{"title":"通过布尔格斯方程和奥尔德罗伊德方程建立可压缩粘性流体模型","authors":"C. Giorgi, A. Morro","doi":"10.1111/sapm.12701","DOIUrl":null,"url":null,"abstract":"<p>The paper develops some generalizations of the Burgers and the Oldroyd equations for the dynamics of fluids. To account for compressibility, in addition to viscosity, first the Oldroyd derivative is replaced with the Truesdell derivative. Consequently, the two equations can be given a linear form within the Lagrangian formulation. Furthermore, possible anisotropies are modeled by replacing some (scalar) coefficients with tensors. To emphasize the compressibility property, generalizations are established to allow for nonzero longitudinal viscosity. Next, the thermodynamic consistency is investigated by regarding both types of equations as rate equations, of second order and first order. The requirements on the parameters entering the two equations are derived while the linearity of the two equations allow the free energy potential be quadratic. The Oldroyd equation is found to be compatible via appropriate restrictions of the tensor coefficients, through different pairs of free energy and entropy production.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"153 2","pages":""},"PeriodicalIF":2.6000,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the modeling of compressible viscous fluids via Burgers and Oldroyd equations\",\"authors\":\"C. Giorgi, A. Morro\",\"doi\":\"10.1111/sapm.12701\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>The paper develops some generalizations of the Burgers and the Oldroyd equations for the dynamics of fluids. To account for compressibility, in addition to viscosity, first the Oldroyd derivative is replaced with the Truesdell derivative. Consequently, the two equations can be given a linear form within the Lagrangian formulation. Furthermore, possible anisotropies are modeled by replacing some (scalar) coefficients with tensors. To emphasize the compressibility property, generalizations are established to allow for nonzero longitudinal viscosity. Next, the thermodynamic consistency is investigated by regarding both types of equations as rate equations, of second order and first order. The requirements on the parameters entering the two equations are derived while the linearity of the two equations allow the free energy potential be quadratic. The Oldroyd equation is found to be compatible via appropriate restrictions of the tensor coefficients, through different pairs of free energy and entropy production.</p>\",\"PeriodicalId\":51174,\"journal\":{\"name\":\"Studies in Applied Mathematics\",\"volume\":\"153 2\",\"pages\":\"\"},\"PeriodicalIF\":2.6000,\"publicationDate\":\"2024-04-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Studies in Applied Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1111/sapm.12701\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Studies in Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1111/sapm.12701","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
On the modeling of compressible viscous fluids via Burgers and Oldroyd equations
The paper develops some generalizations of the Burgers and the Oldroyd equations for the dynamics of fluids. To account for compressibility, in addition to viscosity, first the Oldroyd derivative is replaced with the Truesdell derivative. Consequently, the two equations can be given a linear form within the Lagrangian formulation. Furthermore, possible anisotropies are modeled by replacing some (scalar) coefficients with tensors. To emphasize the compressibility property, generalizations are established to allow for nonzero longitudinal viscosity. Next, the thermodynamic consistency is investigated by regarding both types of equations as rate equations, of second order and first order. The requirements on the parameters entering the two equations are derived while the linearity of the two equations allow the free energy potential be quadratic. The Oldroyd equation is found to be compatible via appropriate restrictions of the tensor coefficients, through different pairs of free energy and entropy production.
期刊介绍:
Studies in Applied Mathematics explores the interplay between mathematics and the applied disciplines. It publishes papers that advance the understanding of physical processes, or develop new mathematical techniques applicable to physical and real-world problems. Its main themes include (but are not limited to) nonlinear phenomena, mathematical modeling, integrable systems, asymptotic analysis, inverse problems, numerical analysis, dynamical systems, scientific computing and applications to areas such as fluid mechanics, mathematical biology, and optics.