A vanishing viscosity fluidized bed model. (English) Zbl 1161.76554

Galiano, Gonzalo; Velasco, Julián; de Vicente, Santiago

Differ. Integral Equ. 16, No. 4, 473-498 (2003).

Summary: The evolution of one-dimensional fluidized beds may be modeled in form of a system of partial differential equations of the compressible Navier-Stokes type where the viscosity depends on the density, which may vanish, the source term is nonlinear, and the constitutive law for the pressure blows up for finite values of the density. A finite-differences scheme is used to solve an approximated problem in Lagrangian coordinates, which we show to be equivalent to the corresponding problem in Eulerian coordinates. We then prove compactness and convergence properties of the sequence of solutions of the approximated problems and partially identify the limit as a solution of the original problem.

MSC:

76N10	Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35Q30	Navier-Stokes equations
76T10	Liquid-gas two-phase flows, bubbly flows