The source-sink term in water temperature models represents the net heat absorbed or released by a water system. This term is very important because it accounts for solar radiation that can significantly affect water temperature, especially in lakes. However, existing numerical methods for discretizing the source-sink term are very simplistic, causing significant deviations between simulation results and measured data. To address this problem, we present a numerical method specific to the source-sink term. A vertical one-dimensional heat conduction equation was chosen to describe water temperature changes. A two-step operator-splitting method was adopted as the numerical solution. In the first step, using the undetermined coefficient method, a high-order scheme was adopted for discretizing the source-sink term. In the second step, the diffusion term was discretized using the Crank-Nicolson scheme. The effectiveness and capability of the numerical method was assessed by performing numerical tests. Then, the proposed numerical method was applied to a simulation of Guozheng Lake (located in central China). The modeling results were in an excellent agreement with measured data.
School of Hydropower and Information Engineering, Huazhong University of Science and Technology, Wuhan, China;School of Hydropower and Information Engineering, Huazhong University of Science and Technology, Wuhan, China
Recommended Citation:
Zheng Jing,Ling Kang. High-order scheme for the source-sink term in a one-dimensional water temperature model[J]. PLOS ONE,2017-01-01,12(3)