implicit method

Phase Change Materials (PCMs) have been the subject of many researches in recent years due to the storage and release of energy at low temperature ranges. PCMs store or releasing a large amount of energy at a constant temperature range leads to saving energy. In this paper, the numerical modelling of a multilayer composite wall including PCM located on the southern side of a building is carried out using an implicit method. The data correspond the fifteenth day of each month in Tehran. The governing equations are discretized by the implicit Crank Nicolson method and solved by iteration method using MATLAB software. Finally, the location and volume fraction of PCM in the wall of the building are studied to achieve maximum efficiency. The results show that the effect of latent and sensible heat results in a reduction in the input heat flux and thermal load to the building. The optimum location for the PCM layer is the middle layer of the composite wall to reduce the heat transfer rate inside the building. In addition, it is found that the PCM volume fraction in gypsum does not have a significant effect on the thermal performance of the multi-layer composite wall. Hence, low volume fraction reduces the costs without affecting the thermal performance of the building.

A dual-time implicit mesh-less method is presented for unsteady compressible flow calculations. Polynomial least-square (PLS) and Taylor series least-square (TLS) procedures are used to estimate the spatial derivatives at each node and their computational efficiencies are compared. Also, the effect of the neighbor stencil selection on the accuracy of the method is investigated. As a new approach, different neighboring stencils are used for the highly stretched point distribution inside the boundary layer region and the inviscid isotropic point distribution outside this area. The unsteady flows over stationary and moving objects at subsonic and transonic flow conditions are solved. Results indicate the computational efficiency of the method in comparison with the alternative approaches. The convergence histories of the flow solution show that the PLS method is computationally faster than TLS method. In addition, the eight point neighboring stencil inside the viscous region is more efficient than other choices.