Global random walk on grid algorithm for solving Navier–Stokes and Burgers equations

Sabelfeld Karl K. () and Bukhasheev Oleg ()
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Sabelfeld Karl K.: Institute of Computational Mathematics and Mathematical Geophysics, Russian Academy of Sciences, Novosibirsk, Russia
Bukhasheev Oleg: Institute of Computational Mathematics and Mathematical Geophysics, Russian Academy of Sciences, Novosibirsk, Russia

Monte Carlo Methods and Applications, 2022, vol. 28, issue 4, 293-305

Abstract: The global random walk on grid method (GRWG) is developed for solving two-dimensional nonlinear systems of equations, the Navier–Stokes and Burgers equations. This study extends the GRWG which we have earlier developed for solving the nonlinear drift-diffusion-Poisson equation of semiconductors (Physica A 556 (2020), Article ID 124800). The Burgers equation is solved by a direct iteration of a system of linear drift-diffusion equations, while the Navier–Stokes equation is solved in the stream function-vorticity formulation.

Keywords: Global random walk on grid; Navier–Stokes equation; Burgers equation; drift-diffusion equation (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1515/mcma-2022-2126

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