Troubled-Cell Indicator Based on Mean Value Property for Hybrid WENO Schemes

In this paper, we introduce a new type of troubled-cell indicator to improve hybrid weighted essentially non-oscillatory (WENO) schemes for solving the hyperbolic conservation laws. The hybrid WENO schemes selectively adopt the high-order linear upwind scheme or the WENO scheme to avoid the local characteristic decompositions and calculations of the nonlinear weights in smooth regions. Therefore, they can reduce computational cost while maintaining non-oscillatory properties in non-smooth regions. Reliable troubled-cell indicators are essential for efficient hybrid WENO methods. Most of troubled-cell indicators require proper parameters to detect discontinuities precisely, but it is very difficult to determine the parameters automatically. We develop a new troubled-cell indicator derived from the mean value theorem that does not require any variable parameters. Additionally, we investigate the characteristics of indicator variable; one of the conserved properties or the entropy is considered as indicator variable. Detailed numerical tests for 1D and 2D Euler equations are conducted to demonstrate the performance of the proposed indicator. The results with the proposed troubled-cell indicator are in good agreement with pure WENO schemes. Also the new indicator has advantages in the computational cost compared with the other indicators.     

Mixed Reality Combined with Three‐Dimensional Printing Technology in Total Hip Arthroplasty: An Updated Review with a Preliminary Case Presentation

Three‐dimensional (3D) printing technology, virtual reality, and augmented reality technology have been used to help surgeons to complete complex total hip arthroplasty, while their respective shortcomings limit their further application. With the development of technology, mixed reality (MR) technology has been applied to improve the success rate of complicated hip arthroplasty because of its unique advantages. We presented a case of a 59‐year‐old man with an intertrochanteric fracture in the left femur, who had received a prior left hip fusion. After admission to our hospital, a left total hip arthroplasty was performed on the patient using a combination of MR technology and 3D printing technology. Before surgery, 3D reconstruction of a certain bony landmark exposed in the surgical area was first performed. Then a veneer part was designed according to the bony landmark and connected to a reference registration landmark outside the body through a connecting rod. After that, the series of parts were made into a holistic reference registration instrument using 3D printing technology, and the patient's data for bone and surrounding tissue, along with digital 3D information of the reference registration instrument, were imported into the head‐mounted display (HMD). During the operation, the disinfected reference registration instrument was installed on the selected bony landmark, and then the automatic real‐time registration was realized by HMD through recognizing the registration landmark on the reference registration instrument, whereby the patient's virtual bone and other anatomical structures were quickly and accurately superimposed on the real body of the patient. To the best of our knowledge, this is the first report to use MR combined with 3D printing technology in total hip arthroplasty.