{"title":"动脉血流模型中静止波与稀释波和冲击波的相互作用","authors":"Wancheng Sheng, Shufang Xu","doi":"10.1007/s00033-024-02295-8","DOIUrl":null,"url":null,"abstract":"<p>The <span>\\(3\\times 3\\)</span> blood flow dynamic model describes the flow of blood in flexible vessels. We study the inviscous blood flow in arteries model in this paper. The elementary waves of the blood flow in arteries include the rarefaction wave, the shock wave and the stationary wave which appears where the material properties of vessel wall change. The interactions of stationary wave with rarefaction wave and shock wave in arteries are discussed in detail. We focus on the changes of the cross-sectional area of the blood vessel and the averaged axial velocity of blood flow after the rarefaction wave and the shock wave penetrate the stationary wave. They change after interactions.</p>","PeriodicalId":501481,"journal":{"name":"Zeitschrift für angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Interactions of stationary wave with rarefaction wave and shock wave for a blood flow model in arteries\",\"authors\":\"Wancheng Sheng, Shufang Xu\",\"doi\":\"10.1007/s00033-024-02295-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The <span>\\\\(3\\\\times 3\\\\)</span> blood flow dynamic model describes the flow of blood in flexible vessels. We study the inviscous blood flow in arteries model in this paper. The elementary waves of the blood flow in arteries include the rarefaction wave, the shock wave and the stationary wave which appears where the material properties of vessel wall change. The interactions of stationary wave with rarefaction wave and shock wave in arteries are discussed in detail. We focus on the changes of the cross-sectional area of the blood vessel and the averaged axial velocity of blood flow after the rarefaction wave and the shock wave penetrate the stationary wave. They change after interactions.</p>\",\"PeriodicalId\":501481,\"journal\":{\"name\":\"Zeitschrift für angewandte Mathematik und Physik\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Zeitschrift für angewandte Mathematik und Physik\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s00033-024-02295-8\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Zeitschrift für angewandte Mathematik und Physik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s00033-024-02295-8","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Interactions of stationary wave with rarefaction wave and shock wave for a blood flow model in arteries
The \(3\times 3\) blood flow dynamic model describes the flow of blood in flexible vessels. We study the inviscous blood flow in arteries model in this paper. The elementary waves of the blood flow in arteries include the rarefaction wave, the shock wave and the stationary wave which appears where the material properties of vessel wall change. The interactions of stationary wave with rarefaction wave and shock wave in arteries are discussed in detail. We focus on the changes of the cross-sectional area of the blood vessel and the averaged axial velocity of blood flow after the rarefaction wave and the shock wave penetrate the stationary wave. They change after interactions.
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