In this paper we consider a passive scalar transported in two-dimensional flow. The governing equation is that of the convection–diffusion–reaction equation. For purposes of computational efficiency, we apply an alternating-direction implicit scheme akin to that proposed by Polezhaev. Use of this implicit operator-splitting scheme allows the application of a tridiagonal Thomas solver to obtain ...

Based on the combined compact difference scheme, an alternating direction implicit method is proposed for solving two-dimensional cubic nonlinear Schrödinger equations. The proposed method is sixth-order accurate in space and second-order accurate in time. The linear Fourier analysis method is exploited to study the stability of the proposed method. The efficiency and accuracy of the proposed m...

In this paper, two different finite differences schemes are presented for numerical solution of two-dimensional moving boundary problem. The methods are illustrated by solving sample problem in two-dimensional solidification of the square prism. The finite difference schemes developed for this purpose are based on the method of lines using interpolation polynomials. The fully explicit method de...

We address the problem of computing a low-rank estimate Y of the solution X of the Lyapunov equation AX + XA′ + Q = 0 without computing the matrix X itself. This problem has applications in both the reduced-order modeling and the control of large dimensional systems as well as in a hybrid algorithm for the rapid numerical solution of the Lyapunov equation via the alternating direction implicit ...

A numerical method is presented to solve a two-dimensional hyperbolic diffusion problem where is assumed that both convection and diffusion are responsible for flow motion. Since direct solutions based on implicit schemes for multidimensional problems are computa-tionally inefficient, we apply an alternating direction method which is second order accurate in time and space. The stability of the...

sedimentation is one of the most important problems in harbors that results in considerable economic costs. harbor planforms affects the flow pattern in the harbor basin and consequently, plays an important role in sediment transport and sedimentation. in the present study, a two dimensional depth-averaged hydrodynamic and sediment transport model has been developed to investigate the effect of...

In this paper, an alternating implicit block method for solving two dimensional scalar wave equation is presented. The new method consist of two stages for each time step implemented in alternating directions which are very simple in computation. To increase the speed of computation, a group of adjacent points is computed simultaneously. It is shown that the presented method increase the maximu...

Standard explicit schemes for parabolic equations are not very convenient for computing practice due to the fact that they have strong restrictions on a time step. More promising explicit schemes are associated with explicit-implicit splitting of the problem operator (Saul’yev asymmetric schemes, explicit alternating direction (ADE) schemes, group explicit method). These schemes belong to the c...

In this paper, a set of new alternating segment explicit-implicit (NASEI) schemes is derived based on an one-dimensional diffusion problem. The schemes are capable of parallel computation; third-order accurate in space; and stable under a reasonable mesh condition. The numerical examples show that the NASEI schemes are more accurate than either the old ASEI or the ASCN schemes.