We discuss the methodology of the validation of a higher order discontinuous Galerkin scheme for acoustic computations. That includes an accurate definition of the exact solution in the problem as well as careful study of convergence properties of a DG scheme for a chosen acoustic problem. The efficiency of a higher order scheme will be confirmed for computations on coarse meshes.

We develop spectral element methods for a timeand space-fractional advection equation of the form 0Dt u(x, t) + θ 0Dxu(x, t) = f(x, t), of order τ ∈ (0, 1], ν ∈ (0, 1), subject to Dirichlet initial/boundary conditions. We present two spectrally accurate and efficient methods for global discretization of both temporal and spatial terms, instead of employing traditional low-order time-integration...

Discontinuous Galerkin (DG) methods have recently received much attention because of their portability to complex geometries, scalability in parallel architectures and relatively simple extension to high order. However, their implementation for compressible turbulence problems is not straightforward, e.g., due to parameter-free limiting for orders greater than first and the lack of a consistent...

The aim of this paper is to study the high order difference scheme for the solution of a fractional partial differential equation (PDE) in the electroanalytical chemistry. The space fractional derivative is described in the Riemann-Liouville sense. In the proposed scheme we discretize the space derivative with a fourth-order compact scheme and use the Grunwald- Letnikov discretization of the Ri...

One of the main challenges in computational simulations of gas detonation propagation is that negative density or negative pressure may emerge during the time evolution, which will cause blow-ups. Therefore, schemes with provable positivity-preserving of certain quantities such as density and pressure are desired. First order and second order positivity-preserving schemes were well studied, e.g...

In this paper, an adaptive approach based on a time discontinuous Galerkin method (dG) is proposed. For large time steps and in a linear non-autonomous case, it reduces to the asymptotically second-order accurate Lobatto IIIC type implicit Runge-Kutta method, which is equal to the Padé-(0,2) approximation of the exponential function. In the asymptotic range it will result in the asymptotically ...

We study stability properties and truncation errors of the finite-volume ADER schemes on structured meshes as applied to the linear advection equation with constant coefficients in one-, twoand threespatial dimensions. Stability of linear ADER schemes is analysed by means of the von Neumann method. For nonlinear schemes, we deduce the stability region from numerical experiments. The truncation ...

abstract: in this paper a control scheme for grid-connected operation mode and the island state of distributed generation is presented. in normal conditions, every inverter dg system in micro-grids to supply a preset power, normally operate in a constant current control mode. when micro-grids removed from the network, dg inverter of each system must recognize the island and change position to v...

In [19, 20, 22], we constructed uniformly high order accurate discontinuous Galerkin (DG) which preserve positivity of density and pressure for the Euler equations of compressible gas dynamics. The technique also applies to high order accurate finite volume schemes. In this paper, we show an extension of this framework to construct positivity-preserving high order essentially non-oscillatory (E...