Abstract

A new method for the numerical solution of the passive scalar transport equation in the framework of hydrodynamic equations in the shallow water approximation is described. The method is based on previously developed quasi-gasdynamic algorithms for numerical simulation of compressible gas flows. Smoothed equations are derived, and their difference approximations, including for flows with a pollutant source, are presented. The numerical algorithms are tested as applied to one- and two-dimensional flows. As an example, the algorithm is used to solve the problem of water circulation in Lake Vallunden. The constructed approach is generalized to passive scalar transport in the case of viscous incompressible flows.

中文翻译：

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基于准气动力方法的浅水被动标量输运的数值模拟

摘要

描述了一种在浅水近似的水动力方程框架内求解被动标量输运方程数值解的新方法。该方法基于先前开发的用于可压缩气流数值模拟的拟气动力学算法。推导了平滑方程，并给出了它们的差分近似值，包括带有污染物源的流量。测试数值算法是否适用于一维和二维流。例如，该算法用于解决瓦伦登湖的水循环问题。在粘性不可压缩流的情况下，所构造的方法可以推广到被动标量传输。