Related papers: A simple finite difference method for time-depende…

In this paper, we present a new multiscale model reduction technique for the Stokes flows in heterogeneous perforated domains. The challenge in the numerical simulations of this problem lies in the fact that the solution contains many…

We develop and implement a Bayesian approach for the estimation of the shape of a two dimensional annular domain enclosing a Stokes flow from sparse and noisy observations of the enclosed fluid. Our setup includes the case of direct…

We develop a Nitsche fictitious domain method for the Stokes problem starting from a stabilized Galerkin finite element method with low order elements for both the velocity and the pressure. By introducing additional penalty terms for the…

A new framework is proposed for analyzing staggered-grid finite difference finite volume methods on unstructured meshes. The new framework employs the concept of external approximation of function spaces, and gauge convergence of numerical…

We propose a Hybrid High-Order (HHO) formulation of the incompressible Navier--Stokes equations, that is well suited to be employed for the simulation of turbulent flows. The spatial discretization relies on hybrid velocity and pressure…

We consider the numerical approximation of a sharp-interface model for two-phase flow, which is given by the incompressible Navier-Stokes equations in the bulk domain together with the classical interface conditions on the interface. We…

We investigate the dynamics of several slender rigid bodies moving in a flow driven by the three-dimensional steady Stokes system in presence of a smooth background flow. More precisely we consider the limit where the thickness of these…

A finite difference scheme is used to develop a numerical method to solve the flow of an unbounded viscoelastic fluid with zero to moderate inertia around a prolate spheroidal particle. The equations are written in prolate spheroidal…

In transient simulations of particulate Stokes flow, to accurately capture the interaction between the constituent particles and the confining wall, the discretization of the wall often needs to be locally refined in the region approached…

We propose and analyse an augmented mixed finite element method for the Navier--Stokes equations written in terms of velocity, vorticity, and pressure with non-constant viscosity and no-slip boundary conditions. The weak formulation…

We present a finite element method for the Stokes equations involving two immiscible incompressible fluids with different viscosities and with surface tension. The interface separating the two fluids does not need to align with the mesh. We…

We show that in bounded domains with no-slip boundary conditions, the Navier-Stokes pressure can be determined in a such way that it is strictly dominated by viscosity. As a consequence, in a general domain we can treat the Navier-Stokes…

In this paper, a novel immersed boundary method is developed, validated, and applied. Through devising a second-order three-step flow reconstruction scheme, the proposed method is able to enforce the Dirichlet, Neumann, Robin, and Cauchy…

The Immersed Boundary method is a simple, efficient, and robust numerical scheme for solving PDE in general domains, yet for fluid problems it only achieves first-order spatial accuracy near embedded boundaries for the velocity field and…

We consider numerical algorithms for the simulation of the rheology of two-dimensional vesicles suspended in a viscous Stokesian fluid. The vesicle evolution dynamics is governed by hydrodynamic and elastic forces. The elastic forces are…

Both Newtonian and non-Newtonian fluids may exhibit complex slip behaviour at the boundary. We examine a broad class of slip boundary conditions that generalises the commonly used Navier slip, perfect slip, stick-slip and Tresca friction…

This work develops scientific computing techniques to further the exploration of using boundary control alone to optimize mixing in Stokes flows. The theoretical foundation including mathematical model and the optimality conditions for…

This work presents the design of nonlinear stabilization techniques for the finite element discretization of Euler equations in both steady and transient form. Implicit time integration is used in the case of the transient form. A…

In this paper, we construct and analyze divergence-free finite element methods for the Stokes problem on smooth domains. The discrete spaces are based on the Scott-Vogelius finite element pair of arbitrary polynomial degree greater than…

We evaluate an efficient overset grid method for two-dimensional and three-dimensional particulate flows for small numbers of particles at finite Reynolds number. The rigid particles are discretised using moving overset grids overlaid on a…