Related papers: Binary neutron star mergers using a discontinuous …
The study of uncertainty propagation poses a great challenge to design numerical solvers with high fidelity. Based on the stochastic Galerkin formulation, this paper addresses the idea and implementation of the first flux reconstruction…
In this paper, we concentrate on the superconvergence of the local discontinuous Galerkin method with generalized numerical fluxes for one-dimensional linear time-dependent fourth-order equations. The adjustable numerical viscosity of the…
Streamer discharges are important both in theory and industry applications. This paper proposed a local discontinuous Galerkin method to simulate the convection dominated fluid model of streamer discharges. To simulate the rapid transient…
As an extension of our previous work in Sun et.al (2018) [41], we develop a discontinuous Galerkin method for solving cross-diffusion systems with a formal gradient flow structure. These systems are associated with non-increasing entropy…
We analyze an iterative coupling of mixed and discontinuous Galerkin methods for numerical modelling of coupled flow and mechanical deformation in porous media. The iteration is based on an optimized fixed-stress split along with a…
This paper studies high-order accurate entropy stable nodal discontinuous Galerkin (DG) schemes for the ideal special relativistic magnetohydrodynamics (RMHD). It is built on the modified RMHD equations with a particular source term, which…
In this article, we propose high order discontinuous Galerkin entropy stable schemes for ten-moment Gaussian closure equations, which is based on the suitable quadrature rules (see [8]). The key components of the proposed method are the use…
A novel discontinuous Galerkin (DG) method is developed to solve time-dependent bi-harmonic type equations involving fourth derivatives in one and multiple space dimensions. We present the spatial DG discretization based on a mixed…
This paper deals with a fully discrete numerical scheme for the incompressible Chemotaxis(Keller-Segel)-Navier-Stokes system. Based on a discontinuous Galerkin finite element scheme in the spatial directions, a semi-implicit first-order…
The 2017 detection of the in-spiral and merger of two neutron stars was a landmark discovery in astrophysics. We now know that such mergers are central engines of short gamma ray bursts and sites of r-process nucleosynthesis, where the…
Binary neutron star mergers provide a laboratory for probing fundamental physics through their gravitational-wave emission and electromagnetic counterparts. In particular, they may allow us to explore signatures of physics beyond the…
High-order methods are well-suited for the numerical simulation of complex compressible turbulent flows, but require additional stabilization techniques to capture instabilities arising from the underlying non-linear hyperbolic equations.…
We demonstrate Bayesian analyses of the complete gravitational-wave spectrum of binary neutron star mergers events with the next-generation detector Einstein Telescope. Our mock analyses are performed for 20 different signals using the…
A binary neutron star merger has been observed in a multi-messenger detection of gravitational wave (GW) and electromagnetic (EM) radiation. Binary neutron stars that merge within a Hubble time, as well as many other compact binaries, are…
We present analysis of two lowest-order hybridizable discontinuous Galerkin methods for the Stokes problem, while making only minimal regularity assumptions on the exact solution. The methods under consideration have previously been shown…
We study the general dynamics of the spherically symmetric gravitational collapse of a massless scalar field. We apply the Galerkin projection method to transform a system of partial differential equations into a set of ordinary…
Discontinuous Galerkin (DG) methods provide a means to obtain high-order accurate solutions in regions of smooth fluid flow while, with the aid of limiters, still resolving strong shocks. These and other properties make DG methods…
In this article, a hybridizable discontinuous Galerkin (HDG) method is proposed and analyzed for the Klein-Gordon equation with local Lipschitz-type non-linearity. {\it A priori} error estimates are derived, and it is proved that…
We present a novel implementation of the modal discontinuous Galerkin (DG) method for hyperbolic conservation laws in two dimensions on graphics processing units (GPUs) using NVIDIA's Compute Unified Device Architecture (CUDA). Both…
Binary neutron star mergers observations are a unique way to constrain fundamental physics and astrophysics at the extreme. The interpretation of gravitational-wave events and their electromagnetic counterparts crucially relies on…