Qiushi Ding

To achieve the high‐precision characteristics within the smooth regions while maintaining stable, non‐oscillatory, and sharp discontinuity transitions, the weighted essentially non‐oscillatory (WENO) scheme and its variants have been developed. However, when there are multiple discontinuities close to each other, the numerical accuracy and robustness of the traditional schemes are probably affected. To this end, a hierarchical multi‐resolution WENO (MR‐WENO) scheme is proposed in the present study to suppress the overshoot and improve the accuracy of the original MR‐WENO scheme in the vicinity of discontinuities. It could achieve an adaptive selection of the substencils and optimal accuracy due to the hierarchical strategy and the new smoothness indicator. The performances of the hierarchical MR‐WENO scheme have been tested in 1D and 2D cases. The accuracy has been validated and the influences of weights of both large stencils and small substencils have been comprehensively discussed. The linear weights are adjusted aiming at improving the resolution of discontinuities and suppressing the unexpected weight oscillations. As a result, discontinuities like shock waves and contact discontinuities could be accurately resolved, while overshoot phenomena in the MR‐WENO scheme are effectively suppressed in both 1D and 2D cases. Especially, the numerical error of the Lax problem has been reduced by one or two orders of magnitude in the vicinity of discontinuities. With an implementation of the KXRCF indicator, the computational cost has been controlled while maintaining the present superiority of shock capturing capacity.

All the static performance, dynamic characteristics, and stability are strongly associated with the flow field inside the aerostatic bearings. Therefore, a high-precision numerical method is beneficial for the detailed description of the bearing flow field. To this end, a modified interior penalty discontinuous Galerkin method was introduced here. Actually, a lift operator was included to eliminate the so-called homogeneity tensor connecting the viscous term and variable gradient, which could improve the numerical feasibility. The accuracy of the above numerical method has been comprehensively validated through viscous cases, including Couette flow and shear-driven cavity flow. Then, the flow fields of three aerostatic bearings were simulated with different orifice geometries. As a result, the Mach number distributions and static pressure could be estimated together with the integration of the pressure acting upon the thrust surface. The acceleration within the orifice and air film could be detected, and the influence of the orifice geometry has been systematically discussed.

Building age-friendly cities with good accessibility and social equity can help improve older adults’ well-being and quality of life. However, current accessibility analysis of service facilities tends to target most general users, while few studies have been conducted regarding hospitals from an age-friendly perspective. This study aims to measure accessibility to tertiary hospitals and conduct its equity analysis for older adults aged 65 years or over. First, the gravity-based model and geographic information system are utilized to measure accessibility to tertiary hospitals within regions and across regions, and the overall accessibility of a region. Second, coefficient of variation and global Moran’s I are adopted to investigate differences in accessibility to tertiary hospitals by type among regions. Third, Lorenz curves and Gini coefficients are employed to analyze social equity of access to medical services for the elderly. Taking Tianjin, China as the case study, the results show that there exist spatial clusters in terms of accessibility to tertiary hospitals within districts, across districts, and of the whole district. Most districts in the city center have better access to these hospitals than the peripheral and suburban districts. The social equity of accessibility to tertiary hospitals is slightly better in the senior population than in the total population. This study can help the governments improve the spatial distribution and allocation of urban health care resources in a more equitable manner and promote the development of age-friendly cities in future.