High-order scheme for the source-sink term in a one-dimensional water temperature model

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.