The interaction of shock waves with viscosity is one of the central problems in the supersonic regime of compressible fluid flow. In this work, numerical solutions of unmagnetised fluid equations, with the viscous stress tensor, are investigated for a one-dimensional shock wave. In the algorithm developed the viscous stress terms are expressed in terms of the relevant Reynolds number. The algorithm concentrated on the compression rate, the entropy change, pressures, and Mach number ratios across the shock wave. The behaviour of solutions is obtained for the Reynolds and Mach numbers defining the medium and shock wave in the supersonic limits.
The Sun constantly releases radiation and plasma into the heliosphere. Sporadically, the Sun launches solar eruptions such as flares and coronal mass ejections (CMEs). CMEs carry away a huge amount of mass and magnetic flux with them. An Earth-directed CME can cause serious consequences to the human system. It can destroy power grids/pipelines, satellites, and communications. Therefore, accurately monitoring and predicting CMEs is important to minimize damages to the human system. In this study we propose an ensemble learning approach, named CMETNet, for predicting the arrival time of CMEs from the Sun to the Earth. We collect and integrate eruptive events from two solar cycles, #23 and #24, from 1996 to 2021 with a total of 363 geoeffective CMEs. The data used for making predictions include CME features, solar wind parameters and CME images obtained from the SOHO/LASCO C2 coronagraph. Our ensemble learning framework comprises regression algorithms for numerical data analysis and a convolutional neural network for image processing. Experimental results show that CMETNet performs better than existing machine learning methods reported in the literature, with a Pearson product-moment correlation coefficient of 0.83 and a mean absolute error of 9.75 h.
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