Space-time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows. Part I. General formulation

A new space-time discontinuous Galerkin finite element method for the solution of the Euler equations of gas dynamics in time-dependent flow domains is presented. The discontinuous Galerkin discretization results in an efficient element-wise conservative upwind finite element method, which is particularly well suited for local mesh refinement. The upwind scheme uses a formulation of the HLLC flux applicable to moving meshes and several formulations for the stabilization operator to ensure monotone solutions around discontinuities are investigated. The non-linear equations of the space-time discretization are solved using a multigrid accelerated pseudo-time integration technique with an optimized Runge-Kutta method. The linear stability of the pseudo-time integration method is investigated for the linear advection equation. The numerical scheme is demonstrated with simulations of the flow field in a shock tube, a channel with a bump, and an oscillating NACA 0012 airfoil. These simulations show that the accuracy of the numerical discretization is $O(h^{5/2})$ in space for smooth subsonic flows, both on structured and locally refined meshes, and that the space-time adaptation can significantly improve the accuracy and efficiency of the numerical method. \u

Space-time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows. Part II. Efficient flux quadrature

A new and efficient quadrature rule for the flux integrals arising in the space-time discontinuous Galerkin discretization of the Euler equations in a moving and deforming space-time domain is presented and analyzed. The quadrature rule is a factor three more efficient than the commonly applied quadrature rule and does not affect the local truncation error and stability of the numerical scheme. The local truncation error of the resulting numerical discretization is determined and is shown to be the same as when product Gauss quadrature rules are used. Details of the approximation of the dissipation in the numerical flux are presented, which render the scheme consistent and stable. The method is succesfully applied to the simulation of a three-dimensional, transonic flow over a deforming wing. \u

GPS analysis of a team competing at a national Under 18 field hockey tournament

The purpose of this study was to utilise global-positioning system (GPS) technology to quantify the running demands of national Under 18 field hockey players competing in a regional field hockey tournament. Ten male players (mean ± SD; age 17.2 ± 0.4 years; stature 178.1 ± 5.2 cm; body mass 78.8 ± 8.8 kg) wore GPS units while competing in six matches over seven days at the 2018 New Zealand national under 18 field hockey tournament. GPS enabled the measurement of total distance (TD), low-speed activity (LSA; 0 -14.9 km/hr), and high-speed running (HSR; ≥ 15 km/hr) distances. Differences in running demands (TD, LSA, HSR) between positions were assessed using effect size and percent difference ± 90% confidence intervals. Midfielders covered the most TD and LSA per game and strikers the most HSR during the 6 matches. There were “very large” differences between strikers and midfielders for TD and LSA, strikers and defenders for LSA and HSR, and defenders and midfielders for LSA. These results suggest that these playing positions are sufficiently different to warrant specialised position-specific conditioning training leading into a field hockey tournament

Multiphoton inner-shell ionization of the carbon atom

We apply time-dependent R-matrix theory to study inner-shell ionization of C atoms in ultra-short high-frequency light fields with a photon energy between 170 and 245 eV. At an intensity of 10$^{17}$ W/cm$^2$, ionization is dominated by single-photon emission of a $2\ell$ electron, with two-photon emission of a 1s electron accounting for about 2-3\% of all emission processes, and two-photon emission of $2\ell$ contributing about 0.5-1\%. Three-photon emission of a 1s electron is estimated to contribute about 0.01-0.03\%. Around a photon energy of 225 eV, two-photon emission of a 1s electron, leaving C$^+$ in either 1s2s2p$^3$ or 1s2p$^4$ is resonantly enhanced by intermediate 1s2s$^2$2p$^3$ states. The results demonstrate the capability of time-dependent R-matrix theory to describe inner-shell ionization processes including rearrangement of the outer electrons.Comment: 7 pages, 2 figures, 2 table

Space-time discontinuous Galerkin method for the compressible Navier-Stokes equations on deforming meshes

An overview is given of a space-time discontinuous Galerkin finite element method for the compressible Navier-Stokes equations. This method is well suited for problems with moving (free) boundaries which require the use of deforming elements. In addition, due to the local discretization, the space-time discontinuous Galerkin method is well suited for mesh adaptation and parallel computing. The algorithm is demonstrated with computations of the unsteady \ud ow field about a delta wing and a NACA0012 airfoil in rapid pitch up motion