Related papers: Shape optimization for surface functionals in Navi…
We present a versatile high-level programming-language implementation of nonlinear topology optimization. Our implementation is based on the commercial software package Femlab, and it allows a wide range of optimization objectives to be…
The incompressible Navier-Stokes equations are re-formulated to involve an arbitrary time dilation; and in this manner, the modified Navier-Stokes equations are obtained which have some penalization terms in the right hand side. Then, the…
A phase-field model for three-phase flows is established by combining the Navier-Stokes (NS) and the energy equations, with the Allen-Cahn (AC) and Cahn-Hilliard (CH) equations and is demonstrated analytically to satisfy the energy…
A new approach to model order reduction of the Navier-Stokes equations at high Reynolds number is proposed. Unlike traditional approaches, this method does not rely on empirical turbulence modeling or modification of the Navier-Stokes…
This work proposes a new stabilized $P_1\times P_0$ finite element method for solving the incompressible Navier--Stokes equations. The numerical scheme is based on a reduced Bernardi--Raugel element with statically condensed face bubbles…
In this paper we consider a fully discrete numerical method for the unsteady Navier-Stokes equations on a smooth closed stationary surface in $\mathbb{R}^3$. We use the surface finite element method (SFEM) with a generalized Taylor-Hood…
The phase-field method is reviewed from the general perspective of converting a free boundary problem into a set of coupled partial differential equations. Its main advantage is that it avoids front tracking by using phase fields to locate…
We propose a particle-based method to simulate thin-film fluid that jointly facilitates aggressive surface deformation and vigorous tangential flows. We build our dynamics model from the surface tension driven Navier-Stokes equation with…
We propose a thermodynamically consistent phase-field model for the flow of a mixture of two different viscous incompressible fluids of equal density in a bounded domain. We prove the well-posedness of local-in-time strong solutions by…
Incorporating molecular-scale effects in the description of contact line motion is essential for accurately capturing all sources of energy dissipation in wetting dynamics. This holds particularly true in the cases where contact line…
Anisotropic fluids, such as nematic liquid crystals, can form non-spherical equilibrium shapes known as tactoids. Predicting the shape of these structures as a function of material parameters is challenging and paradigmatic of a broader…
A new model for the numerical simulation of a rigid body moving in a viscous fluid flow using FEM is presented. One of the most interesting features of this approach is the small computational effort required to solve the motion of the…
Coarse-grained continuous descriptions for lipid bilayers are typically based on minimizing the Helfrich energy. Such models consider the fluid properties of these structures only implicitly and have been shown to nicely reproduce…
We present a novel numerical method to solve the incompressible Navier-Stokes equations for two-phase flows with phase change, using a one-fluid approach. Separate phases are tracked using a geometric Volume-Of-Fluid (VOF) method with…
A robust control scheme is derived and tested for the Navier-Stokes equations for two-dimensional multiphase flow of a thin film underneath an inclined solid surface. Control is exerted via the use of an electrode parallel to the substrate,…
In the theory of the Navier-Stokes equations, the viscous fluid in incompressible flow is modelled as a homogeneous and dense assemblage of constituent "fluid particles" with viscous stress proportional to rate of strain. The crucial…
A diffuse interface model for surfactants in multi-phase flow with three or more fluids is derived. A system of Cahn-Hilliard equations is coupled with a Navier-Stokes system and an advection-diffusion equation for the surfactant ensuring…
This paper presents a streamfunction-vorticity formulation for the Navier--Stokes and Euler equations on general surfaces. Notably, this includes non-simply connected surfaces, on which the harmonic components of the velocity field play a…
We present a general numerical approach to shape optimization with state constraints for 2-dimensional geometries, without relaxing the constraints. To do this we reformulate the problem on a fixed reference domain using a conformal…
This paper proposes a novel particle scheme that provides convergent approximations of a weak solution of the Navier-Stokes equations for the 1-D flow of a viscous compressible fluid. Moreover, it is shown that all differential inequalities…