FEM and/or BEM for numerical simulation of Marangoni flow
AbstractThe aim of this work is the numerical study of Marangoni effect using three different methods. They are a finite…
PDEs (numerical)
The numerical approximation to positive solution for some reaction-diffusion problems
Abstract A one-dimensional reaction-diffusion problem, with the reaction term of the form \(u^{p}\), \(p>1\) is considered. For \(p=3\), we deduce…
Surface mobility of surfactant solutions XVI. Involvement of the fluid viscosities in the Marangoni flow – some aspects
AbstractThe influence of viscosity upon the Marangoni flow (induced by surface tension differences) in competition with the gravity flow, through…
Numerical methods in establishment of concentration profile for the flows with chemical reactions over rotating disk
AbstractA viscous flow due to a rotating disk involving homogeneous as well as heterogeneous chemical reactions is considered. We simplify…
On the bifurcation and variational approximation of the positive solution of a nonlinear reaction-diffusion problem
Abstract We consider a nonlinear, second-order, two-point boundary value problem that models some reaction-diffusion processes. When the reaction term has…
On the use of Green’s formula for the solution of the Navier-Stokes equations
AbstractA general iterative procedure for solving Navier-Stokes system in stream function-vorticity variables is considered. Using the fundamental solution for Laplace…
On the existence and uniqueness of positive solutions of some mildly nonlinear elliptic boundary value problems
AbstractFor a homogeneous Dirichlet problem attached to a semilinear elliptic equation we study the existence and uniqueness of non-negative solutions.…
On the Chebyshev-tau approximation for some singularly perturbed two point boundary value problems – Numerical experiments
AbstractIn this paper we are concerned with numerical stability of Chebyshev-tau method in solving some singularly perturbed two-point boundary value…
A unified treatment of boundary layer and lubrication approximations in viscous fluid mechanics
AbstractIt is a matter of every day experience to find the boundary layer and lubrication approximations exposed as if they…
Spectral methods in linear stability. Applications to thermal convection with variable gravity field
AbstractThe onset of convection in a horizontal layer of fluid heated from below in the presence of a gravity field…