A fast high‐resolution algorithm for linear convection problems: particle transport method

Abstract

Abstract The paper is devoted to a novel explicit technique, the particle transport method (PTM), for solving linear convection problems. While being a Lagrangian (characteristic based) method, PTM has the advantage of Eulerian methods to represent the solution on a fixed mesh. The proposed approach belongs to the class of monotone high‐resolution numerical schemes, possesses the property of unconditional stability and works with structured and unstructured meshes. It is also demonstrated that the method has a linear computational complexity. The performance of the presented algorithm is tested on one‐ and two‐dimensional benchmark problems. The numerical results confirm that the method has the 2nd‐order spatial accuracy and can be significantly faster than the grid‐based methods of the same order. Copyright © 2006 John Wiley & Sons, Ltd.