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The single droplet under shear is a foundational problem in fluid mechanics. In computational fluid dynamics, the two-dimensional (2D) formulation offers advantages in both computational efficiency and relevance, yet its theoretical…
Lubrication theory makes use of the assumptions of a long and thin fluid domain and a small scaled Reynolds number to formulate a linearized approximation to the Navier-Stokes equations. Extended lubrication theory aims to improve the model…
Smoothing properties of two-color distributive relaxation for solving a two-dimensional (2D) Stokes flow by multigrid method are theoretically investigated by using the local Fourier analysis (LFA) method. The governing equation of the 2D…
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…
Resolvent analysis is a powerful tool for modeling and analyzing turbulent flows and in particular provides an approximation of coherent flow structures. Despite recent algorithmic advances, computing resolvent modes for flows with more…
Inspired by the numerical immersed boundary method, we introduce regularized Stokes immersed boundary problems in two dimensions to describe regularized motion of a 1-D closed elastic string in a 2-D Stokes flow, in which a regularized…
We study the two-phase Stokes flow driven by surface tension with two fluids of equal viscosity, separated by an asymptotically flat interface with graph geometry. The flow is assumed to be two-dimensional with the fluids filling the entire…
In this paper we study the stochastic Navier-Stokes equation with artificial compressibility. The main results of this work are the existence and uniqueness theorem for strong solutions and the limit to incompressible flow. These results…
We derive the linear acoustic and Stokes-Fourier equations as the limiting dynamics of a system of N hard spheres of diameter $\epsilon$ in two space dimensions, when N $\rightarrow$ $\infty$, $\epsilon$ $\rightarrow$ 0, N $\epsilon$ =…
The Green's functions of Stokes flow are widely used analytical and computational tools for microscale flows. We adapt a procedure from H.A. Lorentz for the method of images in Stokes flow to the regularized setting. Our solutions differ…
Suspensions with fiber-like particles in the low Reynolds number regime are modeled by two different approaches that both use a Lagrangian representation of individual particles. The first method is the well-established formulation based on…
Many problems in fluid dynamics are effectively modeled as Stokes flows - slow, viscous flows where the Reynolds number is small. Boundary integral equations are often used to solve these problems, where the fundamental solutions for the…
We study the weak steady Stokes problem, associated with a flow of a Newtonian incompressible fluid through a spatially periodic profile cascade, in the Lr-framework. The used mathematical model is based on the reduction to one spatial…
We study Dirichlet boundary control of Stokes flows in 2D polygonal domains. We consider cost functionals with two different boundary control regularization terms: the $L^2$ norm and an energy space seminorm. We prove well-posedness and…
In this paper, we study a multi-scale deep neural network (MscaleDNN) as a meshless numerical method for computing oscillatory Stokes flows in complex domains. The MscaleDNN employs a multi-scale structure in the design of its DNN using…
We consider the bidimensional Stokes problem for incompressible fluids in stream function-vorticity. For this problem, the classical finite elements method of degree one converges only to order one-half for the L2 norm of the vorticity. We…
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…
The presented research paper illustrates the development of a new methodology to solve 2-dimensional (2D) Navier-Stoke equations, which Pukhnachev proposed through introducing unknown functions in the stream and pressure functions of fluid…
Neural networks have been used to solve different types of large data related problems in many different fields.This project takes a novel approach to solving the Navier-Stokes Equations for turbulence by training a neural network using…
This study investigates the asymptotic behavior of the steady-state quasi-Newtonian Stokesflow with viscosity given by the Carreau law within a thin domain, focusing on the effects of a slightly rough boundary of the domain. Employing…