Mass transport and diffusion phenomena in the arterial lumen are studied through a mathematical model. Blood flow is described by the unsteady Navier-Stokes equation and solute dynamics by an advection-diffusion equation, the convective field being provided by the fluid velocity. A linearization procedure over the steady state solution is carried out and an asymptotic analysis is used to study ...

A finite element based level set method is proposed for structural topology optimization. Because both the level set equation and the reinitialization equation are advection dominated partial differential equations, the standard Galerkin finite element method may produce oscillating results. In this paper, both equations are solved using a streamline diffusion finite element method (SDFEM). The...

We investigate the nonlocal behavior of passive tracer dispersion with random stopping at various sites in fluids. This kind of dispersion processes is modeled by an integral partial differential equation, i.e., an advection-diffusion equation with a memory term. We have shown the exponential decay of the passive tracer concentration, under suitable conditions for the velocity field and the pro...

Abstract Using a set of modified cubic trigonometric B-splines as test functions, a new differential quadrature technique is proposed for the 1D and 2D transient advection-diffusion equations of order α ∈ (0, 1]. The weighted coefficients are determined via solving the system of algebraic equations with a strictly diagonally dominant tri-diagonal matrix. Then, the original equation is converted...

A numerical model for electro-osmotic flow is described. The advecting velocity field is computed by solving the incompressible Navier–Stokes equation. The method uses a semi-implicit multigrid algorithm to compute the divergence-free velocity at each grid point. The finite differences are second-order accurate and centered in space; however, the traditional second-order compact finite differen...

In this paper, we consider the variable-order Galilei advection diffusion equation with a nonlinear source term. A numerical scheme with first order temporal accuracy and second order spatial accuracy is developed to simulate the equation. The stability and convergence of the numerical scheme are analyzed. Besides, another numerical scheme for improving temporal accuracy is also developed. Fina...

We present a numerical algorithm for the incorporation of the active cosmic ray transport, into the ZEUS-3D magnetohydrodynamical code. The cosmic ray transport is described by the diffusion-advection equation. The applied form of the diffusion tensor allows for anisotropic diffusion of cosmic rays along and across the magnetic field direction, which is controlled by two parameters: the paralle...

This work deals with mixing and dissipation ehancement for the solution of advection-diffusion equation driven by a Ornstein-Uhlenbeck velocity field. We are able to prove quantitative result, uniform in diffusion parameter, enhancement over finite time horizon.

In this paper, we solve the two-dimensional advection-diffusion equation with random transport velocity. The generalized polynomial chaos expansion is employed to discretize the equation in random space while the spectral/hp element method is used for spatial discretization. Numerical results which demonstrate the convergence of generalized polynomial chaos are presented. Specifically, it appea...