zbMATH — the first resource for mathematics

Small solids in an inviscid fluid. (English) Zbl 1262.35180
Summary: We present several results concerning a simple model of interaction between an inviscid fluid, modeled by the Burgers equation, and a particle, assumed to be point-wise. It is composed by a first-order partial differential equation which involves a singular source term and by an ordinary differential equation. The coupling is ensured through a drag force that can be linear or quadratic. Though this model can be considered as a simple one, its mathematical analysis is involved. We put forward a notion of entropy solution to our model, define a Riemann solver and make first steps towards well-posedness results. The main goal is to construct easy-to-implement and yet reliable numerical approximation methods; we design several finite volume schemes, which are analyzed and tested.

35Q35 PDEs in connection with fluid mechanics
35A35 Theoretical approximation in context of PDEs
35F25 Initial value problems for nonlinear first-order PDEs
35L80 Degenerate hyperbolic equations
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
Full Text: DOI