Several different ways to increase the accuracy of the numerical solution of the first order wave equation

The article presents several different ways to increase the accuracy of the numerical solution of differential equations. The comparison of schemes with different accuracy for the first order wave equation problem is presented. The schemes of the first order of upwind scheme, the second order of accuracy of McCormack, the third order of accuracy of Warming–Cutler–Lomax, and the scheme of the fourth order of accuracy of Abarbanel–Gotlieb–Turkel were applied. The condensed computational grids for the McCormack scheme are used, and the results using an adaptive grid for the McCormack scheme were compared

Numerical Simulation Of The Energy Separation Effect In The Ranke-Hilsch Tube

Currently, there are many applications of vortex technologies. The vortex effect is used in gas-dynamic cold generators and vortex refrigerating chambers. Vortex devices are also used as dehumidifiers, separators, for cooling and heating hydraulic fluids, separation of two-phase media, gas mixtures. Scientists are studying the applicability of vortex equipment for traditional and freeze-drying of agricultural products. However, the influence of the geometric parameters of vortex devices on the performance and energy efficiency of the temperature separation of gas flows has been poorly studied. Research aimed at finding opportunities and expanding the scope of application of vortex tubes is an urgent task. The article describes three-dimensional mathematical models of a swirling gas flow arising in a vortex tube. It presents the results of its implementation in the Comsol Multiphysics 5.6 software package. Thermodynamic and hydrodynamic characteristics confirm the effect of temperature separation in a vortex tube. The dependences of the temperature separation on the flow velocity at are obtained. For the three-dimensional vortex tube model, calculations were carried out using the turbulence model v2-f

Several different ways to increase the accuracy of the numerical solution of the first order wave equation

The article presents several different ways to increase the accuracy of the numerical solution of differential equations. The comparison of schemes with different accuracy for the first order wave equation problem is presented. The schemes of the first order of upwind scheme, the second order of accuracy of McCormack, the third order of accuracy of Warming–Cutler–Lomax, and the scheme of the fourth order of accuracy of Abarbanel–Gotlieb–Turkel were applied. The condensed computational grids for the McCormack scheme are used, and the results using an adaptive grid for the McCormack scheme were compared