Assessment of a non-traditional operator split algorithm for simulation of reactive transport

Authors:
Matthew J. Simpson;Kerry A. Landman;T.Prabhakar Clement
Affiliations:
Department of Mathematics and Statistics, University of Melbourne, Vic. 3010, Australia;Department of Mathematics and Statistics, University of Melbourne, Vic. 3010, Australia;Department of Civil Engineering, Auburn University, AL 36849-5337, USA
Venue:
Mathematics and Computers in Simulation
Year:
2005

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Abstract

A non-traditional operator split (OS) scheme for the solution of the advection-diffusion-reaction (ADR) equation is proposed. The scheme is implemented with the recently published central scheme [A. Kurganov, E. Tadmor, New high-resolution central schemes for non-linear conservation laws and convection-diffusion equations, J. Comput. Phys. 160 (2000) 241-282] to accurately simulate advection-reaction processes. The governing partial differential equation (PDE) is split into two PDEs, which are solved sequentially within each time step. Unlike traditional methods, the proposed scheme provides a very efficient method to solve the ADR equation for any value of the grid-Peclet number. An analytical mass balance error analysis shows that the proposed non-traditional scheme incurs a splitting error, which behaves differently to the splitting error incurred in traditional OS schemes. Numerical results are presented to illustrate the robustness of the proposed scheme.