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We propose a new formula for the nonlinear viscous numerical flux and extend the direct discontinuous Galerkin method with interface correction (DDGIC) of Liu and Yan (H. Liu, J. Yan, The direct discontinuous Galerkin (DDG) method for…

Numerical Analysis · Mathematics 2022-09-29 Mustafa E. Danis , Jue Yan

We present a robust and accurate discretization approach for incompressible turbulent flows based on high-order discontinuous Galerkin methods. The DG discretization of the incompressible Navier-Stokes equations uses the local…

Fluid Dynamics · Physics 2018-08-01 Niklas Fehn , Wolfgang A Wall , Martin Kronbichler

This paper presents a high-order discontinuous Galerkin finite element method to solve the barotropic version of the conservative symmetric hyperbolic and thermodynamically compatible (SHTC) model of compressible two-phase flow, introduced…

Numerical Analysis · Mathematics 2025-01-29 Laura Río-Martín , Michael Dumbser

We present reliable a posteriori estimators for some fully discrete schemes applied to nonlinear systems of hyperbolic conservation laws in one space dimension with strictly convex entropy. The schemes are based on a method of lines…

Numerical Analysis · Mathematics 2017-09-08 Andreas Dedner , Jan Giesselmann

In this paper we consider discontinuous Galerkin (DG) methods for the incompressible Navier-Stokes equations in the framework of projection methods. In particular we employ symmetric interior penalty DG methods within the second-order…

Numerical Analysis · Mathematics 2017-11-27 Marian Piatkowski , Steffen Müthing , Peter Bastian

The present paper addresses the development and implementation of the first high-order Flux Reconstruction (FR) solver for high-speed flows within the open-source COOLFluiD (Computational Object-Oriented Libraries for Fluid Dynamics)…

Computational Physics · Physics 2019-07-24 Ray Vandenhoeck , Andrea Lani

The conservation laws of continuum mechanic written in an Eulerian frame make no difference between fluids and solids except in the expression of the stress tensors, usually with Newton's hypothesis for the fluids and Helmholtz potentials…

Computational Engineering, Finance, and Science · Computer Science 2017-05-12 Olivier Pironneau

We present a high-order hybridizable discontinuous Galerkin method for the numerical solution of time-dependent three-phase flow in heterogeneous porous media. The underlying algorithm is a semi-implicit operator splitting approach that…

Computational Engineering, Finance, and Science · Computer Science 2025-03-07 Maurice S. Fabien

A high-order Flux reconstruction implementation of the hyperbolic formulation for the incompressible Navier-Stokes equation is presented. The governing equations employ Chorin's classical artificial compressibility (AC) formulation cast in…

Computational Physics · Physics 2021-06-04 Mohamed M. Kamra , Jabir Al-Salami , Changhong Hu

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…

Numerical Analysis · Mathematics 2026-04-16 Bikram Bir , Harsha Hutridurga , Amiya K. Pani

This article provides a reduced-order modelling framework for turbulent compressible flows discretized by the use of finite volume approaches. The basic idea behind this work is the construction of a reduced-order model capable of providing…

Fluid Dynamics · Physics 2024-05-31 Matteo Zancanaro , Valentin Nkana Ngan , Giovanni Stabile , Gianluigi Rozza

We propose a new parallel Discontinuous Galerkin method for the approximation of hyperbolic systems of conservation laws. The method remains stable with large time steps, while keeping the complexity of an explicit scheme: it does not…

Numerical Analysis · Mathematics 2024-02-27 Pierre Gerhard , Philippe Helluy , Victor Michel-Dansac , Bruno Weber

Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by…

Computational Physics · Physics 2015-04-22 Sebastian Acosta , Charles Puelz , Beatrice Riviere , Daniel J. Penny , Craig G. Rusin

This paper proposes a novel computational framework for the solution of geometrically parametrised flow problems governed by the Stokes equation. The proposed method uses a high-order hybridisable discontinuous Galerkin formulation and the…

Numerical Analysis · Mathematics 2020-09-10 Ruben Sevilla , Luca Borchini , Matteo Giacomini , Antonio Huerta

High-order Discontinuous Galerkin Spectral Element Methods (DGSEM) provide excellent accuracy for complex flow simulations, but their computational cost increases sharply with higher polynomial orders. %that provide very accurate solutions.…

Fluid Dynamics · Physics 2025-12-11 Xukun Wang , Oscar A. Marino , Esteban Ferrer

We propose a limiting procedure to preserve invariant domains with time explicit discrete high-order spectral discontinuous approximate solutions to hyperbolic systems of conservation laws. Provided the scheme is discretely conservative and…

Numerical Analysis · Mathematics 2022-03-15 Florent Renac , Valentin Carlier

The DFLU numerical flux was introduced in order to solve hyperbolic scalar conservation laws with a flux function discontinuous in space. We show how this flux can be used to solve certain class of systems of conservation laws such as…

Numerical Analysis · Computer Science 2014-01-16 Adi Adimurthi , G. D. Veerappa Gowda , Jérôme Jaffré

We develop an entropy stable two-phase incompressible Navier--Stokes/Cahn--Hilliard discontinuous Galerkin (DG) flow solver method. The model poses the Cahn-Hilliard equation as the phase field method, a skew-symmetric form of the momentum…

Numerical Analysis · Mathematics 2020-04-22 Juan Manzanero , Gonzalo Rubio , David A. Kopriva , Esteban Ferrer , Eusebio Valero

Modeling and simulation of fluid-structure interactions are crucial to the success of aerospace engineering. This work addresses a novel hybrid algorithm that models the close coupling between compressible flows and deformable materials…

Computational Physics · Physics 2025-04-16 Mingshuo Han , Shiwei Hu , Tianbai Xiao , Yonghao Zhang

In this paper we present energy-conserving, mixed discontinuous Galerkin (DG) and continuous Galerkin (CG) schemes for the solution of a broad class of physical systems described by Hamiltonian evolution equations. These systems often arise…

Computational Physics · Physics 2019-08-07 A. Hakim , G. Hammett , E. Shi , N. Mandell