A system of boundary integral equations is derived for flows in domains composed of a porous medium of permeability k 1 , surrounded by another porous medium of different permeability, k 2 . The incompressible Brinkman equation is used to describe the flow in the porous media. We first apply a boundary integral representation of the Brinkman flow on each side of the dividing interface, and impose continuity of the velocity at the interface to derive the final formulation in terms of the interfacial velocity and surface forces. We discuss relations between the surface stresses based on the additional conditions imposed at the interface that depend on the porosity and permeability of the media and the structural composition of the interface. We present simulated results for test problems and different interface stress conditions. The results show significant sensitivity to the choice of the interface conditions, especially when the permeability is large. Since the Brinkman equation approaches the Stokes equation when the permeability approaches infinity, our boundary integral formulation can also be used to model the flow in sub-categories of Stokes-Stokes and Stokes-Brinkman configurations by considering infinite permeability in the Stokes fluid domain.

Article HistoryOne of the most important debates on energy is planning for the best carriers in each region and determined based on each country's energy basket. The importance of preserving fossil resources becomes evident when we made the prediction. Iran's oil and gas resources will finish up to 136 years to 79 years. Since the clean energy production is a new source in interested field of researchers. Here we study the performance of overtopping with a circular ramp which can be used as a model of wave energy converter.

In this study a new meshless method is presented for the analysis of heat transfer in heterogeneous solid structures. The presented meshless method is based on the integral form of energy equation for the sub-particles in the domain of the material. A micromechanical model based on the presented meshless method is presented for analysis of heat transfer, temperature distribution and steady-state effective thermal conductivities of fiber-matrix type of composite materials. Because the domain integration is eliminated in the presented meshless formulation, the computational efforts in presented method are decreased substantially. A small area of the composite system called the representative volume element (RVE) is considered as the solution domain. The fully bonded fiber-matrix interface is considered and contact thermal resistant is neglected in the fiber-matrix interface and so the continuity of temperature and reciprocity of heat flux is satisfied in the fiber-matrix interface. A direct interpolation method is employed for enforcement the appropriate boundary conditions to the RVE. Numerical results are presented for temperature distribution, heat flux and thermal conductivity. Numerical results show that presented meshless method is simple, effective, accurate and less costly method in micromechanical modeling of heat conduction in heterogeneous materials.

A truly meshless method based on the integral form of equilibrium equations is formulated. A micromechanical model is developed to study micro-stresses in normal and shear loading of unidirectional fiber reinforced composites. A small repeating area of composite including a fiber surrounded by matrix called representative volume element (RVE) is considered as solution domain. A direct method is proposed for enforcement of the appropriate periodic boundary conditions for shear and normal loading. Especially transverse shear loading is considered in this analysis. Fully bonded interface condition is investigated and the continuity of displacements and traction is imposed to the fiber-matrix interface. Comparison of the predicted results shows excellent agreement with results in available literature. Results of this study also revealed that the presented model can provide highly accurate predictions with respectively small number of nodes and small computation time without the complexity of mesh generation.