Available Riemann solutions for the pressureless Burgers fluid–particle system illustrating the specially simplified particle-laden flow are explicitly presented in six different structures. Interestingly, the distributional solution including Dirac delta function called as delta shock wave is constructed in two different circumstances, which is also rigorously testified in the space of distributions. Moreover, the interacting problem of delta shock wave is meticulously discussed in the specially designed initial data with constant states in three pieces separated by two jumping points. Additionally, several typical numerical experiments presented are highly consistent with our theoretically obtained Riemann solutions.
Lin et al. (Tue,) studied this question.