Particle transport method for linear problem of convective transport

Abstract

The paper is devoted to a novel explicit technique, the Particle Transport Method (PTM), used to solve 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 can be equally applied with success on structured and unstructured meshes. It is also demonstrated that the method has the linear computational complexity.
The performance of the presented algorithm is tested using three classical problems. The first two problems are the wave-packet and step-function transport, the third problem is the rigid-body rotation of a slotted cylinder.