Related papers: A phase-field approximation of the Willmore flow w…
Time fractional advection-dispersion equations arise as generalizations of classical integer order advection-dispersion equations and are increasingly used to model fluid flow problems through porous media. In this paper we develop an…
The aim of this paper is to approximate a finite-state Markov process by another process with fewer states, called herein the approximating process. The approximation problem is formulated using two different methods. The first method,…
The famous thresholding scheme by Merriman, Bence, and Osher (Motion of multiple junctions: A level set approach. Journal of Computational Physics 112.2 (1994): 334-363.) proved itself as a very efficient time discretization of mean…
We present here first-of-a-kind experimental measurements of the flow field around a swimming water droplet, using confocal PIV in three dimensions. The droplet is denser than the continuous oil phase, and swims close and parallel to the…
We consider the dynamics of vector fields on three-manifolds which are constrained to lie within a plane field, such as occurs in nonholonomic dynamics. On compact manifolds, such vector fields force dynamics beyond that of a gradient flow,…
In this paper, we discover the fundamental quantity that Nature minimizes in almost all flows encountered in everyday life: river, rain, flow in a pipe, blood flow, airflow over an airplane, etc. We show that the norm of the pressure…
The semi-analytical wall boundary conditions present a mathematically rigorous framework to prescribe the influence of solid walls in SPH for fluid flows. In this paper they are investigated with respect to the skew-adjoint property which…
In this paper we consider the entire weak solutions of the equations for stationary flows of shear thickening fluids in the plane and prove Liouville theorem under the global boundedness condition of velocity fields.
The precise set of parameters governing the transition to turbulence in wall-bounded shear flows remains an open question; many theoretical bounds have been obtained, but there is not yet a consensus between these bounds and…
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…
The hydrodynamics of viscoelastic materials (for example polymer melts and solutions) presents interesting and complex phenomena, for example instabilities and turbulent flow at very low Reynolds numbers due to normal stress effects and the…
Understanding the physics of blood is challenging due to its nature as a suspension of soft particles and the fact that typical problems involve different scales. This is valid also for numerical investigations. In fact, many computational…
Two finite volume methods are derived and applied to the solution of problems of incompressible flow. In particular, external inviscid flows and boundary-layer flows are examined. The firstmethod analyzed is a cell-centered finite volume…
We develop a method for modeling and simulating a class of two-phase flows consisting of two immiscible incompressible dielectric fluids and their interactions with imposed external electric fields in two and three dimensions. We first…
We develop the theory of fractional gradient flows: an evolution aimed at the minimization of a convex, l.s.c.~energy, with memory effects. This memory is characterized by the fact that the negative of the (sub)gradient of the energy equals…
In this paper, we consider numerical approximation of constrained gradient flows of planar closed curves, including the Willmore and the Helfrich flows. These equations have energy dissipation and the latter has conservation properties due…
We propose a two-point flux approximation finite-volume scheme for a stochastic non-linear parabolic equation with a multiplicative noise. The time discretization is implicit except for the stochastic noise term in order to be compatible…
Realistic two-phase flow problems of interest often involve high $Re$ flows with high density ratios. Accurate and robust simulation of such problems requires special treatments. In this work, we present a consistent, energy-conserving…
We study the convergence and error estimates of a finite volume method for the compressible Navier-Stokes-Fourier system with Dirichlet boundary conditions. Physical fluid domain is typically smooth and needs to be approximated by a…
A new time discretization scheme for the numerical simulation of two-phase flow governed by a thermodynamically consistent diffuse interface model is presented. The scheme is consistent in the sense that it allows for a discrete in time…