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

Mathematical modeling of particle movement in laminar flow in a pipe

The article provides basic information about the principles of calculations for solving the system of Navier–Stokes equations using the control volume method. The calculation of the incompressible fluid velocity field and pressure is found using the SIMPLE algorithm and MacCormack method. Particle trajectories were determined using the Lagrangian approach

Mathematical modeling of particle movement in laminar flow in a pipe

The article provides basic information about the principles of calculations for solving the system of Navier–Stokes equations using the control volume method. The calculation of the incompressible fluid velocity field and pressure is found using the SIMPLE algorithm and MacCormack method. Particle trajectories were determined using the Lagrangian approach

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