This article is cited in 2 papers

Discretization scheme of the induction equation on a staggered grid in orthogonal curvilinear coordinates

Igor V. Bychin^ab, Andrey V. Gorelikov^ab, Aleksey V. Ryakhovsky<sup>ba

a</sup> Surgut Branch of Federal State Institute “Scientific Research Institute for System Analysis of the Russian Academy of Sciences”, Surgut, Russian Federation
^b Surgut State University, Surgut, Russian Federation

Abstract: A discretization scheme of the magnetic field induction equation is considered for the model of nonideal magnetic hydrodynamics within the framework of the control volume method. A constrained transfer algorithm is used to discretize the induction equation, which provides a solenoidal numerical solution. A detailed elaboration of the discrete analog of the induction equation in arbitrary orthogonal curvilinear coordinates for staggered structured computational grids is presented. The convective flows in the induction equation are approximated with the counterflow scheme using quadratic interpolation and the deferred correction method.

Keywords: induction equation, discrete analog, numerical method, magnetohydrodynamics.

DOI: 10.51790/2712-9942-2022-3-2-8