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A mechanical model and finite element method for the simultaneous solution of Stokes and incompressible Navier-Stokes flows on multiple curved surfaces over a bulk domain are proposed. The two-dimensional surfaces are defined implicitly by…

Computational Engineering, Finance, and Science · Computer Science 2025-10-09 Michael Wolfgang Kaiser , Thomas-Peter Fries

Rational approximation has proven to be a powerful method for solving two-dimensional (2D) fluid problems. At small Reynolds numbers, 2D Stokes flows can be represented by two analytic functions, known as Goursat functions. Xue, Waters and…

Fluid Dynamics · Physics 2025-12-18 Yidan Xue

Simulating the interaction of fluids with immersed moving solids is playing an important role for gaining a better quantitative understanding of how fluid dynamics is altered by the presence of obstacles and which forces are exerted on the…

A two-phase, low-Mach-number flow solver is created and verified for variable-density liquid and gas with phase change. The interface is sharply captured using a split Volume-of-Fluid method generalized for a non-divergence-free liquid…

Fluid Dynamics · Physics 2022-06-08 Jordi Poblador-Ibanez , William A. Sirignano

Continuing on our previous work [ArXiv:1212.2644], we develop semi-implicit numerical methods for solving low Mach number fluctuating hydrodynamic equations appropriate for modeling diffusive mixing in isothermal mixtures of fluids with…

Numerical Analysis · Mathematics 2016-01-20 A. J. Nonaka , Y. Sun , J. B. Bell , A. Donev

A computationally efficient method for solving three-dimensional, viscous, incompressible flows on unbounded domains is presented. The method formally discretizes the incompressible Navier-Stokes equations on an unbounded staggered…

Fluid Dynamics · Physics 2016-05-25 Sebastian Liska , Tim Colonius

We investigate in this article the boundary layers appearing for a fluid under moderate rotation when the viscosity is small. The fluid is modeled by rotating type Stokes equations known also as the Barotropric mode equations in the…

Analysis of PDEs · Mathematics 2016-07-12 Soumaya Ben Chaabane , Makram Hamouda , Mahdi Tekitek

Reduced-order models have been widely adopted in fluid mechanics, particularly in the context of Newtonian fluid flows. These models offer the ability to predict complex dynamics, such as instabilities and oscillations, at a considerably…

Fluid Dynamics · Physics 2023-12-05 Cassio M. Oishi , Alan A. Kaptanoglu , J. Nathan Kutz , Steven L. Brunton

Stokes flows are a type of fluid flow where convective forces are small in comparison with viscous forces, and momentum transport is entirely due to viscous diffusion. Besides being routinely used as benchmark test cases in numerical fluid…

Numerical Analysis · Mathematics 2021-12-16 Andrea Cioncolini , Daniele Boffi

Three algorithms are developed for uncertainty quantification in modeling coupled Stokes and Darcy flows. The porous media may consist of multiple regions with different properties. The permeability is modeled as a non-stationary stochastic…

Numerical Analysis · Mathematics 2019-03-05 Ilona Ambartsumyan , Eldar Khattatov , ChangQing Wang , Ivan Yotov

We present the components of a high-order accurate Navier-Stokes solver designed to simulate high-Reynolds-number stratified flows. The proposed numerical model addresses some of the numerical and computational challenges that…

Fluid Dynamics · Physics 2025-10-01 Nidia Reyes-Gil , Greg Thomsen , Kristopher Rowe , Peter Diamessis

We propose a seamless multiscale method which approximates the macroscopic behavior of the passive advection-diffusion equations with steady incompressible velocity fields with multi-spatial scales. The method uses decompositions of the…

Numerical Analysis · Mathematics 2016-06-22 Yoonsang Lee , Bjorn Engquist

The study solves the general solution to 2D steady Navier-Stokes equation for incompressible flow without vorticity diffusion, which is more general than Stokes flow. In order to obtain the general solution, two potential functions are…

Fluid Dynamics · Physics 2023-01-11 Peng Shi

The developments over the last five decades concerning numerical discretisations of the incompressible Navier--Stokes equations have lead to reliable tools for their approximation: those include stable methods to properly address the…

Numerical Analysis · Mathematics 2025-08-12 Dominic Breit , Andreas Prohl , Jörn Wichmann

We propose a mixed finite element method for Stokes flow with one degree of freedom per element and facet of simplicial grids. The method is derived by considering the vorticity-velocity-pressure formulation and eliminating the vorticity…

Numerical Analysis · Mathematics 2022-08-30 Wietse M. Boon , Alessio Fumagalli

Using limited observations of the velocity field of the two-dimensional Navier-Stokes equations, we successfully reconstruct the steady body force that drives the flow. The number of observed data points is less than 10\% of the number of…

Fluid Dynamics · Physics 2024-02-26 Aseel Farhat , Adam Larios , Vincent R. Martinez , Jared P. Whitehead

A novel algorithm for the direct numerical simulation of the variable-density, low-Mach Navier-Stokes equations extending the method of Kim, Moin, and Moser (1987) for incompressible flow is presented here. A Fourier representation is…

Fluid Dynamics · Physics 2022-06-22 Bryan W. Reuter , Todd A. Oliver , Robert D. Moser

In this work, we present a parametric finite element approximation of two-phase Navier-Stokes flow with viscoelasticity. The free boundary problem is given by the viscoelastic Navier-Stokes equations in the two fluid phases, connected by…

Numerical Analysis · Mathematics 2026-02-11 Harald Garcke , Robert Nürnberg , Dennis Trautwein

This paper presents a computational approach for finding the optimal shapes of peristaltic pumps transporting rigid particles in Stokes flow. In particular, we consider shapes that minimize the rate of energy dissipation while pumping a…

Optimization and Control · Mathematics 2021-10-05 Marc Bonnet , Ruowen Liu , Shravan Veerapaneni , Hai Zhu

This paper is devoted to the efficient numerical solution of the Helmholtz equation in a two- or three-dimensional rectangular domain with an absorbing boundary condition (ABC). The Helmholtz problem is discretized by standard bilinear and…

Numerical Analysis · Computer Science 2019-10-24 Jari Toivanen , Monika Wolfmayr