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The study performs large-eddy simulations of supersonic free jet flows using the Discontinuous Galerkin Spectral Element Method (DGSEM). The main objective of the present work is to assess the resolution requirements for adequate simulation…

Fluid Dynamics · Physics 2024-03-22 Diego F. Abreu , João Luiz F. Azevedo , Carlos Junqueira-Junior

The numerical solution of partial differential equations is at the heart of many grand challenges in supercomputing. Solvers based on high-order discontinuous Galerkin (DG) discretisation have been shown to scale on large supercomputers…

Mathematical Software · Computer Science 2020-11-12 Carsten Uphoff , Michael Bader

Real-time accurate solutions of large-scale complex dynamical systems are critically needed for control, optimization, uncertainty quantification, and decision-making in practical engineering and science applications, particularly in…

Machine Learning · Statistics 2024-12-06 Hai V. Nguyen , Jau-Uei Chen , Tan Bui-Thanh

High-order Discontinuous Galerkin (DG) methods offer excellent accuracy for turbulent flow simulations, especially when implemented on GPU-oriented architectures that favor very high polynomial orders. On modern GPUs, high-order polynomial…

We present a new family of high order accurate fully discrete one-step Discontinuous Galerkin (DG) finite element schemes on moving unstructured meshes for the solution of nonlinear hyperbolic PDE in multiple space dimensions, which may…

Numerical Analysis · Mathematics 2017-08-23 Walter Boscheri , Michael Dumbser

This thesis deals with the investigation of a H(div)-conforming hybrid discontinuous Galerkin discretization for incompressible turbulent flows. The discretization method provides many physical and solving-oriented properties, which may be…

Computational Engineering, Finance, and Science · Computer Science 2020-09-25 Xaver Mooslechner

In this paper, a uniformly high-order discontinuous Galerkin gas kinetic scheme (DG-HGKS) is proposed to solve the Euler equations of compressible flows. The new scheme is an extension of the one-stage compact and efficient high-order GKS…

Numerical Analysis · Mathematics 2025-10-14 Mengqing Zhang , Shiyi Li , Dongmi Luo , Jianxian Qiu , Yibing Chen

Many modern discontinuous Galerkin (DG) methods for conservation laws make use of summation by parts operators and flux differencing to achieve kinetic energy preservation or entropy stability. While these techniques increase the robustness…

In this work we consider Runge-Kutta discontinuous Galerkin methods (RKDG) for the solution of hyperbolic equations enabling high order discretization in space and time. We aim at an efficient implementation of DG for Euler equations on…

Numerical Analysis · Mathematics 2021-04-12 M. Siebenborn , V. Schulz , S. Schmidt

We present a novel discontinuous Galerkin finite element method for numerical simulations of the rotating thermal shallow water equations in complex geometries using curvilinear meshes, with arbitrary accuracy. We derive an entropy…

Numerical Analysis · Mathematics 2024-01-19 Kieran Ricardo , Kenneth Duru , David Lee

For hyperbolic conservation laws, traditional methods and physics-informed neural networks (PINNs) often encounter difficulties in capturing sharp discontinuities and maintaining temporal consistency. To address these challenges, we…

Numerical Analysis · Mathematics 2025-08-25 Yan Shen , Jingrun Chen , Keke Wu

In recent years, high-order discontinuous Galerkin (DG) methods have emerged as an attractive approach for numerical simulations of compressible flows. This paper presents an overview of the recent development of DG methods for compressible…

The long-time evolution of extreme mass-ratio inspiral systems requires minimal phase and dispersion errors to accurately compute far-field waveforms, while high accuracy is essential near the smaller black hole (modeled as a Dirac delta…

General Relativity and Quantum Cosmology · Physics 2025-09-16 Manas Vishal , Scott E. Field , Sigal Gottlieb , Jennifer Ryan

We develop an entropy-stable high-order numerical method for the two-dimensional compressible Euler equations on general curvilinear meshes. The proposed approach is based on a nodal discontinuous Galerkin spectral element method (DGSEM)…

Numerical Analysis · Mathematics 2026-02-20 Jielin Yang , Guosheng Fu

The discontinuous Galerkin (DG) method has been widely considered in recent years to develop scalable flow solvers for its ability to handle discontinuities, such as shocks and detonations, with greater accuracy and high arithmetic…

Computational Physics · Physics 2025-01-06 Aswin Kumar Arumugam , Konduri Aditya

We present the recent development of hybridizable and embedded discontinuous Galerkin (DG) methods for wave propagation problems in fluids, solids, and electromagnetism. In each of these areas, we describe the methods, discuss their main…

Numerical Analysis · Mathematics 2018-07-03 Pablo Fernandez , Alexandra Christophe , Sebastien Terrana , Ngoc-Cuong Nguyen , Jaime Peraire

We propose energy-conserving discontinuous Galerkin (DG) methods for symmetric linear hyperbolic systems on general unstructured meshes. Optimal a priori error estimates of order $k+1$ are obtained for the semi-discrete scheme in one…

Numerical Analysis · Mathematics 2019-06-26 Guosheng Fu , Chi-Wang Shu

The application of discontinuous Galerkin (DG) schemes to hyperbolic systems of conservation laws requires a careful interplay between space discretization, carried out with local polynomials and numerical fluxes at inter-cells, and…

Numerical Analysis · Mathematics 2025-11-11 Maya Briani , Gabriella Puppo , Giuseppe Visconti

We present a Discontinuous Galerkin (DG) solver for the compressible Navier-Stokes system, designed for applications of technological and industrial interest in the subsonic region. More precisely, this work aims to exploit the…

Numerical Analysis · Mathematics 2025-08-26 Spiros Zafeiris , Emmanuil H. Georgoulis , George Papadakis

In this study, three-dimensional simulations of a reacting hydrogen jet in supersonic crossflow using a structure-preserving discontinuous Galerkin (DG) formulation are examined. The hydrogen jet, with a momentum flux ratio of five, is…

Fluid Dynamics · Physics 2025-08-13 Cal J. Rising , Eric J. Ching , Ryan F. Johnson