An Analysis of Solution Point Coordinates for Flux Reconstruction Schemes on Tetrahedral Elements

The flux reconstruction (FR) approach offers an efficient route to high-order accuracy on unstructured grids. In this work we study the effect of solution point placement on the stability and accuracy of FR schemes on tetrahedral grids. To accomplish this we generate a large number of solution point candidates that satisfy various criteria at polynomial orders ℘=3,4,5℘=3,4,5 . We then proceed to assess their properties by using them to solve the non-linear Euler equations on both structured and unstructured meshes. The results demonstrate that the location of the solution points is important in terms of both the stability and accuracy. Across a range of cases it is possible to outperform the solution points of Shunn and Ham for specific problems. However, there appears to be a degree of problem-dependence with regards to the optimal point set, and hence overall it is concluded that the Shunn and Ham points offer a good compromise in terms of practical utility

Beneficial autoimmunity at body surfaces – immune surveillance and rapid type 2 immunity regulate tissue homeostasis and cancer

Epithelial cells line body surface tissues and provide a physicochemical barrier to the external environment. Frequent microbial and non-microbial challenges such as those imposed by mechanical disruption, injury or exposure to noxious environmental substances including chemicals, carcinogens, ultraviolet-irradiation or toxins cause activation of epithelial cells with release of cytokines and chemokines as well as alterations in the expression of cell surface ligands. Such display of epithelial stress is rapidly sensed by tissue resident immunocytes, which can directly interact with self-moieties on epithelial cells and initiate both local and systemic immune responses. Epithelial cells are thus key drivers of immune surveillance at body surface tissues. However, epithelial cells have a propensity to drive type 2 immunity (rather than type 1) upon non-invasive challenge or stress – a type of immunity whose regulation and function still remain enigmatic. Here we review the induction and possible role of type 2 immunity in epithelial tissues and propose that rapid immune surveillance and type 2 immunity are key regulators of tissue homeostasis and carcinogenesis