A non-iterative immersed boundary-lattice Boltzmann method with boundary condition enforced for fluid–solid flows

A non-iterative immersed boundary lattice Boltzmann method (IB-LBM) is proposed in this work for the simulation of fluid–solid flows. In the scheme, the interface is implemented by the correction of the neighboring distribution functions, similar to that of the LBM. Such treatment of the boundary is contrary to the traditional methods, where the interface is usually modeled as a generator of external force. Therefore, an advantage of the present method is to remove the efforts to evaluate the IB force and then incorporate it into the governing equation. Furthermore, an adjustment parameter is introduced to the immersed boundary scheme, which ensures the interpolated distribution functions derive the desired velocity at the boundary. Compared with the solution of a large boundary matrix and the multiple force correction that generally used in the previous studies, the present method is simpler and efficient without any iterative procedures. Those above-mentioned features make the present scheme based on the correction of the distribution function, with the enforcement of no-slip boundary condition. Simulation of flow past a fixed cylinder shows that there is no penetration of streamlines to the cylinder surface, indicating a well enforcement of the no-slip boundary condition. This scheme is further validated in the flows of a cylinder oscillating in a quiescent fluid, circular and elliptical particles settling in a channel. The results have good agreement with those data available in the literature.     

Reflection and refraction of a plane thermoelastic wave at a solid–solid interface under perfect boundary condition,in presence of normal initial stress

Using the basic governing equations for isotropic and homogeneous generalized thermo elastic media under initial stress, the reflection and refraction of thermo elastic plane waves at the interface of two dissimilar thermo elastic solid half-spaces has been investigated. The amplitude ratios of various reflected and refracted waves are obtained for an ideal boundary for the incidence of SV-wave. The numerical computations are carried out for a particular model. The effect of initial stress on the amplitude ratios are shown graphically after numerical calculation.     

Reflection and refraction of P-, SV- and thermal wave,at an initially stressed solid–liquid interface in generalized thermoelasticity

We have investigated the problem of reflection and refraction of thermoelastic wave at a solid–liquid interface in presence of initial stress. Using the theory of generalized thermoelasticity the problem has been solved in the context of various linear theories of thermoelasticity namely Lord–Shulmon, Green–Lindsay and coupled thermoelasticity. The appropriate expressions to find the amplitude ratios for all the three cases of P-wave incidence, SV-wave incidence and thermal wave incidence have been developed. However the ratios of amplitudes of reflected and refracted waves to that of incident wave are computed numerically for earth’s crust-water interface, for incident P-wave only, considering the initial stress to be tensile as well as compressional both. The results obtained are discussed and compared in the three models of thermoelasticity. The variations of the amplitude ratios with initial stress in G–L model have also been shown.     

Estimates for the difference between exact and approximate solutions of parabolic equations on the basis of Poincaré inequalities for traces of functions on the boundary

We study a method for the derivation of majorants for the distance between the exact solution of an initial–boundary value reaction–convection–diffusion problem of the parabolic type and an arbitrary function in the corresponding energy class. We obtain an estimate (for the deviation from the exact solution) of a new type with the use of a maximally broad set of admissible fluxes. In the definition of this set, the requirement of pointwise continuity of normal components of the dual variable (which was a necessary condition in earlier-obtained estimates) is replaced by the requirement of continuity in the weak (integral) sense. This result can be achieved with the use of the domain decomposition and special embedding inequalities for functions with zero mean on part of the boundary or for functions with the zero mean over the entire domain.     

Energy decay and global solutions for a damped free boundary fluid–elastic structure interface model with variable coefficients in elasticity

ABSTRACT

We study a free boundary fluid-structure interaction model. In the model, a viscous incompressible fluid interacts with an elastic body via the common boundary. The motion of the fluid is governed by Navier–Stokes equations while the displacement of the elastic structure is described by variable coefficient wave equations. The dissipation is placed on the common boundary between the fluid and the elastic body. Given small initial data, the global existence of the solutions of this system is proved and the exponential decay of solutions is obtained.     

Computation of eigenfunctions and eigenvalues for the Sturm–Liouville problem with Dirichlet boundary conditions at the left endpoint and Neumann conditions at the right endpoint

A functional-based variational method is proposed for finding the eigenfunctions and eigenvalues in the Sturm–Liouville problem with Dirichlet boundary conditions at the left endpoint and Neumann conditions at the right endpoint. Computations are performed for three potentials: sin((x–π)²/π), cos(4x), and a high nonisosceles triangle.