A comparative study of numerical simulations via UAT and UAH tension B-splines for coupled Navier–Stokes equation with statistical validation

Q1 Mathematics Partial Differential Equations in Applied Mathematics Pub Date : 2025-02-20 DOI:10.1016/j.padiff.2025.101127

Mamta Kapoor

{"title":"A comparative study of numerical simulations via UAT and UAH tension B-splines for coupled Navier–Stokes equation with statistical validation","authors":"Mamta Kapoor","doi":"10.1016/j.padiff.2025.101127","DOIUrl":null,"url":null,"abstract":"<div><div>The present paper deals with the numerical simulation of coupled <span><math><mrow><mn>2</mn><mi>D</mi></mrow></math></span> and <span><math><mrow><mn>3</mn><mi>D</mi></mrow></math></span> Navier–Stokes equations. For this purpose, two novel regimes “MCUAT tension B-spline” and “MCUAH tension B-spline” based DQMs are implemented. The spatial discretization is tackled via mentioned B-spline DQMs and the generated ODE system is solved using SSPRK-43 method. Graphical compatibility of approximated and exact outcomes is also tested. Method II has slight reduced error than Method I. The correlation matrix heatmap is also provided to test the type of correlation. <span><math><mrow><msup><mrow></mrow><mrow><mo>′</mo></mrow></msup><msup><mrow><mi>t</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></math></span> Test is applied for testing significant difference between errors generated. The present work is a fusion of numerical analysis and statistics to deal with the complex-natured PDEs with statistical aspect.</div></div>","PeriodicalId":34531,"journal":{"name":"Partial Differential Equations in Applied Mathematics","volume":"13 ","pages":"Article 101127"},"PeriodicalIF":0.0000,"publicationDate":"2025-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Partial Differential Equations in Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2666818125000543","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Mathematics","Score":null,"Total":0}

引用次数: 0

Abstract

The present paper deals with the numerical simulation of coupled

2 D

and

3 D

Navier–Stokes equations. For this purpose, two novel regimes “MCUAT tension B-spline” and “MCUAH tension B-spline” based DQMs are implemented. The spatial discretization is tackled via mentioned B-spline DQMs and the generated ODE system is solved using SSPRK-43 method. Graphical compatibility of approximated and exact outcomes is also tested. Method II has slight reduced error than Method I. The correlation matrix heatmap is also provided to test the type of correlation.

^{'} t^{'}

Test is applied for testing significant difference between errors generated. The present work is a fusion of numerical analysis and statistics to deal with the complex-natured PDEs with statistical aspect.

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

基于UAT和UAH张力b样条的Navier-Stokes耦合方程数值模拟对比研究，并进行了统计验证

本文研究了二维和三维耦合Navier-Stokes方程的数值模拟。为此，实现了基于“MCUAT张力b样条”和“MCUAH张力b样条”两种新体制的DQMs。利用b样条dqm进行空间离散化处理，利用SSPRK-43方法求解生成的ODE系统。还测试了近似结果和精确结果的图形兼容性。方法二的误差比方法一略小，并提供了相关矩阵热图来检验相关类型。“t”检验用于检验产生的错误之间的显著性差异。本文将数值分析与统计学相结合，从统计学的角度来研究复杂性质的偏微分方程。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文去求助

来源期刊