A multi-step computation scheme: Decoupling kinetic processes from physical transport in water quality models

This paper presents a computation scheme that considers accuracy and efficiency in the numerical treatment of the kinetic processes in water quality models. The proposed scheme involves decoupling of physical transport and kinetic processes in the governing mass-balance equations. The decoupled equations are solved by employing multi-step computation, in which the kinetic processes are applied for the first half time step, followed by the physical transport for a full time step, and the kinetic processes are applied again for the remaining second half time step. The kinetic equations are solved numerically or analytically, which may require prior linearization of the equations. The numerical solution scheme of the kinetic equations alternates between explicit and implicit schemes, and is equivalent to the second-order accurate Crank-Nicolson solution. A hypothetical model, which is simple enough to have an analytical solution, is used to explain the concept, and to demonstrate the accuracy and computational efficiency of the proposed scheme. The proposed scheme and three other traditional solution schemes are compared to the analytical solution. The proposed scheme shows better accuracy and computational efficiency compared to other schemes.