Summary A meshless method – The Least Square Finite Difference scheme (LSFD) with diffusion is analyzed and applied to inviscid flows. The scheme is made second‐order by using a modified difference in the formulation of LSFD. Several numerical experiments, namely the Sod shock tube and the shallow water problems, are carried out and, in the limelight of the results obtained, the ability of the scheme to resolve shock wave, rarefaction wave, and contact discontinuity is discussed. The conditional stability of the LSFD scheme is established. The LSFD uses weights to diagonalize the least square matrix resulting in the spatial discretization in order to gain computational time. We prove that there exists a unique weight for the resulting optimization problem. The weighted version of LSFD is used to solve the isentropic vortex problem numerically and the results are used to discuss the dissipative nature of the scheme. Five configurations of the two‐dimensional Riemann problems are used in our numerical experiments. The capability of the scheme to capture the complex interaction of multiple planar waves is discussed in the limelight of the results on the Riemann problems. The result of the shock reflection problem shows that the scheme is minimally dissipative and leads to sharp and well‐resolved shocks.

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In this article, we analyze the performance of a family of nonlinear, shock-capturing mesh-free finite-difference schemes in wavenumber space. These finite difference methods are based on the use of a weighted least-square approximation procedure together with a Taylor series expansion of the unknown function. The influence of weights on the spectral properties of these schemes are studied using the approximate dispersion relation. The numerical study evidences that an appropriate choice of the weighting functions reduces dissipation and dispersion inherent to the schemes. The meshless schemes studied in this work, are then used to simulate 2D internal inviscid subsonic and transonic flows respectively in a channel with a bump. The results in 2D corroborate with the 1D analyses and reveal that when the supporting nodes closer to the reference node are assigned a greater weightage value in the computation of the 1st order spatial derivatives, better spectral properties are achieved at low wavenumber. However, the present numerical study shows that weighting function does not shift the frequency of the errors and thus in order to accelerate the convergence of these schemes, methods such as the classic multigrid can be used.

A horizontal ground heat exchanger has been applied as a simpler sustainability measure in buildings compared to its vertical counterpart, making it more suitable for residential application. A lack of contextual scientific findings within the specific construction culture has precluded its widespread application in the developing world. In this study, an experimental and simulation investigation was carried out on the thermal performance of an air-based horizontal ground-coupled heat exchanger buried 3 m below the ground. The study was performed in the tropical climate of Mauritius with a focus on space cooling. The ground temperature and air temperature inside the pipeline at several locations of the installation was measured. A CFD simulation model was developed and calibrated against the experimental data, which allowed further analyses on the influence of system parameters on performance. The study allowed to confirm the performance of the technology for application as a sustainability measure in the local construction industry and to identify practical challenge that need to be addressed. A drop in temperature of up to 5C was achieved at 2.3 m/s and 8C at 4 m/s. The latter result holds promise to achieve thermal comfort by achieving indoor air temperature of 27 C or lower when ambient air is at 33-34C during typical summer periods.