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In this paper, we prove the convergence of a class of finite volume schemesfor the model of coupling between a Burgers fluid and a pointwise particleintroduced in [LST08]. In this model, the particle is seen as a movinginterface through which an interface condition is imposed, which links thevelocity of the fluid on the left and on the right of the particle and thevelocity of the particle (the three quantities are all not equal in general).The total impulsion of the system is conserved through time.The proposedschemes are consistent with a "large enough" part of the interface conditions.The proof of convergence is an extension of the one of [AS12] to the case wherethe particle moves under the influence of the fluid. It yields two maindifficulties: first, we have to deal with time-dependent flux and interfacecondition, and second with the coupling between and ODE and a PDE.

Convergence of finite volumes schemes for the coupling between the inviscid Burgers equation and a particle