挑流喷溅水滴的数论分档随机喷溅数学模型  

Mathematical model of random splashing by number theory classification of splashing water droplets

作　　者：张华[1] 姚钰波 张雨辰 ZHANG Hua;YAO Yubo;ZHANG Yuchen(School of Water Resources and Hydropower Engineering,North China Electric Power University,Beijing 102206,China)

机构地区：[1]华北电力大学水利与水电工程学院,北京102206

出　　处：《水力发电学报》2024年第7期41-50,共10页Journal of Hydroelectric Engineering

基　　金：国家自然科学基金项目(52279065)。

摘　　要：挑流泄洪雾化时,水舌与下游水垫塘的碰撞会喷溅大量随机运动的水滴,它构成了喷溅水滴运动的初值问题,基于数论方法在选点较少的情况下仍然有较好的均匀性的思想。本文提出了数论分档水滴的概念,通过数论方法对水滴进行分档,并将高维相空间降维到一维相空间来计算,建立了水滴数论分档随机喷溅数学模型。对比其数值解和高精度解的结果表明:在计算水滴数相同时,本文数学模型的误差最小,随着水滴数的增加,其误差减小的也最快并迅速接近高精度解。因此,水滴数论分档随机喷溅数学模型不仅能够用更少的水滴获得更高的计算精度,而且能够实现高维初值相空间降维到一维相空间的简洁表达。During flood discharge atomization,collision between the water nappes and the water body in the downstream scour pool causes numerous water droplets to splash out in random directions.This creates an initial value problem for the movement of splashing water droplets.This paper develops a concept of number theory graded water droplets,which adopts the number theory method to grade water droplets,based on the idea that this method maintains good uniformity even with a small number of selected points.Using the concept,we can simplify the high dimensional phase space to one-dimensional,and develop a mathematical model for simulation of random splashing water droplets using number theory classification.Comparison of the numerical calculations with the high-accuracy solution reveals that the error of our model is lower for a given number of droplets.As the number of droplets increases,the error decreases at a faster rate and approaches the high-precision solution more rapidly.Thus,by simulating random splashing water droplets using number theory classification,this new model not only achieves higher calculation accuracy with a smaller number of droplets,but simplifies the expression of the high dimensional initial value phase space to one-dimensional.

关 键 词：挑流泄洪 喷溅水滴 水滴随机喷溅 水滴分档随机喷溅 水滴数论分档随机喷溅 

分 类 号：TV131.2[水利工程—水力学及河流动力学]