Keywords:Low Mach number flows Discontinuous Galerkin finite element method Preconditioning Euler equations Compressible flows Roe scheme a b s t r a c tIn this work we extend the high-order discontinuous Galerkin (DG) finite element method to inviscid low Mach number flows. The method here presented is designed to improve the accuracy and efficiency of the solution at low Mach numbers using both explicit and implicit schemes for the temporal discretization of the compressible Euler equations. The algorithm is based on a classical preconditioning technique that in general entails modifying both the instationary term of the governing equations and the dissipative term of the numerical flux function (full preconditioning approach). In the paper we show that full preconditioning is beneficial for explicit time integration while the implicit scheme turns out to be efficient and accurate using just the modified numerical flux function. Thus the implicit scheme could also be used for time accurate computations. The performance of the method is demonstrated by solving an inviscid flow past a NACA0012 airfoil at different low Mach numbers using various degrees of polynomial approximations. Computations with and without preconditioning are performed on different grid topologies to analyze the influence of the spatial discretization on the accuracy of the DG solutions at low Mach numbers.

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May-Hegglin anomaly, Sebastian syndrome, Fechtner syndrome, and Epstein syndrome are autosomal dominant macrothrombocytopenias distinguished by different combinations of clinical and laboratory signs, such as sensorineural hearing loss, cataract, nephritis, and polymorphonuclear Döhle-like bodies. Mutations in the MYH9 gene encoding for the nonmuscle myosin heavy chain IIA (NMMHC-IIA) have been identified in all these syndromes. To understand the role of the MYH9 mutations, we report the molecular defects in 12 new cases, which together with our previous works represent a cohort of 19 families. Since no genotype-phenotype correlation was established, we performed an accurate clinical and biochemical re-evaluation of patients. In addition to macrothrombocytopenia, an abnormal distribution of NMMHC-IIA within leukocytes was observed in all individuals, including those without Döhle-like bodies. Selective, high-tone hearing deficiency and cataract was diagnosed in 83% and 23%, respectively, of patients initially referred as having May-Hegglin anomaly or Sebastian syndrome. Kidney abnormalities, such as hematuria and proteinuria, affected not only patients referred as Fechtner syndrome and Epstein syndrome but also those referred as May-Hegglin anomaly and Sebastian syndrome. These findings allowed us to conclude that May-Hegglin anomaly, Sebastian syndrome, Fechtner syndrome, and Epstein syndrome are not distinct entities but rather a single disorder with a continuous clinical spectrum varying from mild macrothrombocytopenia with leukocyte inclusions to a severe form complicated by hearing loss, cataracts, and renal failure. For this new nosologic entity, we propose the term "MHY9-related disease," which better interprets the recent knowledge in this field and identifies all patients at risk of developing renal, hearing, or visual defects.