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In this paper we propose a novel arbitrary high order accurate semi-implicit space-time DG method for the solution of the three-dimensional incompressible Navier-Stokes equations on staggered unstructured curved tetrahedral meshes. As…

Numerical Analysis · Mathematics 2016-06-22 Maurizio Tavelli , Michael Dumbser

The goal of this paper is to create a fruitful bridge between the numerical methods for approximating partial differential equations (PDEs) in fluid dynamics and the (iterative) numerical methods for dealing with the resulting large linear…

Numerical Analysis · Mathematics 2016-12-15 M. Dumbser , F. Fambri , I. Furci , M. Mazza , M. Tavelli , S. Serra-Capizzano

We study the steady-state Navier-Stokes equations in the context of stochastic finite element discretizations. Specifically, we assume that the viscosity is a random field given in the form of a generalized polynomial chaos expansion. For…

Numerical Analysis · Mathematics 2016-04-26 Bedřich Sousedík , Howard C. Elman

This work presents the discontinuous Galerkin discretization of the consistent splitting scheme proposed by Liu [J. Liu, J. Comp. Phys., 228(19), 2009]. The method enforces the divergence-free constraint implicitly, removing…

Numerical Analysis · Mathematics 2026-04-29 Dominik Still , Natalia Nebulishvili , Richard Schussnig , Katharina Kormann , Martin Kronbichler

This paper presents robust discontinuous Galerkin methods for the incompressible Navier-Stokes equations on moving meshes. High-order accurate arbitrary Lagrangian-Eulerian formulations are proposed in a unified framework for both…

Computational Physics · Physics 2021-03-17 Niklas Fehn , Johannes Heinz , Wolfgang A. Wall , Martin Kronbichler

In this paper, we use an implicit two-derivative deferred correction time discretization approach and combine it with a spatial discretization of the discontinuous Galerkin spectral element method to solve (non-)linear PDEs. The resulting…

Numerical Analysis · Mathematics 2022-07-13 Jonas Zeifang , Jochen Schuetz

The present paper addresses the numerical solution of turbulent flows with high-order discontinuous Galerkin methods for discretizing the incompressible Navier-Stokes equations. The efficiency of high-order methods when applied to…

Fluid Dynamics · Physics 2018-08-29 Niklas Fehn , Wolfgang A. Wall , Martin Kronbichler

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 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

We introduce and analyze a space-time hybridized discontinuous Galerkin method for the evolutionary Navier--Stokes equations. Key features of the numerical scheme include point-wise mass conservation, energy stability, and pressure…

Numerical Analysis · Mathematics 2023-07-07 Keegan L. A. Kirk , Tamás L. Horváth , Sander Rhebergen

This paper presents a new numerical method for the compressible Navier-Stokes equations governing the flow of an ideal isentropic gas. To approximate the continuity equation, the method utilizes a discontinuous Galerkin discretization on…

Numerical Analysis · Mathematics 2012-06-21 Trygve K. Karper

We present a static-condensation method for time-implicit discretizations of the Discontinuous Galerkin Spectral Element Method on Gauss-Lobatto points (GL-DGSEM). We show that, when solving the compressible Navier-Stokes equations, it is…

Computational Physics · Physics 2019-12-16 Andrés M. Rueda-Ramírez , Esteban Ferrer , David A. Kopriva , Gonzalo Rubio , Eusebio Valero

In this paper a new high order semi-implicit discontinuous Galerkin method (SI-DG) is presented for the solution of the incompressible Navier-Stokes equations on staggered space-time adaptive Cartesian grids (AMR) in two and three…

Numerical Analysis · Mathematics 2017-08-02 Francesco Fambri , Michael Dumbser

We present a strongly conservative and pressure-robust hybridizable discontinuous Galerkin method for the coupled time-dependent Navier-Stokes and Darcy problem. We show existence and uniqueness of a solution and present an optimal a priori…

Numerical Analysis · Mathematics 2023-03-20 A. Cesmelioglu , J. J. Lee , S. Rhebergen

In this paper we present a hybridizable discontinuous Galerkin method for the time-dependent Navier-Stokes equations coupled to the quasi-static poroelasticity equations via interface conditions. We determine a bound on the data that…

Numerical Analysis · Mathematics 2023-08-31 Aycil Cesmelioglu , Jeonghun J. Lee , Sander Rhebergen

We propose a new arbitrary high order accurate semi-implicit space-time discontinuous Galerkin (DG) method for the solution of the two and three dimensional compressible Euler and Navier-Stokes equations on staggered unstructured curved…

Numerical Analysis · Mathematics 2017-05-24 Maurizio Tavelli , Michael Dumbser

We apply a composite idea of semi-discrete finite difference approximation in time and Galerkin finite element method in space to solve the Navier-Stokes equations with Caputo derivative of order 0 < {\alpha} < 1. The stability properties…

Numerical Analysis · Mathematics 2018-02-28 Guang-an Zou , Yong Zhou , Bashir Ahmad , Ahmed Alsaedi

This paper presents an enriched Galerkin (EG) finite element method for the incompressible Navier--Stokes equations. The method augments continuous piecewise linear velocity spaces with elementwise bubble functions, yielding a locally…

Numerical Analysis · Mathematics 2025-11-26 Chun Song , Minfu Feng

This paper develops and analyses semi-discrete numerical method for two dimensional Vlasov-Stokes' system with periodic boundary condition. The method is based on coupling of semi-discrete discontinuous Galerkin method for the Vlasov…

Numerical Analysis · Mathematics 2023-12-18 Harsha Hutridurga , Krishan Kumar , Amiya K. Pani

We develop a stochastic Galerkin method for a coupled Navier-Stokes-cloud system that models dynamics of warm clouds. Our goal is to explicitly describe the evolution of uncertainties that arise due to unknown input data, such as model…

Numerical Analysis · Mathematics 2022-04-20 A. Chertock , A. Kurganov , M. Lukáčová-Medviďová , P. Spichtinger , B. Wiebe