Self-adaptive isogeometric spatial discretisations of the first and second-order forms of the neutron transport equation with dual-weighted residual error measures and diffusion acceleration

As implemented in a new modern-Fortran code, NURBS-based isogeometric analysis (IGA) spatial discretisations and self-adaptive mesh refinement (AMR) algorithms are developed in the application to the first-order and second-order forms of the neutron transport equation (NTE). These AMR algorithms are shown to be computationally efficient and numerically accurate when compared to standard approaches. IGA methods are very competitive and offer certain unique advantages over standard finite element methods (FEM), not least of all because the numerical analysis is performed over an exact representation of the underlying geometry, which is generally available in some computer-aided design (CAD) software description. Furthermore, mesh refinement can be performed within the analysis program at run-time, without the need to revisit any ancillary mesh generator. Two error measures are described for the IGA-based AMR algorithms, both of which can be employed in conjunction with energy-dependent meshes. The first heuristically minimises any local contributions to the global discretisation error, as per some appropriate user-prescribed norm. The second employs duality arguments to minimise important local contributions to the error as measured in some quantity of interest; this is commonly known as a dual-weighted residual (DWR) error measure and it demands the solution to both the forward (primal) and the adjoint (dual) NTE. Finally, convergent and stable diffusion acceleration and generalised minimal residual (GMRes) algorithms, compatible with the aforementioned AMR algorithms, are introduced to accelerate the convergence of the within-group self-scattering sources for scattering-dominated problems for the first and second-order forms of the NTE. A variety of verification benchmark problems are analysed to demonstrate the computational performance and efficiency of these acceleration techniques.Open Acces

A Decade of Hα Transits for HD 189733 b: Stellar Activity versus Absorption in the Extended Atmosphere

HD 189733 b is one of the most well studied exoplanets due to its large transit depth and host star brightness. The focus on this object has produced a number of high-cadence transit observations using high-resolution optical spectrographs. Here we present an analysis of seven full Hα transits of HD 189733 b using HARPS on the 3.6 meter La Silla telescope and HIRES on Keck I, taken over the course of nine years from 2006 to 2015. Hα transmission signals are analyzed as a function of the stellar activity level, as measured using the normalized core flux of the Ca II H and K lines. We find strong variations in the strength of the Hα transmission spectrum from epoch to epoch. However, there is no clear trend between the Ca II core emission and the strength of the in-transit Hα signal, although the transit showing the largest absorption value also occurs when the star is the most active. We present simulations of the in-transit contrast effect and find that the planet must consistently transit active latitudes with very strong facular and plage emission regions in order to reproduce the observed line strengths. We also investigate the measured velocity centroids with models of planetary rotation and show that the small line profile velocities could be due to large velocities in the upper atmosphere of the planet. Overall, we find it more likely that the measured Hα signals arise in the extended planetary atmosphere, although a better understanding of active region emission for active stars such as HD 189733 is needed

A Decade of Hα Transits for HD 189733 b: Stellar Activity versus Absorption in the Extended Atmosphere

HD 189733 b is one of the most well studied exoplanets due to its large transit depth and host star brightness. The focus on this object has produced a number of high-cadence transit observations using high-resolution optical spectrographs. Here we present an analysis of seven full Hα transits of HD 189733 b using HARPS on the 3.6 meter La Silla telescope and HIRES on Keck I, taken over the course of nine years from 2006 to 2015. Hα transmission signals are analyzed as a function of the stellar activity level, as measured using the normalized core flux of the Ca II H and K lines. We find strong variations in the strength of the Hα transmission spectrum from epoch to epoch. However, there is no clear trend between the Ca II core emission and the strength of the in-transit Hα signal, although the transit showing the largest absorption value also occurs when the star is the most active. We present simulations of the in-transit contrast effect and find that the planet must consistently transit active latitudes with very strong facular and plage emission regions in order to reproduce the observed line strengths. We also investigate the measured velocity centroids with models of planetary rotation and show that the small line profile velocities could be due to large velocities in the upper atmosphere of the planet. Overall, we find it more likely that the measured Hα signals arise in the extended planetary atmosphere, although a better understanding of active region emission for active stars such as HD 189733 is needed