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The flow of incompressible fluid in highly permeable porous media in vorticity - velocity - Bernoulli pressure form leads to a double saddle-point problem in the Navier--Stokes--Brinkman--Forchheimer equations. The paper establishes, for…

Numerical Analysis · Mathematics 2025-10-23 Santiago Badia , Carsten Carstensen , Alberto F. Martin , Ricardo Ruiz-Baier , Segundo Villa-Fuentes

In this study, we develop an efficient approach for approximating resolvent modes via spatial marching. Building on the methodology from Part 1, we leverage the ability of the projection-based formulation of the one-way Navier-Stokes…

Fluid Dynamics · Physics 2021-11-18 Georgios Rigas , Omar Kamal , Aaron Towne , Tim Colonius

In this paper we consider the numerical approximation of the incompressible surface Navier--Stokes equations on an evolving surface. For the discrete representation of the moving surface we use parametric finite elements of degree $\ell…

Numerical Analysis · Mathematics 2026-01-09 Harald Garcke , Robert Nürnberg

A family of Virtual Element Methods for the 2D Navier-Stokes equations is proposed and analysed. The schemes provide a discrete velocity field which is point-wise divergence-free. A rigorous error analysis is developed, showing that the…

Numerical Analysis · Mathematics 2017-03-07 L. Beirão da Veiga , C. Lovadina , G. Vacca

We show that in bounded domains with no-slip boundary conditions, the Navier-Stokes pressure can be determined in a such way that it is strictly dominated by viscosity. As a consequence, in a general domain we can treat the Navier-Stokes…

Analysis of PDEs · Mathematics 2007-05-23 Jian-Guo Liu , Jie Liu , Robert L. Pego

The companion paper "Higher-order in time quasi-unconditionally stable ADI solvers for the compressible Navier-Stokes equations in 2D and 3D curvilinear domains", which is referred to as Part I in what follows, introduces ADI (Alternating…

Computational Physics · Physics 2018-01-11 Oscar Bruno , Max Cubillos

We consider a time discretization of incompressible Navier-Stokes equations with spatial periodic boundary conditions in the vorticity-velocity formulation. The approximation is based on freezing the velocity on time subintervals resulting…

Numerical Analysis · Mathematics 2020-10-12 G. N. Milstein , M. V. Tretyakov

An efficient numerical scheme based on the scalar auxiliary variable (SAV) and marker and cell scheme (MAC) is constructed for the Navier-Stokes equations. A particular feature of the scheme is that the nonlinear term is treated explicitly…

Numerical Analysis · Mathematics 2019-09-12 Xiaoli Li , Jie Shen

We propose a novel method for the direct numerical simulation of interfacial flows involving large density contrasts, using a Volume-of-Fluid method. We employ the conservative formulation of the incompressible Navier-Stokes equations for…

Computational Physics · Physics 2021-01-13 Sagar Pal , Daniel Fuster , Stéphane Zaleski

We extend to multi-dimensions the work of [1], where new fully explicit kinetic methods were built for the approximation of linear and non-linear convection-diffusion problems. The fundamental principles from the earlier work are retained:…

Numerical Analysis · Mathematics 2023-12-29 Gauthier Wissocq , Rémi Abgrall

We use a method based on the lubrication approximation in conjunction with a residual-based mass-continuity iterative solution scheme to compute the flow rate and pressure field in distensible converging-diverging tubes for Navier-Stokes…

Fluid Dynamics · Physics 2015-04-30 Taha Sochi

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

This paper describes in detail the implementation of a finite element technique for solving the compressible Navier-Stokes equations that is provably robust and demonstrates excellent performance on modern computer hardware. The method is…

Numerical Analysis · Mathematics 2022-02-02 Jean-Luc Guermond , Martin Kronbichler , Matthias Maier , Bojan Popov , Ignacio Tomas

Computational physics simulation can be a powerful tool to accelerate industry deployment of new scientific technologies. However, it must address the challenge of computationally tractable, moderately accurate prediction at large industry…

The goal of this study is to develop an efficient numerical algorithm applicable to a wide range of compressible multicomponent flows. Although many highly efficient algorithms have been proposed for simulating each type of the flows, the…

Computational Physics · Physics 2018-10-04 Roman Frolov

This is the first of two papers concerning the asymptotic behavior of the incompressible Navier-Stokes equations in a half-space at high Reynolds numbers, with initial data given by a point vortex. In the present work, we establish the…

Analysis of PDEs · Mathematics 2026-04-08 Chao Wang , Jingchao Yue , Zhifei Zhang

An efficient and accurate finite-element algorithm is described for the numerical solution of the incompressible Navier-Stokes (INS) equations. The new algorithm that solves the INS equations in a velocity-pressure reformulation is based on…

Numerical Analysis · Mathematics 2020-02-19 Longfei Li

Implicit time-stepping for advection is applied locally in space and time where Courant numbers are large, but standard explicit time-stepping is used for the remaining solution which is typically the majority. This adaptively implicit…

Fluid Dynamics · Physics 2024-06-14 Hilary Weller , Christian Kuehnlein , Piotr K. Smolarkiewicz

We propose a mixed finite element method for the motion of a strongly viscous, ideal, and isentropic gas. At the boundary we impose a Navier-slip condition such that the velocity equation can be posed in mixed form with the vorticity as an…

Numerical Analysis · Mathematics 2009-11-11 Kenneth Karlsen , Trygve Karper

A new fourth order compact formulation for the steady 2-D incompressible Navier-Stokes equations is presented. The formulation is in the same form of the Navier-Stokes equations such that any numerical method that solve the Navier-Stokes…

Numerical Analysis · Mathematics 2025-10-20 E. Erturk , C. Gokcol