Divergence-Conforming Isogeometric Collocation Methods for the Incompressible Navier-Stokes Equations

We develop two isogeometric divergence-conforming collocation schemes for incompressible flow. The first is based on the standard, velocity-pressure formulation of the Navier-Stokes equations, while the second is based on the rotational form and includes the vorticity as an unknown in addition to the velocity and pressure. We describe the process of discretizing each unknown using B-splines that conform to a discrete de Rham complex and collocating each governing equation at the Greville abcissae corresponding to each discrete space. Results on complex domains are obtained by mapping the equations back to a parametric domain using structure-preserving transformations. Numerical results show the promise of the method, including accelerated convergence rates of the three field, vorticity-velocity-pressure scheme when compared to the two field, velocity-pressure scheme

Stabilized Isogeometric Collocation Methods For Scalar Transport and Incompressible Fluid Flow

In this work we adapt classical residual-based stabilization techniques to the spline collocation setting. Inspired by the Streamline-Upwind-Petrov-Galerkin and Pressure-Stabilizing-Petrov-Galerkin methods, our stabilized collocation schemes address spurious oscillations that can arise from advection and pressure instabilities. Numerical examples for the advection-diffusion equation, Stokes equations, and incompressible Navier-Stokes equations show the effectiveness of the proposed stabilized schemes while maintaining the high-order convergence rates and accuracy of standard isogeometric collocation on smooth problems

Si microwire-array solar cells

Si microwire-array solar cells with Air Mass 1.5 Global conversion efficiencies of up to 7.9% have been fabricated using an active volume of Si equivalent to a 4 μm thick Si wafer. These solar cells exhibited open-circuit voltages of 500 mV, short-circuit current densities (J_(sc)) of up to 24 mA cm^(-2), and fill factors >65% and employed Al_2O_3 dielectric particles that scattered light incident in the space between the wires, a Ag back reflector that prevented the escape of incident illumination from the back surface of the solar cell, and an a-SiN_x:H passivation/anti-reflection layer. Wire-array solar cells without some or all of these design features were also fabricated to demonstrate the importance of the light-trapping elements in achieving a high J_(sc). Scanning photocurrent microscopy images of the microwire-array solar cells revealed that the higher J_(sc) of the most advanced cell design resulted from an increased absorption of light incident in the space between the wires. Spectral response measurements further revealed that solar cells with light-trapping elements exhibited improved red and infrared response, as compared to solar cells without light-trapping elements

High-performance Si microwire photovoltaics

Crystalline Si wires, grown by the vapor–liquid–solid (VLS) process, have emerged as promising candidate materials for lowcost, thin-film photovoltaics. Here, we demonstrate VLS-grown Si microwires that have suitable electrical properties for high-performance photovoltaic applications, including long minority-carrier diffusion lengths (L_n » 30 µm) and low surface recombination velocities (S « 70 cm·s^(-1)). Single-wire radial p–n junction solar cells were fabricated with amorphous silicon and silicon nitride surface coatings, achieving up to 9.0% apparent photovoltaic efficiency, and exhibiting up to ~600 mV open-circuit voltage with over 80% fill factor. Projective single-wire measurements and optoelectronic simulations suggest that large-area Si wire-array solar cells have the potential to exceed 17% energy-conversion efficiency, offering a promising route toward cost-effective crystalline Si photovoltaics