A fully Sinc-Galerkin method for solving advection-di usion equations subject to arbitrary radiation boundary conditions is presented. This procedure gives rise to a discretization which has it's most natural representation in the form of a Sylvester system where the coe cient matrix for the temporal discretization is full. The word \full" often implies a computationally more complex method com...

We present a simple filtering procedure for stabilizing the spectral element method (SEM) for the unsteady advection-diffusion and Navier-Stokes equations. A number of example applications are presented, along with basic analysis for the advection-diffusion case. Stabilisation par filtrage pour la méthode des éléments spectraux Résumé. Nous présentons une procédure simple de filtrage pour la st...

We present a semi-Lagrangian method for advection–diffusion and incompressible Navier–Stokes equations. The focus is on constructing stable schemes of secondorder temporal accuracy, as this is a crucial element for the successful application of semi-Lagrangian methods to turbulence simulations. We implement the method in the context of unstructured spectral/hp element discretization, which allo...

We present a Lagrangian—Eulerian method with adaptively local ZOOMing and Peak/valley Capturing approach (LEZOOMPC), consisting of advection—diffusion decoupling, backward particle tracking, forward particle tracking, adaptively local zooming, peak/valley capturing, and slave point utilization, to solve three-dimensional advection—diffusion transport equations. This approach and the associated ...

This study develops and analyzes preconditioned Krylov subspace methods to solve linear systems arising from discretization of the time-independent space-fractional models. First, we apply shifted Grunwald formulas to obtain a stable finite difference approximation to fractional advection-diffusion equations. Then, we employee two preconditioned iterative methods, namely, the preconditioned gen...

Fractional-order diffusion equations are viewed as generalizations of classical diffusion equations, treating super-diffusive flow processes. In this paper, in order to solve the fractional advection-diffusion equation, the fractional characteristic finite difference method is presented, which is based on the method of characteristics (MOC) and fractional finite difference (FD) procedures. The ...

a two-dimensional two-phase numerical model is developed to predict transport and fate of oil slicks which resulted the concentration distribution of oil on the water surface. two dimensional governing equation of fluid flow which consists mass and momentum conservation was solved using the finite difference method on the structured staggered grid system. the resulted algebric equations were so...

We develop an optimization-based approach for additive decomposition and reconnection of algebraic problems arising from discretization of partial differential equations (PDEs). Application to a scalar advection-diffusion PDE illustrates the new approach. In particular, we obtain a robust iterative solver for advection-dominated problems using standard multi-level solvers for the Poisson equation.