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Hydrodynamical numerical methods that converge with high-order hold particular promise for astrophysical studies, as they can in principle reach prescribed accuracy goals with higher computational efficiency than standard second- or…

Instrumentation and Methods for Astrophysics · Physics 2023-05-05 Miha Cernetic , Volker Springel , Thomas Guillet , Rüdiger Pakmor

This paper introduces a high order numerical framework for efficient and robust simulation of compressible flows. To address the inefficiencies of standard hybridized discontinuous Galerkin (HDG) methods in large scale settings, we develop…

Computational Engineering, Finance, and Science · Computer Science 2025-07-31 Vahid Badrkhani , Marco F. P. ten Eikelder , Dominik Schillinger

Based on the Jacobi polynomial expansion, an arbitrary high-order Discontinuous Galerkin solver for compressible flows on unstructured meshes is proposed in the present work. First, we construct orthogonal polynomials for 2D and 3D…

Computational Physics · Physics 2024-11-26 Yu-Xiang Peng , Biao Wang , Peng-Nan Sun , A-Man Zhang

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 paper, we propose a unified numerical framework for the time-dependent incompressible Navier--Stokes equation which yields the $H^1$-, $H(\text{div})$-conforming, and discontinuous Galerkin methods with the use of different viscous…

Numerical Analysis · Mathematics 2020-11-16 Xi Chen , Yuwen Li , Corina Drapaca , John Cimbala

We present a generalized discontinuous Galerkin method for a multicomponent compressible barotropic Navier-Stokes system of equations. The system presented has a functional viscosity nu which depends on the pressure p=p(rho,mu_i) of the…

Computational Physics · Physics 2010-12-30 C. Michoski , J. A. Evans , P. G. Schmitz , A. Vasseur

Both compressible and incompressible Navier-Stokes solvers can be used and are used to solve incompressible turbulent flow problems. In the compressible case, the Mach number is then considered as a solver parameter that is set to a small…

Fluid Dynamics · Physics 2018-12-26 Niklas Fehn , Wolfgang A. Wall , Martin Kronbichler

The accurate numerical simulation of high Reynolds number incompressible flows is a challenging topic in computational fluid dynamics. Classical inf-sup stable methods like the Taylor-Hood element or only $L^2$-conforming discontinuous…

Numerical Analysis · Mathematics 2019-12-24 Marian Piatkowski , Peter Bastian

In this paper, we develop a new mass conservative numerical scheme for the simulations of a class of fluid-structure interaction problems. We will use the immersed boundary method to model the fluid-structure interaction, while the fluid…

Numerical Analysis · Mathematics 2018-06-21 Siu Wun Cheung , Eric Chung , Hyea Hyun Kim

High-order discontinuous Galerkin (DG) methods equipped with subcell finite-volume (FV) limiters provide an efficient framework for the simulation of nonlinear hyperbolic balance laws featuring shocks and complex flow structures. However,…

Numerical Analysis · Mathematics 2026-05-05 Andrés M. Rueda-Ramírez , Patrick Ersing , Andrew R. Winters , Gregor J. Gassner

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

A novel class of Runge-Kutta discontinuous Galerkin schemes for coupled systems of conservation laws in multiple space dimensions that are separated by a fixed sharp interface is introduced. The schemes are derived from a relaxation…

Numerical Analysis · Mathematics 2026-01-19 Niklas Kolbe , Siegfried Müller , Aleksey Sikstel

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

Kinetic schemes for compressible flow of gases are constructed by exploiting the connection between Boltzmann equation and the Navier-Stokes equations. This connection allows us to construct a flux splitting for the Navier-Stokes equations…

Numerical Analysis · Computer Science 2015-06-11 Praveen Chandrashekar

This work presents a novel stabilization strategy for the Galerkin formulation of the incompressible Navier-Stokes equations, developed to achieve high accuracy while ensuring convergence and compatibility with high-order elements on…

Numerical Analysis · Mathematics 2025-09-05 Antonio Blanco-Casares , Vishal Kumar , Daniel Mira , Oriol Lehmkuhl

Computational advances have fundamentally transformed the landscape of numerical simulations, enabling unprecedented levels of complexity and precision in modeling physical phenomena. While these high-fidelity simulations offer invaluable…

Fluid Dynamics · Physics 2025-09-09 Shinhoo Kang , Emil M. Constantinescu

In this paper we present an efficient discretization method for the solution of the unsteady incompressible Navier-Stokes equations based on a high order (Hybrid) Discontinuous Galerkin formulation. The crucial component for the efficiency…

Numerical Analysis · Mathematics 2016-06-29 Christoph Lehrenfeld , Joachim Schöberl

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

The development and application of the Discontinuous Galerkin (DG) method have attracted great attention in computational fluid dynamics (CFD) com- munity in the past decades. The underlying reason for such an intensive investigation is due…

Numerical Analysis · Mathematics 2016-01-20 Kun Xu , Chang Liu , Xiaodong Ren

We present a high-order discontinuous Galerkin (DG) solver of the compressible Navier-Stokes equations for cloud formation processes. The scheme exploits an underlying parallelized implementation of the ADER-DG method with dynamic adaptive…

Computational Physics · Physics 2020-05-18 Lukas Krenz , Leonhard Rannabauer , Michael Bader