In this paper, we investigate electroconvective ion transport at cation exchange membranes with different geometry square-wave structures (line undulations) experimentally and numerically. Electroconvective microvortices are induced by strong concentration polarization once a threshold potential difference is applied. The applied potential required to start and sustain electroconvection is stro...

We consider convective systems in a bounded domain, in which viscous fluids described by the Stokes system are coupled using the Boussinesq approximation to a reaction-advection-diffusion equation for the temperature. We show that the resulting flows possess relaxation-enhancing properties in the sense of [12]. In particular, we show that solutions of the nonlinear problems become small when th...

We propose and analyze a symmetric weighted interior penalty (SWIP) method to approximate in a Discontinuous Galerkin framework advection-diffusion equations with anisotropic and discontinuous diffusivity. The originality of the method consists in the use of diffusivity-dependent weighted averages to better cope with locally small diffusivity (or equivalently with locally high Péclet numbers) o...

In this paper, self-similarity is illustrated and compared in deterministic and stochastic dissipative systems. Examples are (1) deterministic self-similarity in reaction-diffusion system and Navier-Stokes equations, where solutions eventually decay to zero due to balance of diffusion (viscosity) and nonlinearity; (2) statistical self-similarity in randomly advected passive scalar model of Krai...

In this study, we develop the enhanced unconditionally positive finite difference method (EUPFD), and use it to solve linear nonlinear advection–diffusion–reaction (ADR) equations. This incorporates proper orthogonal decomposition technique (UPFD) reduce degree of freedom ADR We investigate efficiency effectiveness proposed by checking error, convergence rate, computational time that takes conv...

Spectral deferred correction is a flexible technique for constructing high-order, stiffly-stable time integrators using a low order method as a base scheme. Here we examine their use in conjunction with splitting methods to solve initial-boundary value problems for partial differential equations. We exploit their close connection with implicit Runge–Kutta methods to prove that up to the full ac...

The incompressible limit of nonlinear diffusion equations porous medium type has attracted a lot attention in recent years, due to its ability link the weak formulation cell-population models free boundary problems Hele-Shaw type. Although vast literature is available on this singular limit, little known convergence rate solutions. In work, we compute negative Sobolev norm and, upon interpolati...