A modified Holly‐Preissmann scheme for simulating sharp concentration fronts in streams with steep velocity gradients using RIV1Q

Abstract

AbstractRIV1Q is the stand‐alone water quality program of CE‐QUAL‐RIV1, a hydraulic and water quality model developed by U.S. Army Corps of Engineers Waterways Experiment Station. It utilizes an operator‐splitting algorithm and the advection term in governing equation is treated using the explicit two‐point, fourth‐order accurate, Holly‐Preissmann scheme, in order to preserve numerical accuracy for advection of sharp gradients in concentration. In the scheme, the spatial derivative of the transport equation, where the derivative of velocity is included, is introduced to update the first derivative of dependent variable. In the stream with larger cross‐sectional variation, steep velocity gradient can be easily found and should be estimated correctly. In the original version of RIV1Q, however, the derivative of velocity is approximated by a finite difference which is first‐order accurate. Its leading truncation error leads to the numerical error of concentration which is related with the velocity and concentration gradients and increases with the decreasing Courant number. The simulation may also be unstable when a sharp velocity drop occurs. In the present paper, the derivative of velocity is estimated with a modified second‐order accurate scheme and the corresponding numerical error of concentration decreases. Additionally, the stability of the simulation is improved. The modified scheme is verified with a hypothetical channel case and the results demonstrate that satisfactory accuracy and stability can be achieved even when the Courant number is very low. Finally, the applicability of the modified scheme is discussed.