Riemann problem to the transport equations with time-dependent composite source terms
The Riemann problem to the transport equations with time-dependent composite source terms was solved.First,a more general time-dependent variable transformation was introduced to rewrite the non-homogeneous system with source terms into a system of conservation laws,and the Riemann solution containing δ-shock and vacuum was constructed in the framework of con-servation laws.Then,by virtue of the suitable generalized Rankine-Hugoniot relation and entropy condition,the existence and u-niqueness of δ-shock wave solution was established.The results showed that,influenced by the source terms,the Riemann solu-tion of the system was no longer self-similar and all the characteristic lines became curves.Numerical simulation confirmed the theoretical analysis.
transport equationcomposite source termRiemann problemδ-shockvacuumnumerical simulation
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