A new method of modifying the conventional k-w turbulence model for comer separation is proposed in this paper. The production term in the w equation is modified using kinematic vorticity considering fluid rotation an...A new method of modifying the conventional k-w turbulence model for comer separation is proposed in this paper. The production term in the w equation is modified using kinematic vorticity considering fluid rotation and deformation in complex geometric boundary conditions. The corner separation flow in linear compressor cascades is calculated using the original k-w model, the modified k-w model and the Reynolds stress model （RSM）. The numerical results of the modified model are compared with the available experimental data, as well as the corresponding results of the original k-w model and RSM. In terms of accuracy, the modified model, which significantly improves the performance of the original k-w model for predicting comer separation, is quite competitive with the RSM. However, the modified model, which has considerably lower computational cost is more robust than the RSM.展开更多
In this paper, I continue the study of the mathematical models presented in [J. C. Larsen, Models of cancer growth, J. Appl. Math. Comput. 53（1-2） （2015） 613-645] and [J. C. Larsen, The bistability theorem in a mo...In this paper, I continue the study of the mathematical models presented in [J. C. Larsen, Models of cancer growth, J. Appl. Math. Comput. 53（1-2） （2015） 613-645] and [J. C. Larsen, The bistability theorem in a model of metastatic cancer, to appear in Appl. Math.]. I shall prove the bistability theorem for the ODE model from [Larsen, 2015]. It is a mass action kinetic system in the variables C cancer, GF growth factor and GI growth inhibitor. This theorem says that for some values of the parameters, there exist two positive singular points c＊＋ = （C＊＋, GF＊., GI＊＋）, c＊2- = （C＊-, GF＊, GI＊-） of the vector field. Here C＊- 〈 C＊＋ and e. is stable and c＊＋ is unstable, see Sec. 2. There is also a discrete model in [Larsen, 2015], it is a linear map （T） on three-dimensional Euclidean vector space with variables （C, GF, GI）, where these variables have the same meaning as in the ODE model above. In [Larsen, 2015], I showed that one can sometimes find attine vector fields on three-dimensional Euclidean vector space whose time one map is T. I shall also show this in the present paper in a more general setting than in [Larsen, 2015]. This enables me to find an expression for the rate of change of cancer growth on the coordinate hyperplane C = 0 in Euclidean vector space. I also present an ODE model of cancer metastasis with variables C, CM, CF,GI, where C is primary cancer and CM is metastatic cancer and GF, GI are growth factors and growth inhibitors, respectively.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 51376001, 51420105008, 11572025 & 51136003)the National Basic Research Program of China (“973” Project) (Grant No. 2012CB720205 & 2014CB046405)+2 种基金the Beijing Higher Education Young Elite Teacher Projectthe Fundamental Research Funds for the Central Universitiesthe Innovation Foundation of BUAA for Ph D Graduates
文摘A new method of modifying the conventional k-w turbulence model for comer separation is proposed in this paper. The production term in the w equation is modified using kinematic vorticity considering fluid rotation and deformation in complex geometric boundary conditions. The corner separation flow in linear compressor cascades is calculated using the original k-w model, the modified k-w model and the Reynolds stress model （RSM）. The numerical results of the modified model are compared with the available experimental data, as well as the corresponding results of the original k-w model and RSM. In terms of accuracy, the modified model, which significantly improves the performance of the original k-w model for predicting comer separation, is quite competitive with the RSM. However, the modified model, which has considerably lower computational cost is more robust than the RSM.
文摘In this paper, I continue the study of the mathematical models presented in [J. C. Larsen, Models of cancer growth, J. Appl. Math. Comput. 53（1-2） （2015） 613-645] and [J. C. Larsen, The bistability theorem in a model of metastatic cancer, to appear in Appl. Math.]. I shall prove the bistability theorem for the ODE model from [Larsen, 2015]. It is a mass action kinetic system in the variables C cancer, GF growth factor and GI growth inhibitor. This theorem says that for some values of the parameters, there exist two positive singular points c＊＋ = （C＊＋, GF＊., GI＊＋）, c＊2- = （C＊-, GF＊, GI＊-） of the vector field. Here C＊- 〈 C＊＋ and e. is stable and c＊＋ is unstable, see Sec. 2. There is also a discrete model in [Larsen, 2015], it is a linear map （T） on three-dimensional Euclidean vector space with variables （C, GF, GI）, where these variables have the same meaning as in the ODE model above. In [Larsen, 2015], I showed that one can sometimes find attine vector fields on three-dimensional Euclidean vector space whose time one map is T. I shall also show this in the present paper in a more general setting than in [Larsen, 2015]. This enables me to find an expression for the rate of change of cancer growth on the coordinate hyperplane C = 0 in Euclidean vector space. I also present an ODE model of cancer metastasis with variables C, CM, CF,GI, where C is primary cancer and CM is metastatic cancer and GF, GI are growth factors and growth inhibitors, respectively.
