The boundary-layer method is used to study a wide moving jam to a class of higher-order viscous models. The equations for characteristic parameters are derived to determine the asymptotic solution. The sufficient and ...The boundary-layer method is used to study a wide moving jam to a class of higher-order viscous models. The equations for characteristic parameters are derived to determine the asymptotic solution. The sufficient and essential conditions for the wide moving jam formation are discussed in detail, respectively, and then used to prove or disprove the existence of the wide moving jam solutions to many well-known higher-order models. It is shown that the numerical results agree with the analytical results.展开更多
In this paper, a general high-order multi-domain hybrid DG/WENO-FD method, which couples a p^th-order （p ≥ 3） DG method and a q^th-order （q ≥ 3） WENO-FD scheme, is developed. There are two possible coupling appr...In this paper, a general high-order multi-domain hybrid DG/WENO-FD method, which couples a p^th-order （p ≥ 3） DG method and a q^th-order （q ≥ 3） WENO-FD scheme, is developed. There are two possible coupling approaches at the domain interface, one is non-conservative, the other is conservative. The non-conservative coupling approach can preserve optimal order of accuracy and the local conservative error is proved to be upmost third order. As for the conservative coupling approach, accuracy analysis shows the forced conservation strategy at the coupling interface deteriorates the accuracy locally to first- order accuracy at the ＇coupling cell＇. A numerical experiments of numerical stability is also presented for the non-conservative and conservative coupling approaches. Several numerical results are presented to verify the theoretical analysis results and demonstrate the performance of the hybrid DG/WENO-FD solver.展开更多
In[SIAM J.Sci.Comput.,35(2)(2013),A1049–A1072],a class of multi-domain hybrid DG and WENO methods for conservation laws was introduced.Recent applications of this method showed that numerical instability may encounte...In[SIAM J.Sci.Comput.,35(2)(2013),A1049–A1072],a class of multi-domain hybrid DG and WENO methods for conservation laws was introduced.Recent applications of this method showed that numerical instability may encounter if the DG flux with Lagrangian interpolation is applied as the interface flux during the moment of conservative coupling.In this continuation paper,we present a more robust approach in the construction of DG flux at the coupling interface by using WENO procedures of reconstruction.Based on this approach,such numerical instability is overcome very well.In addition,the procedure of coupling a DG method with a WENO-FD scheme on hybrid meshes is disclosed in detail.Typical testing cases are employed to demonstrate the accuracy of this approach and the stability underthe flexibility of using either WENO-FD flux or DG flux at the moment of requiring conservative coupling.展开更多
基金Project supported by the National Natural Science Foundation of China(No.11602128)the Natural Science Foundation of Fujian Province of China(No.2016J01679)
文摘The boundary-layer method is used to study a wide moving jam to a class of higher-order viscous models. The equations for characteristic parameters are derived to determine the asymptotic solution. The sufficient and essential conditions for the wide moving jam formation are discussed in detail, respectively, and then used to prove or disprove the existence of the wide moving jam solutions to many well-known higher-order models. It is shown that the numerical results agree with the analytical results.
基金This work is supported by the Innovation Foundation of BUAA for PhD Graduates, the National Natural Science Foundation of China （Nos. 91130019 and 10931004）, the International Cooperation Project （No. 2010DFR00700）, the State Key Laboratory of Software Development Environment （No. SKLSDE-2011ZX-14） and the National 973 Project （No. 2012CB720205）.
文摘In this paper, a general high-order multi-domain hybrid DG/WENO-FD method, which couples a p^th-order （p ≥ 3） DG method and a q^th-order （q ≥ 3） WENO-FD scheme, is developed. There are two possible coupling approaches at the domain interface, one is non-conservative, the other is conservative. The non-conservative coupling approach can preserve optimal order of accuracy and the local conservative error is proved to be upmost third order. As for the conservative coupling approach, accuracy analysis shows the forced conservation strategy at the coupling interface deteriorates the accuracy locally to first- order accuracy at the ＇coupling cell＇. A numerical experiments of numerical stability is also presented for the non-conservative and conservative coupling approaches. Several numerical results are presented to verify the theoretical analysis results and demonstrate the performance of the hybrid DG/WENO-FD solver.
基金the Innovation Foundation of BUAA for PhD Graduates,the National Natural Science Foundation of China(Nos.91130019 and 10931004)the international cooperation project No.2010DFR00700+1 种基金the Fundamental Research of Civil Aircraft MJ-F-2012-04the National 973 project No.2012CB720205.
文摘In[SIAM J.Sci.Comput.,35(2)(2013),A1049–A1072],a class of multi-domain hybrid DG and WENO methods for conservation laws was introduced.Recent applications of this method showed that numerical instability may encounter if the DG flux with Lagrangian interpolation is applied as the interface flux during the moment of conservative coupling.In this continuation paper,we present a more robust approach in the construction of DG flux at the coupling interface by using WENO procedures of reconstruction.Based on this approach,such numerical instability is overcome very well.In addition,the procedure of coupling a DG method with a WENO-FD scheme on hybrid meshes is disclosed in detail.Typical testing cases are employed to demonstrate the accuracy of this approach and the stability underthe flexibility of using either WENO-FD flux or DG flux at the moment of requiring conservative coupling.
