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We introduce an immersed high-order discontinuous Galerkin method for solving the compressible Navier-Stokes equations on non-boundary-fitted meshes. The flow equations are discretised with a mixed discontinuous Galerkin formulation and are…

Numerical Analysis · Mathematics 2020-01-08 Hong Xiao , Eky Febrianto , Qiaoling Zhang , Fehmi Cirak

We propose and analyze unfitted finite element approximations for the two-phase incompressible Navier--Stokes flow in an axisymmetric setting. The discretized schemes are based on an Eulerian weak formulation for the Navier--Stokes equation…

Numerical Analysis · Mathematics 2023-09-12 Harald Garcke , Robert Nürnberg , Quan Zhao

We propose and analyze a structure-preserving space-time variational discretization method for the Cahn-Hilliard-Navier-Stokes system. Uniqueness and stability for the discrete problem is established in the presence of concentration…

Numerical Analysis · Mathematics 2023-08-29 Aaron Brunk , Herbert Egger , Oliver Habrich , Maria Lukacova-Medvidova

This paper studies fully discrete finite element approximations to the Navier-Stokes equations using inf-sup stable elements and grad-div stabilization. For the time integration two implicit-explicit second order backward differentiation…

Numerical Analysis · Mathematics 2021-12-24 Bosco Garcia-Archilla , Julia Novo

This study proposes an algorithm for modeling compressible flows in spherical shells in nearly incompressible and weakly compressible regimes based on an implicit direction splitting approach. The method retains theoretically expected…

Numerical Analysis · Mathematics 2021-04-21 Roman Frolov , Peter Minev , Aziz Takhirov

Error estimates with optimal convergence orders are proved for a stabilized Lagrange-Galerkin scheme for the Navier-Stokes equations. The scheme is a combination of Lagrange-Galerkin method and Brezzi-Pitkaranta's stabilization method. It…

Numerical Analysis · Mathematics 2015-05-26 Hirofumi Notsu , Masahisa Tabata

In this work we introduce and analyze a novel Hybrid High-Order method for the steady incompressible Navier-Stokes equations. The proposed method is inf-sup stable on general polyhedral meshes, supports arbitrary approximation orders, and…

Numerical Analysis · Mathematics 2018-02-26 Daniele A. Di Pietro , Stella Krell

In this paper, we present an efficient numerical algorithm for solving the time-dependent Cahn--Hilliard--Navier--Stokes equations that model the flow of two phases with different densities. The pressure-correction step in the projection…

Numerical Analysis · Mathematics 2020-11-02 Chen Liu , Deep Ray , Christopher Thiele , Lu Lin , Beatrice Riviere

Recently, a new approach for the stabilization of the incompressible Navier-Stokes equations for higher Reynolds numbers was introduced based on the nonlinear differential filtering of solutions on every time step of a discrete scheme. In…

Numerical Analysis · Mathematics 2013-04-16 Maxim A. Olshanskii , Xin Xiong

We propose and analyze a finite element method for a semi-stationary Stokes system modeling compressible fluid flow subject to a Navier-slip boundary condition. The velocity (momentum) equation is approximated by a mixed finite element…

Numerical Analysis · Mathematics 2009-04-07 Kenneth H. Karlsen , Trygve K. Karper

The recently introduced divergence-conforming B-spline discretizations allow the construction of smooth discrete velocity-pressure pairs for viscous incompressible flows that are at the same time inf-sup stable and divergence-free. When…

Numerical Analysis · Mathematics 2013-09-20 Adriano M. A. Cortes , Alvaro L. G. A. Coutinho

We introduce a hybridized discontinuous Galerkin method for the incompressible Reynolds Averaged Navier-Stokes equations coupled with the Spalart-Allmaras one equation turbulence model. With a special choice of velocity and pressure spaces…

Numerical Analysis · Mathematics 2024-12-20 Eric L. Peters , John A. Evans

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 detailed description and verification of a discontinuous Galerkin finite element method (DG) for the multi-component chemically reacting compressible Navier-Stokes equations that retains the desirable properties of DG, namely…

Computational Physics · Physics 2020-10-28 Ryan F. Johnson , Andrew D. Kercher

In this paper, we design and analyze staggered discontinuous Galerkin methods of arbitrary polynomial orders for the stationary Navier-Stokes equations on polygonal meshes. The exact divergence-free condition for the velocity is satisfied…

Numerical Analysis · Mathematics 2021-07-21 Dohyun Kim , Lina Zhao , Eric Chung , Eun-Jae Park

High-order time-stepping schemes are crucial for simulating incompressible fluid flows due to their ability to capture complex turbulent behavior and unsteady motion. In this work, we propose a third-order accurate numerical scheme for the…

Numerical Analysis · Mathematics 2025-12-22 Kelong Cheng , Jingwei Sun , Hong Zhang

This paper investigates a modification of the fictitious domain method with continuation in the lower-order coefficients for the unsteady Navier-Stokes equations governing the motion of an incompressible homogeneous fluid in a bounded 2D or…

Numerical Analysis · Mathematics 2025-12-23 Zhanybek Baitulenov , Maxim Olshanskii , Almas Temirbekov , Nurlan Temirbekov , Syrym Kasenov

We consider error estimates for the fully discretized instationary Navier-Stokes problem. For the spatial approximation we use conforming inf-sup stable finite element methods in conjunction with grad-div and local projection stabilization…

Numerical Analysis · Mathematics 2016-09-06 Daniel Arndt , Helene Dallmann , Gert Lube

We study a colocated cell centered finite volume method for the approximation of the incompressible Navier-Stokes equations posed on a 2D or 3D finite domain. The discrete unknowns are the components of the velocity and the pressures, all…

Numerical Analysis · Mathematics 2008-04-30 Robert Eymard , Raphaele Herbin , Jean-Claude Latché

We analyze two fully time-discrete numerical schemes for the incompressible Navier-Stokes equations posed on evolving surfaces in $\mathbb{R}^3$ with prescribed normal velocity using the evolving surface finite element method (ESFEM). We…

Numerical Analysis · Mathematics 2025-12-15 Charles M. Elliott , Achilleas Mavrakis