Convergence of finite volumes schemes for the coupling between the inviscid Burgers equation and a particle
Provides a rigorous convergence proof for numerical schemes in a specific fluid-particle interaction model, which is an incremental extension of existing theory.
This paper proves the convergence of a class of finite volume schemes for a coupled system of an inviscid Burgers equation and a pointwise particle, extending previous work to handle time-dependent flux and interface conditions as well as ODE-PDE coupling.
In this paper, we prove the convergence of a class of finite volume schemes for the model of coupling between a Burgers fluid and a pointwise particle introduced in [LST08]. In this model, the particle is seen as a moving interface through which an interface condition is imposed, which links the velocity of the fluid on the left and on the right of the particle and the velocity of the particle (the three quantities are all not equal in general). The total impulsion of the system is conserved through time.The proposed schemes 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 where the particle moves under the influence of the fluid. It yields two main difficulties: first, we have to deal with time-dependent flux and interface condition, and second with the coupling between and ODE and a PDE.