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The Navier--Stokes equations are commonly used to model and to simulate flow phenomena. We introduce the basic equations and discuss the standard methods for the spatial and temporal discretization. We analyse the semi-discrete equations --…

Numerical Analysis · Mathematics 2024-12-20 Robert Altmann , Jan Heiland

In this article we address flow problems that carry a multiscale character in time. In particular we consider the Navier-Stokes flow in a channel on a fast scale that influences the movement of the boundary which undergoes a deformation on…

Numerical Analysis · Mathematics 2020-08-11 Stefan Frei , Thomas Richter

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 present and analyze a fully discrete fractional time stepping technique for the solution of the micropolar Navier Stokes equations, which is a system of equations that describes the evolution of an incompressible fluid whose material…

Numerical Analysis · Mathematics 2013-12-06 Abner J. Salgado

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

We construct high-order semi-discrete-in-time and fully discrete (with Fourier-Galerkin in space) schemes for the incompressible Navier-Stokes equations with periodic boundary conditions, and carry out corresponding error analysis. The…

Numerical Analysis · Mathematics 2021-03-23 Fukeng Huang , Jie Shen

A conforming finite element scheme with mixed explicit-implicit time discretization for quasi-incompressible Navier-Stokes-Maxwell-Stefan systems in a bounded domain with periodic boundary conditions is presented. The system consists of the…

Numerical Analysis · Mathematics 2026-02-05 Aaron Brunk , Ansgar Jüngel , Maria Lukáčová-Medvid'ová

In the present study, the efficiency of preconditioners for solving linear systems associated with the discretized variable-density incompressible Navier-Stokes equations with semiimplicit second-order accuracy in time and spectral accuracy…

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

In this paper, we investigate numerically a diffuse interface model for the Navier-Stokes equation with fluid-fluid interface when the fluids have different densities \cite{Lowengrub1998}. Under minor reformulation of the system, we show…

Mathematical Physics · Physics 2015-06-18 Zhenlin Guo , Ping Lin , John S. Lowengrub

We study the deterministic reiterated homogenization of the non-stationary Navier-Stokes type equations in fixed domains with periodically rapidly varying coefficients. One convergence theorem and a corrector result are proved, and we…

Analysis of PDEs · Mathematics 2026-05-22 Lazarus Signing

The paper develops a finite element method for the Navier-Stokes equations of incompressible viscous fluid in a time-dependent domain. The method builds on a quasi-Lagrangian formulation of the problem. The paper provides stability and…

Numerical Analysis · Mathematics 2018-05-15 Alexander Lozovskiy , Maxim A. Olshanskii , Yuri V. Vassilevski

We develop a novel and efficient iterative scheme for solving incompressible steady Navier-Stokes equations. The method is an adaptation of the Incremental Viscosity Splitting approximation for unsteady flows to steady equations. At each…

Numerical Analysis · Mathematics 2026-05-07 Aziz Takhirov , Driss Yakoubi

In this paper, we study the behaviour at low Mach number of numerical schemes based on staggered discretizations for the barotropic Navier-Stokes equations. Three time discretizations are considered: the implicit-in-time scheme and two…

Numerical Analysis · Mathematics 2018-04-02 R. Herbin , J. -C Latché , Khaled Saleh

The 3D spatially periodic Navier-Stokes equation is posed as a nonlinear matrix differential equation. When the flow is assumed to be a time series having unknown wavenumber coefficients, then the matrix in this periodic Navier-Stokes…

Analysis of PDEs · Mathematics 2008-08-28 David T. Purvance

We consider coupled models for particulate flows, where the disperse phase is made of particles with distinct sizes. We are thus led to a system coupling the incompressible Navier-Stokes equations to the multi-component Vlasov-Fokker-Planck…

Numerical Analysis · Mathematics 2022-12-20 Shi Jin , Yiwen Lin

We report on simulations of two-phase flows with deforming interfaces at various density contrasts by solving thermodynamically consistent Cahn-Hilliard Navier-Stokes equations. An (essentially) unconditionally energy-stable…

We present new error estimates for the finite volume and finite difference methods applied to the compressible Navier-Stokes equations. The main innovative ingredients of the improved error estimates are a refined consistency analysis…

Numerical Analysis · Mathematics 2022-05-10 Eduard Feireisl , Mária Lukáčová-Medviďová , Bangwei She

We present an exponentially convergent semi-implicit meshless algorithm for the solution of Navier-Stokes equations in complex domains. The algorithm discretizes partial derivatives at scattered points using radial basis functions as…

Numerical Analysis · Mathematics 2021-06-15 Shantanu Shahane , Surya Pratap Vanka

We consider two-dimensional nonstationary Navier-Stokes shear flow with multivalued and nonmonotone boundary conditions on a part of the boundary of the flow domain. We prove the existence of global in time solutions of the considered…

Analysis of PDEs · Mathematics 2015-09-28 P. Kalita , G. Łukaszewicz