On the convergence of a vortical numerical method for three-dimensional Euler equations in Lagrangian coordinates Авторстатья
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Дата последнего поиска статьи во внешних источниках: 23 декабря 2016 г.
Аннотация:In the present paper, we investigate the problems of regularization and numerical solution of
a three-dimensional vorticity transport equation for an ideal incompressible fluid in Lagrangian
coordinates (the Euler equation in the vortex–velocity variables).
In the present paper, we first perform the regularization of the vorticity transport equations
by smoothing the singularity in the integral representation of the velocity fields via the vorticity
according to the Biot–Savart law. Under the assumption of the existence of a smooth solution of
original equations on some finite time interval, we prove the solvability of the smoothed equations
on the same time interval and the convergence of their solutions to the solutions of the original
equations. In addition, the velocity field is considered in the space of functions that have H¨older
continuous first derivatives. We perform discretization of the smoothed equations and prove the
convergence of the approximate velocity and vorticity fields on a grid in the uniform metric.