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Diabetic myonecrosis is an infrequent complication of long-standing, uncontrolled diabetes mellitus. It usually involves the muscles of the lower limbs presenting with acute onset pain and swelling. It is often seen in association with chronic kidney disease. We present a case series of seven episodes seen over 5-year duration. All these patients had a long duration of poorly controlled diabetes associated with other microvascular complications. They were treated conservatively with bed rest, analgesics, vasodilators, and aspirin. The diagnosis is often missed due to its uncommon presentation and a lack of awareness. The disease resolves spontaneously but with poor long-term prognosis. [ABSTRACT FROM AUTHOR]

The shear shallow water model is a higher order model for shallow flows which includes some shear effects that are neglected in the classical shallow models. The model is a non-conservative hyperbolic system which can admit shocks, rarefactions, shear and contact waves. The notion of weak solution is based on a path but the choice of the correct path is not known for this problem. In this paper, we construct exact solution for the Riemann problem assuming a linear path in the space of conserved variables, which is also used in approximate Riemann solvers. We compare the exact solutions with those obtained from a path conservative finite volume scheme on some representative test cases. [ABSTRACT FROM AUTHOR]

We study the numerical stabilization of the two dimensional Boussinesq equations. The stabilization is achieved by boundary feedback controls of finite dimension applied on the velocity and temperature, and localized on parts of the domain boundary. We consider a stationary solution of the Boussinesq system which is linearly unstable. The linearized system around this unstable stationary solution is used to construct a feedback law. For that, we determine the projected linearized system onto an invariant subspace (including the unstable subspace), and we determine a feedback control law stabilizing this projected system, by solving a Riccati equation, of small dimension, associated with this system. The degrees of stabilizability of the different real generalized eigenspaces of the control system are used to determine the invariant subspace on which the linearized system is projected. Next, the linear feedback law, stabilizing the projected system, is applied to the nonlinear model to study its ability to locally stabilize the flow and its temperature. [ABSTRACT FROM AUTHOR]

Modern astrophysical simulations aim to accurately model an ever-growing array of physical processes, including the interaction of fluids with magnetic fields, under increasingly stringent performance and scalability requirements driven by present-day trends in computing architectures. Discontinuous Galerkin (DG) methods have recently gained some traction in astrophysics, because of their arbitrarily high order and controllable numerical diffusion, combined with attractive characteristics for high-performance computing. In this paper, we describe and test our implementation of a DG scheme for ideal magnetohydrodynamics (MHD) in the arepo-dg code. Our DG-MHD scheme relies on a modal expansion of the solution on Legendre polynomials inside the cells of an Eulerian octree-based adaptive mesh refinement grid. The divergence-free constraint of the magnetic field is enforced using one out of two distinct cell-centred schemes: either a Powell-type scheme based on non-conservative source terms, or a hyperbolic divergence cleaning method. The Powell scheme relies on a basis of locally divergence-free vector polynomials inside each cell to represent the magnetic field. Limiting prescriptions are implemented to ensure non-oscillatory and positive solutions. We show that the resulting scheme is accurate and robust: it can achieve high-order and low numerical diffusion, as well as accurately capture strong MHD shocks. In addition, we show that our scheme exhibits a number of attractive properties for astrophysical simulations, such as lower advection errors and better Galilean invariance at reduced resolution, together with more accurate capturing of barely resolved flow features. We discuss the prospects of our implementation, and DG methods in general, for scalable astrophysical simulations. [ABSTRACT FROM AUTHOR]

Abstract We design and analyze a discontinuous Galerkin scheme for the initial–boundary value problem associated with the magnetic induction equations using standard discontinuous Lagrange basis functions. The semi-discrete scheme is constructed by using the symmetrized version of the equation as introduced by Godunov. The resulting schemes are shown to be stable. Numerical experiments are performed in order to demonstrate the accuracy and convergence of the DG scheme through the L 2 -error and divergence error analysis. In the presence of discontinuities we add an artificial viscosity term to stabilize the solution. [ABSTRACT FROM AUTHOR]

We construct a finite volume scheme for the compressible Navier–Stokes equations on triangular grids which are entropy stable at the semi-discrete level. This is achieved by using entropy stable inviscid fluxes constructed in the recently published work titled Entropy Stable Scheme on Two-Dimensional Unstructured Grids for Euler Equations by Ray, Chandrashekar, Fjordholm and Mishra, (2016), and computing viscous fluxes in terms of entropy variables. Wall boundary conditions are also constructed to be entropy stable and are imposed in a weak manner. The resulting scheme is applied to solve several standard viscous test cases, such as flow over a flat-plat, flow past a NACA-0012 airfoil and unsteady flow past a cylinder, to demonstrate its stability and accuracy. [ABSTRACT FROM AUTHOR]

Solving the Euler equations of ideal hydrodynamics as accurately and efficiently as possible is a key requirement in many astrophysical simulations. It is therefore important to continuously advance the numerical methods implemented in current astrophysical codes, especially also in light of evolving computer technology, which favours certain computational approaches over others. Here we introduce the new adaptive mesh refinement (AMR) code tenet, which employs a high-order discontinuous Galerkin (DG) scheme for hydrodynamics. The Euler equations in this method are solved in a weak formulation with a polynomial basis by means of explicit Runge-Kutta time integration and Gauss-Legendre quadrature. This approach offers significant advantages over commonly employed second-order finite-volume (FV) solvers. In particular, the higher order capability renders it computationally more efficient, in the sense that the same precision can be obtained at significantly less computational cost. Also, the DG scheme inherently conserves angular momentum in regions where no limiting takes place, and it typically produces much smaller numerical diffusion and advection errors than an FV approach. A further advantage lies in a more natural handling of AMR refinement boundaries, where a fall-back to first order can be avoided. Finally, DG requires no wide stencils at high order, and offers an improved data locality and a focus on local computations, which is favourable for current and upcoming highly parallel supercomputers. We describe the formulation and implementation details of our new code, and demonstrate its performance and accuracy with a set of two- and three-dimensional test problems. The results confirm that DG schemes have a high potential for astrophysical applications. [ABSTRACT FROM AUTHOR]

We present a novel well-balanced second order Godunov-type finite volume scheme for compressible Euler equations with gravity. The well-balanced property is achieved by a specific combination of source term discretization, hydrostatic reconstruction, and numerical flux that exactly resolves stationary contacts. The scheme is able to preserve isothermal and polytropic stationary solutions up to machine precision. It is applied on several examples using the numerical flux of Roe to demonstrate its well-balanced property and the improved resolution of small perturbations around the stationary solution. [ABSTRACT FROM AUTHOR]