On a Transversality Condition for One Variation Problem with Moving Boundary

In this paper the investigation of the axisymmetric flow of a liquid with a boundary perpendicular to the flow is considered. Analytical equations are derived for the radial and axial velocity and pressure components of fluid flow in a pipe of finite length with a movable right boundary, and boundary conditions on the moving boundary are also defined. A numerical solution of the problem on a finite-difference grid by the iterative Newton-Raphson method for various velocities of the boundary motion is obtained.

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Numerical Solution of a Nonlinear Diffusion Model for Soybean Hydration with Moving Boundary

International Journal of Food Engineering ◽

10.1515/ijfe-2015-0035 ◽

2015 ◽

Vol 11 (5) ◽

pp. 587-595 ◽

Cited By ~ 2

Author(s):

Douglas J. Nicolin ◽

Gisleine E. C. da Silva ◽

Regina Maria M. Jorge ◽

Luiz Mario M. Jorge

Keyword(s):

Differential Equation ◽

Diffusion Model ◽

Nonlinear Diffusion ◽

Numerical Scheme ◽

Moving Boundary ◽

Grid Method ◽

Variable Diffusivity ◽

Variable Space ◽

Diffusive Fluxes ◽

Moisture Profiles

Abstract Variable diffusivity and volume of the grains are taken into account in the diffusion model that describes mass transfer in soybean hydration. The variable space grid method (VSGM) was used to consider the increase in grain size, and the diffusivity was considered an exponential function of the moisture content. An equation for the behavior of the grain radius as a function of time was obtained by global mass balance over the soybean grain and the differential equation considered that the increase in radius happens due to the influence of the convective and diffusive fluxes at the surface of the grains. The model was solved by an explicit numerical scheme which presented satisfactory results. The results showed the behavior of moisture profiles obtained as a function of time and radial position and also showed how the grain radius increased with time and changed the solution domain of the diffusion equation.

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An Incompressible Polymer Fluid Interacting with a Koiter Shell

Journal of Nonlinear Science ◽

10.1007/s00332-021-09678-5 ◽

2021 ◽

Vol 31 (1) ◽

Author(s):

Dominic Breit ◽

Prince Romeo Mensah

Keyword(s):

Moving Boundary ◽

Classical Model ◽

Elastic Shell ◽

Planck Equation ◽

Navier Stokes ◽

Flexible Shell ◽

Navier Stokes Equation ◽

Shell System ◽

Forward Equation ◽

Polymer Fluid

AbstractWe study a mutually coupled mesoscopic-macroscopic-shell system of equations modeling a dilute incompressible polymer fluid which is evolving and interacting with a flexible shell of Koiter type. The polymer constitutes a solvent-solute mixture where the solvent is modelled on the macroscopic scale by the incompressible Navier–Stokes equation and the solute is modelled on the mesoscopic scale by a Fokker–Planck equation (Kolmogorov forward equation) for the probability density function of the bead-spring polymer chain configuration. This mixture interacts with a nonlinear elastic shell which serves as a moving boundary of the physical spatial domain of the polymer fluid. We use the classical model by Koiter to describe the shell movement which yields a fully nonlinear fourth order hyperbolic equation. Our main result is the existence of a weak solution to the underlying system which exists until the Koiter energy degenerates or the flexible shell approaches a self-intersection.

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