Advection step in the split-operator approach applied to river modeling

• The governing flow/transport equations are divided with the split-operator approach.
• The performances of the finite difference and the characteristic methods in advection were assessed.
• Numerical tests were conducted on the pure linear and nonlinear advection step equations.
• Numerical test were conducted both on linear and nonlinear advection as a part of the split-operator approach applied to river modeling.
• A modified algorithm based on the characteristics method is proposed, that can endure large computational time steps.

The split-operator approach proposes to divide the numerical solution of the governing flow and constituent transport equations into a series of successive steps, one of them being the numerically most challenging advection step. This paper presents tests of characteristics and finite difference methods used in the numerical solution of one-dimensional linear and nonlinear advection equations that describe the transport and flow advection steps, thus demonstrating their accuracy, oscillations and damping features. The studied methods were incorporated into the split-operator approach and evaluated as a part of the complete solution, which led to the development of numerical models implementing an algorithm that can endure larger time steps without losing much accuracy. This algorithm was tested on both one- and two-dimensional examples, for complex computational domains that predominate in natural watercourses.