Related papers: A study on Marangoni convection by the variational…
The vertical heat transfer in B\'enard-Marangoni convection of a fluid layer with infinite Prandtl number is studied by means of upper bounds on the Nusselt number $Nu$ as a function of the Marangoni number $Ma$. Using the background method…
A high-order finite element method is proposed to solve the nonlinear convection-diffusion equation on a time-varying domain whose boundary is implicitly driven by the solution of the equation. The method is semi-implicit in the sense that…
High-order spatial discretisations and full discretisations of parabolic partial differential equations on evolving surfaces are studied. We prove convergence of the high-order evolving surface finite element method, by showing high-order…
In this paper a Monte-Carlo method for simulating the motion of fluid flow moving along a solid wall is proposed. The random vortex method in the present paper is established by using the reflection technology and perturbation technique.…
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…
We perform three-dimensional direct numerical simulations of surface-driven convection near the temperature of maximum density $\tilde T_{md}$. A dynamic surface boundary condition couples heat flux through the surface to the induced…
A method for the numerical solution of variable order (VO) fractional differential equations (FDE) is presented. The method applies to linear as well as to nonlinear VO-FDEs. The Caputo type VO fractional derivative is employed. First, an…
The paper describes an explicit multi-dimensional numerical scheme for Special Relativistic Two-Fluid Magnetohydrodynamics of electron-positron plasma and a suit of test problems. The scheme utilizes Cartesian grid and the third order WENO…
Theoretical models of evaporating droplets predict Marangoni flows orders of magnitude faster than those observed experimentally. While this discrepancy is often attributed to surface contamination, the underlying mechanism by which…
We present a novel Material Point Method (MPM) discretization of surface tension forces that arise from spatially varying surface energies. These variations typically arise from surface energy dependence on temperature and/or concentration.…
In this paper, we establish several local and global gradient estimates for the positive solution of Porous Medium Equations (PMEs) and Fast Diffusion Equations (FDEs). Our proof is probabilistic and uses martingale techniques.
This paper describes a method to do ab initio molecular dynamics in electronically excited systems within the random phase approximation (RPA). Using a dynamical variational treatment of the RPA frequency, which corresponds to the…
Recently, it has been great interest in the development of methods for solving nonlinear differential equations directly. Here, it is shown an algorithm based on Pad\'e approximants for solving nonlinear partial differential equations…
In this paper we study the well-posedness and long-time dynamics of a diffuse-interface model for the mixture of two viscous incompressible Newtonian fluids with thermo-induced Marangoni effects. The governing system consists of modified…
We present careful numerical convergence studies, using parameterized curves to reach very high resolutions in two dimensions, of a level set method for multiphase curvature motion known as the Voronoi implicit interface method. Our tests…
A numerical technique is described that can efficiently compute solutions in interface problems. These are problems with data, such as the coefficients of differential equations, discontinuous or even singular across one or more interfaces.…
The onset of convection in the form of magneto-inertial waves in a rotating fluid sphere permeated by a constant axial electric current is studied through a perturbation analysis. Explicit expressions for the dependence of the Rayleigh…
A new method for numerical solving of boundary problem for ordinary differential equations with slowly varying coefficients which is aimed at better representation of solutions in the regions of their rapid oscillations or exponential…
We investigate a family of approximate multi-step proximal point methods, accelerated by implicit linear discretizations of gradient flow. The resulting methods are multi-step proximal point methods, with similar computational cost in each…
We study a stochastically perturbed mean curvature flow for graphs in $\mathbb{R}^3$ over the two-dimensional unit-cube subject to periodic boundary conditions. In particular, we establish the existence of a weak martingale solution. The…