Obtaining analytical solutions to Saint-Venant equations using optimization tools
摘要
The Saint-Venant equations are widely used to model real river flows. The solution of these equations requires the use of sophisticated partial differential equation (PDE) solvers. Analytical solutions to the Saint-Venant equations are only available for very specific simplified cases. However, analytical solutions are important for evaluating the reliability of different numerical solvers. In this paper, we present optimization tools for defining analytical solutions of the Saint-Venant equations, with the expectation that the examples produced by these tools will be useful in the numerical context.