Selection of a Method for Solving Nonlinear Equations in Shallow-Water Icing Model Implementation

Ice accretion simulation on aircraft profiles during their flight in an air stream containing supercooled water droplets is an extremely important task for flight safety, since the form of accreted ice significantly affects flight characteristics. In one of the models for solving the problem, the shallow-water icing model (SWIM), the problem of solving nonlinear equations with one variable plays a central role in numerical simulation. Since this problem occupies the overwhelming majority of calculations time, the question of choosing the optimal method for solving nonlinear equations and optimizing these methods becomes especially acute. This article describes the analysis of the use of various methods for solving nonlinear equations in the implementation of the SWIM solver, taking into account the features of the equations being solved, which led to a significant acceleration of the computational codes when performing calculations on JSCC RAS supercomputers.