Boundary value problem
About: Boundary value problem is a(n) research topic. Over the lifetime, 145355 publication(s) have been published within this topic receiving 2731135 citation(s). The topic is also known as: boundary value problems.
Peng Jiang1•Institutions (1)
Abstract: The fluid-particle system is studied in this paper. More precisely, we consider the compressible Navier–Stokes equations coupled to the Vlasov equation through the drag force. This model arises from the research of aerosols, sprays or more generically two-phase flows. We work with one-dimensional case of this model, and prove the existence, uniqueness of global classical solution to an initial-boundary value problem with large initial data and reflection boundary conditions. The proof is based on the local existence theorem and the global a priori estimates. More specifically, we show that the density distribution function of particles has compact support, which plays a crucial role in the hardest part of our proof: the estimates of the higher order derivatives of the solution.
Abstract: Many wave propagation problems involve discontinuous material properties. We propose to solve such problems by non-overlapping domain decomposition combined with the method of difference potentials (MDP). The MDP reduces the Helmholtz equation on each subdomain to a Calderon's boundary equation with projection on the boundary. The unknowns for the Calderon's equation are the Dirichlet and Neumann data. Coupling between neighboring subdomains is rendered by applying their respective Calderon's equations to the same data at the common interface. Solutions on individual subdomains are computed concurrently using a direct solver. Our method proves to be insensitive to large jumps in the wavenumber for transmission problems, as well as interior cross-points and mixed boundary conditions, which may be a challenge to many other domain decomposition methods.
Abstract: This paper presents a mathematical modelling of a novel multiphysics (electro-mechanic coupling) problem of the shear wave propagation in laminated structures (piezoelectric - hydrogel - elastic substrate) using the wave mode method while finding the general solution for each medium. A dynamic mechanical equilibrium equation (for transverse deflection) and Maxwell equation (for electric potential) are solved in a coupled manner over each domain resulting a general closed-form solution. A specific analytical solution is then obtained enforcing the boundary conditions at the top of piezoelectric layer and the interface continuity requirements between each layer and the elastic half-space. A novel approach, to uncouple the coupled equations, is presented resulting in a final systematic solution. The effect of x coordinate (thickness) on the field variables is carefully examined for the electrically open and short cases. The jump in the stress and electric displacement components (causing delamination due to shearing mode of fracture) is present across all the interfaces due to the different bulk material constants. The key contribution of the current work is demonstrating the influence of fixed-charge concentration inside the hydrogel layer on the shear wave propagation. The present study thus provides a new concept for adjusting and controlling the elastic wave propagation in the composite structures, and provides a proper theoretical understanding of wave propagation in the damage tolerance-based design of piezotronics devices.
Abstract: This study investigates the fluid dynamics and performance characteristics in micronozzle flows with changes in various geometric parameters using Navier–Stokes simulation based on slip wall boundary conditions. The various geometric parameters considered for the study are (1) area ratio with fixed throat dimension and (2) the semidivergence angle variation with no change in area ratio. The simulation results show that the flow choking for micronozzle happens not at the geometric throat; rather pushed downstream to the divergent channel of the nozzle. This is due to the thick boundary layer growth, which reduces the effective flow area and shifts the minimum allowable flow area downstream to the throat. The distance to which the choking point shifts downstream to the throat reduces with Maxwell's slip wall conditions compared to the conventional no-slip wall condition. The downstream movement of the choking point from the throat reduces with an increase in area ratio and with increase in divergence angle with fixed area ratio. This is due to the fact that the increase in area ratio and divergence angle increases the nozzle height at any particular section in the divergent portion of the nozzle. As a result of this, the boundary layer profile also moves upward and the restriction of potential core by the thick boundary layer reduces, which in turn leads to an increase in the effective minimum flow area downstream to the throat.
Abstract: In this paper we study the behavior of an incompressible viscous fluid moving between two very close surfaces also in motion. Using the asymptotic expansion method we formally justify two models, a lubrication model and a shallow water model, depending on the boundary conditions imposed. Finally, we discuss under what conditions each of the models would be applicable.