An accurate and efficient gridless method is presented for calculation of inviscid compressible flows in subsonic to supersonic flows. The Taylor series least squares is used for discretization of spatial derivatives at each point. Fast gridless method using the second-and fourth-order artificial dissipation terms is applied for solving the Euler equations. Two methods are proposed for increasing the accuracy; implementing the constrained weights optimization and using high-order Taylor series expansion on the fast gridless method. The explicit and implicit dual-time schemes are applied for temporal discretization. To speed up convergence, local time stepping and residual smoothing techniques are used. The capability and accuracy of the methods are compared with other gridless methods, finite volume method and AGARD data for some test cases in subsonic, transonic and supersonic flows. Results show that the use of the constraint weights optimization increases the accuracy especially with fewer point distributions in comparison with conventional gridless methods and it is more efficient than other gridless methods.

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In this research, the performance of stepped solar still has been experimentally evaluated. For this purpose, a parabolic trough collector has been used to preheat the saline water entering the solar still. Also, two flat external reflectors have been employed to increase the amount of solar energy received by the steps and the collector of the system. The findings of this research indicate that the use of two flat external reflectors is more effective than using the trough collector. Also, it is more efficient to apply both mechanisms simultaneously than to use them separately. According to the obtained results, the distilled water output of the solar still is 760, 1,560, 2,440 and 2,760 ml/m2, respectively, for operating the conventional solar still, using the trough collector, using the two flat external reflectors, and using the collector and reflectors simultaneously. The electrical conductivity due to the presence of salt and chemical substances dissolved in the distilled water discharged from the still is 255, 215, 62 and 38 micro Siemens per centimetre, respectively, for each of the four mentioned cases. These experiments show that by applying the proposed mechanisms, the amount of distilled water can be increased, and its purity can be enhanced.

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