The rightward representation of the Barakat-Clark ADE scheme is extended for the solution of the Multi-dimensional Transport equation. The first-order derivative of the Transport equation is represented by a one-sided multi-level finite-difference. The resulting scheme is an explicit marching type iterative solution. The visibility of using this method for the solution of the Multi-dimensional Transport equations is demonstrated through the solution of each of the Burgers’ equation and the Graetz-Nusselt problem for the thermally developing flow between two-parallel plates at constant temperature (at high and low Peclet numbers) with parabolic velocity distribution. The results are compared with the solutions using other schemes. All of the obtained results are compared with the exact solutions of the analyzed problems. The results show that the proposed scheme is unconditionally stable, better accuracy, faster convergence, and lower storage capacity requirement.

扩展了Barakat-Clark ADE方案的向右表示，以解决多维运输方程。运输方程的一阶导数由一个单边多级有限差分表示。所得方案是显式行进式迭代解决方案。通过每个Burgers方程和Graetz-Nusselt问题的解决方案，证明了该方法在多维输运方程组的求解中在恒定温度下（高温下）在两个平行板之间的热发展流动的可视性。和低Peclet数），并具有抛物线速度分布。将结果与使用其他方案的解决方案进行比较。将所有获得的结果与所分析问题的精确解决方案进行比较。