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In this paper, we combine the multiscale flnite element method to propose an algorithm for solving the non-stationary Stokes-Darcy model, where the permeability coefflcient in the Darcy region exhibits multiscale characteristics. Our…

Numerical Analysis · Mathematics 2024-03-19 Yachen Hong , Wenhan Zhang , Lina Zhao , Haibiao Zheng

We consider a stabilization method for divergence-conforming B-spline discretizations of the incompressible Navier--Stokes problem wherein jumps in high-order normal derivatives of the velocity field are penalized across interior mesh…

Numerical Analysis · Mathematics 2022-01-28 Guoxiang Grayson Tong , David Kamensky , John A. Evans

We show that the standard boundary integral operators, defined on the unit sphere, for the Stokes equations diagonalize on a specific set of vector spherical harmonics and provide formulas for their spectra. We also derive analytical…

Numerical Analysis · Mathematics 2018-04-04 Eduardo Corona , Shravan Veerapaneni

A conservative primitive variable discrete exterior calculus (DEC) discretization of the Navier-Stokes equations is performed. An existing DEC method (Mohamed, M. S., Hirani, A. N., Samtaney, R. (2016). Discrete exterior calculus…

Fluid Dynamics · Physics 2021-02-24 Pankaj Jagad , Abdullah Abukhwejah , Mamdouh Mohamed , Ravi Samtaney

The focus of the present paper is on developing a Virtual Element Method for Darcy and Brinkman equations. In [15] we presented a family of Virtual Elements for Stokes equations and we defined a new Virtual Element space of velocities such…

Numerical Analysis · Mathematics 2017-02-06 Giuseppe Vacca

In this paper, we propose a new approach for the time-discretization of the incompressible stochastic Stokes equations with multiplicative noise. Our new strategy is based on the classical Milstein method from stochastic differential…

Numerical Analysis · Mathematics 2022-12-08 Liet Vo

The simulation of fluid flow problems, specifically incompressible flows governed by the Navier-Stokes equations (NSE), holds fundamental significance in a range of scientific and engineering applications. Traditional numerical methods…

Computational Physics · Physics 2024-09-10 Abdullah Abukhwejah , Pankaj Jagad , Ravi Samtaney , Peter Schmid

We propose an efficient threshold dynamics method for topology optimization for fluids modeled with the Stokes equation. The proposed algorithm is based on minimization of an objective energy function that consists of the dissipation power…

Optimization and Control · Mathematics 2018-12-27 Huangxin Chen , Haitao Leng , Dong Wang , Xiao-Ping Wang

In this paper, we present a geometric multigrid methodology for the solution of matrix systems associated with isogeometric compatible discretizations of the generalized Stokes and Oseen problems. The methodology provably yields a pointwise…

Numerical Analysis · Mathematics 2017-05-26 Christopher Coley , Joseph Benzaken , John A. Evans

A highly accurate method for simulating surfactant-covered droplets in two-dimensional Stokes flow with solid boundaries is presented. The method handles both periodic channel flows of arbitrary shape and stationary solid constrictions. A…

Numerical Analysis · Mathematics 2020-12-02 Sara Pålsson , Anna-Karin Tornberg

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

This paper constructs and analyzes a boundary correction finite element method for the Stokes problem based on the Scott-Vogelius pair on Clough-Tocher splits. The velocity space consists of continuous piecewise quadratic polynomials, and…

Numerical Analysis · Mathematics 2021-05-24 Haoran Liu , Michael Neilan , Baris Otus

We consider a coupled model of free-flow and porous medium flow, governed by stationary Stokes and Darcy flow, respectively. The coupling between the two systems is enforced by introducing a single variable representing the normal flux…

Numerical Analysis · Mathematics 2022-09-28 Wietse M. Boon

This paper contains two major contributions. First we derive, following the discrete de Rham (DDR) and Virtual Element (VEM) paradigms, pressure-robust methods for the Stokes equations that support arbitrary orders and polyhedral meshes.…

Numerical Analysis · Mathematics 2024-06-28 Lourenço Beirão da Veiga , Franco Dassi , Daniele A. Di Pietro , Jérôme Droniou

This paper presents a numerical method based on the variational quantum algorithm to solve potential and Stokes flow problems. In this method, the governing equations for potential and Stokes flows can be respectively written in the form of…

Fluid Dynamics · Physics 2023-03-06 Yangyang Liu , Zhen Chen , Chang Shu , Patrick Rebentrost , Yaguang Liu , S. C. Chew , B. C. Khoo , Y. D. Cui

We present a fast, high-order accurate and adaptive boundary integral scheme for solving the Stokes equations in complex---possibly nonsmooth---geometries in two dimensions. The key ingredient is a set of panel quadrature rules capable of…

Numerical Analysis · Mathematics 2020-04-22 Bowei Wu , Hai Zhu , Alex Barnett , Shravan Veerapaneni

We construct and analyze a strongly consistent second-order finite difference scheme for the steady two-dimensional Stokes flow. The pressure Poisson equation is explicitly incorporated into the scheme. Our approach suggested by the first…

Numerical Analysis · Mathematics 2018-09-05 Yury A. Blinkov , Vladimir P. Gerdt , Dmitry A. Lyakhov , Dominik L. Michels

Free-stream preservation is an essential property for numerical solvers on curvilinear grids. Key to this property is that the metric terms of the curvilinear mapping satisfy discrete metric identities, i.e., have zero divergence.…

Numerical Analysis · Mathematics 2026-05-27 Daniel Bach , Andrés Rueda-Ramírez , David A. Kopriva , Gregor J. Gassner

In this paper, we propose a discretization for the (nonlinearized) compressible Stokes problem with a linear equation of state $\rho=p$, based on Crouzeix-Raviart elements. The approximation of the momentum balance is obtained by usual…

Numerical Analysis · Mathematics 2008-09-18 Thierry Gallouët , Raphaele Herbin , Jean-Claude Latché

In this paper we present an arbitrary-order fully discrete Stokes complex on general polyhedral meshes. We enriche the fully discrete de Rham complex with the addition of a full gradient operator defined on vector fields and fitting into…

Numerical Analysis · Mathematics 2024-01-18 Marien-Lorenzo Hanot