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