Mai Duc Thanh, Dao Huy Cuong
Abstract:
We study the existence of solutions of the Riemann problem for a model
of two-phase flows. The model has the form of a nonconservative hyperbolic
system of balance laws. Based on a phase decomposition approach, we obtain
all the wave curves. By developing an analytic method, we can establish
a system of nonlinear algebraic equations for each solution of the
Riemann problem. The system is under-determined and can be parameterized by
the volume fraction in one phase. Therefore, an argument relying on the
Implicit-Function Theorem leads us to the existence of solutions of
the Riemann problem for the model for sufficiently large initial data.
Furthermore, the structure of the Riemann solutions obtained by this method
can also be obtained.
Submitted November 19, 2014. Published February 5, 2015.
Math Subject Classifications: 35L65, 35L67, 76T10, 76N10.
Key Words: Two-phase flow; nonconservative; source term; jump relation;
shock; Riemann problem.
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Mai Duc Thanh Department of Mathematics, International University Vietnam National University - HCMC, Quarter 6 Linh Trung Ward, Thu Duc District Ho Chi Minh City, Vietnam email: mdthanh@hcmiu.edu.vn |
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Dao Huy Cuong Nguyen Huu Cau High School, 07 Nguyen Anh Thu Trung Chanh Ward, Hoc Mon District Ho Chi Minh City, Vietnam email: cuongnhc82@gmail.com |
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