvers

A residual-based strategy to estimate the local truncation error in a finite volume framework for steady compressible flows is proposed. This estimator, referred to as the -parameter, is derived from the imbalance arising from the use of an exact operator on the numerical solution for conservation laws. The behaviour of the residual estimator for linear and non-linear hyperbolic problems is systematically analysed. The relationship of the residual to the global error is also studied. The -parameter is used to derive a target length scale and consequently devise a suitable criterion for refinement/derefinement. This strategy, devoid of any user-defined parameters, is validated using two standard test cases involving smooth flows. A hybrid adaptive strategy based on both the error indicators and the -parameter, for flows involving shocks is also developed. Numerical studies on several compressible flow cases show that the adaptive algorithm performs excellently well in both two and three dimensions.

Microsphere Bouquets of Bismuth Telluride Nanoplates: Room-Temperature Synthesis and Thermoelectric Properties

We report the synthesis and properties of sphere-shaped microscale aggregates of bismuth telluride nanoplates. We obtain porous microspheres by reducing bismuth chloride and orthotelluric acid with hydrazine in the presence of thioglycolic acid-which serves as the shape-and size-directing agent-followed by room-temperature aging-which promotes nanoplate aggregation. Thin film assemblies of the nanoplate microspheres exhibit n-type behavior due to sulfur doping and a Seebeck coefficient higher than that reported for assemblies of chalcogenide nanostructures. Adaptation of our scalable approach to synthesize and hierarchically assemble nanostructures with controlled doping could be attractive for tailoring novel thermoelectric materials for applications in high-efficiency refrigeration and harvesting electricity from heat.