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The paper considers grad-div stabilized equal-order finite elements (FE) methods for the linearized Navier-Stokes equations. A block triangular preconditioner for the resulting system of algebraic equations is proposed which is closely…

Numerical Analysis · Mathematics 2024-11-12 Yunhui He , Maxim Olshanskii

We present a parametric finite element approximation of two-phase flow. This free boundary problem is given by the Navier--Stokes equations in the two phases, which are coupled via jump conditions across the interface. Using a novel…

Numerical Analysis · Mathematics 2015-06-02 John W. Barrett , Harald Garcke , Robert Nürnberg

In this paper we study the influence of including snapshots that approach the velocity time derivative in the numerical approximation of the incompressible Navier-Stokes equations by means of proper orthogonal decomposition (POD) methods.…

Numerical Analysis · Mathematics 2022-11-01 Bosco García-Archilla , Volker John , Julia Novo

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

The paper aims at developing low-storage implicit Runge-Kutta methods which are easy to implement and achieve higher-order of convergence for both the velocity and pressure in the finite volume formulation of the incompressible…

Numerical Analysis · Mathematics 2019-07-08 Jiawei Wan , Ahsan Kareem , Haili Liao , Yunzhu Cai

We propose in this paper efficient first/second-order time-stepping schemes for the evolutional Navier-Stokes-Nernst-Planck-Poisson equations. The proposed schemes are constructed using an auxiliary variable reformulation and sophisticated…

Numerical Analysis · Mathematics 2023-05-17 Xiaolan Zhou , Chuanju Xu

A new class of fully decoupled consistent splitting schemes for the Navier-Stokes equations are constructed and analyzed in this paper. The schemes are based on the Taylor expansion at $t^{n+\beta}$ with $\beta\ge 1$ being a free parameter.…

Numerical Analysis · Mathematics 2025-07-03 Fukeng Huang , Jie Shen

The objective of this work is to present the existence result of for the non- steady compressible Navier-Stokes equations via time discretization. We consider the two-dimensional case with a slip boundary conditions. First, the existence of…

Classical Analysis and ODEs · Mathematics 2010-09-16 Ewelina Kamińska

This paper is concerned with high moment and pathwise error estimates for fully discrete mixed finite element approximattions of stochastic Navier-Stokes equations with general additive noise. The implicit Euler-Maruyama scheme and standard…

Numerical Analysis · Mathematics 2022-10-04 Xiaobing Feng , Liet Vo

In this work we propose, {analyze}, and validate a stabilized finite element method for a flow problem arising from the assessment of {4D Flow Magnetic Resonance Imaging quality}. Starting from the Navier-Stokes equation and splitting its…

Numerical Analysis · Mathematics 2026-01-27 Gabriel Barrenechea , Cristian Cárcamo , Abner Poza

In this study the numerical performance of the fourth order compact formulation of the steady 2-D incompressible Navier-Stokes equations introduced by Erturk et al. (Int. J. Numer. Methods Fluids, 50, 421-436) will be presented. The…

Fluid Dynamics · Physics 2009-01-05 Ercan Erturk

The reaction-diffusion model can generate a wide variety of spatial patterns, which has been widely applied in chemistry, biology, and physics, even used to explain self-regulated pattern formation in the developing animal embryo. In this…

Numerical Analysis · Mathematics 2020-01-29 Hui Zhang , Xiaoyun Jiang , Fanhai Zeng , George Em Karniadakis

A novel reduced order model (ROM) for incompressible flows is developed by performing a Galerkin projection based on a fully (space and time) discrete full order model (FOM) formulation. This 'discretize-then-project' approach requires no…

Integration of Ordinary Differential Equations (ODEs) using Backward Difference formula (BDF) methods with p backward steps achieves order p accuracy if specific conditions are met. This work extends the composition technique with complex…

Numerical Analysis · Mathematics 2026-05-11 Ahmad Deeb , Denys Dutykh , Maryam Al Zohbi

This article aims at developing a high order pressure-based solver for the solution of the 3D compressible Navier-Stokes system at all Mach numbers. We propose a cell-centered discretization of the governing equations that splits the fluxes…

Numerical Analysis · Mathematics 2021-03-17 Walter Boscheri , Lorenzo Pareschi

In this paper, we consider numerical approximation of an electrically conductive ferrofluid model, which consists of Navier-Stokes equations, magnetization equation, and magnetic induction equation. To solve this highly coupled, nonlinear,…

Numerical Analysis · Mathematics 2025-04-02 Jialin Xie , Xiaodi Zhang

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

The error estimates and convergence rate of a two-level MacCormack rapid solver method for solving a two-dimensional incompressible Navier-Stokes equations are analyzed. This represents a continuation of the work on the stability analysis…

Numerical Analysis · Mathematics 2019-03-27 Eric Ngondiep

A semi-implicit fractional-step method that uses a staggered node layout and radial basis function-finite differences (RBF-FD) to solve the incompressible Navier-Stokes equations is developed. Polyharmonic splines (PHS) with polynomial…

Fluid Dynamics · Physics 2022-12-15 Tianyi Chu , Oliver T. Schmidt

We present a simple and efficient variational finite difference method for simulating time-dependent Stokes flow in the presence of irregular free surfaces and moving solid boundaries. The method uses an embedded boundary approach on…

Computational Physics · Physics 2011-05-25 Christopher Batty , Robert Bridson