Development of particle tracking algorithms for various types of finite elements in multi-dimensions

Abstract

Suk and Yeh (2009) previously reported the development of an accurate and efficient particle tracking algorithm for simulating the pathline under complicated steady and unsteady flow conditions. However, a mathematical derivation of only quadrilateral and hexahedral elements was reported. This study extends the applicability of the particle tracking technique previously proposed by Suk and Yeh (2009) to various types of elements within finite elements in multi-dimensions. Accordingly, an extension of the particle tracking method by Suk and Yeh (2009) (herein referred to as extended method) was designed to incorporate quadrilateral and triangular elements in two dimensions, including triangular prism, tetrahedral, and hexahedral elements in three dimensions. In addition, the performance of the extended method was evaluated by a comparison with the results of Pollock's method. Various examples and applications were used to illustrate the applicability and practicality of the extended method in the field of groundwater flow and transport.