Abstract

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.

中文翻译：

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浅水结冰模型实现中求解非线性方程的方法选择

摘要

飞机在含有过冷水滴的气流中飞行期间对飞机剖面的积冰模拟是飞行安全的一项极其重要的任务，因为积冰的形式显着影响飞行特性。在解决该问题的模型之一，浅水结冰模型 (SWIM) 中，求解具有一个变量的非线性方程的问题在数值模拟中起着核心作用。由于这个问题占据了绝大多数的计算时间，选择求解非线性方程的最优方法并优化这些方法的问题就显得尤为突出。本文介绍了在SWIM求解器的实现中使用各种求解非线性方程的方法的分析，考虑到被求解方程的特点，