Voigt regularization for the explicit time stepping of the Hall effect term

Abstract

This article studies the stabilization of the explicit time stepping methods for Hall Maxwell and incompressible Hall MHD equations. Since the Hall effect term contains two spatial derivatives, classical time-stepping schemes result in very restrictive CFL condition. We consider weakening the restrictive time step condition via Voigt regularization. We establish the energy stability result and validate our approach numerically. Numerical experiments demonstrate that we are able to take larger time steps, compared to classical schemes, at additional, negligible computational cost. ARTICLE HISTORY

Second‐order efficient nonlinear filter stabilization for high Reynolds number flows

“…The corresponding model PDE of (33) is then given by: The last term on the left hand side can be readily recognized as the Voigt regularization term of order , and therefore the time‐relaxation [11, 38] introduced by it should be negligible. The next‐to‐last term can be recognized as an turbulent diffusion term with the turbulent viscosity coefficient .…”

“…The last term on the left hand side can be readily recognized as the Voigt regularization term of order 𝒪 ( 𝛿 2 𝜏 ) , and therefore the time-relaxation [11,38] introduced by it should be negligible. The next-to-last term can be recognized as an turbulent diffusion term with the turbulent viscosity coefficient 𝜈 T = 3𝜒 2𝜏 𝛿 2 a(u).…”

“…In our simulations presented below, we used h min as the value of the filtering radius 𝛿 in (38). However when solving (7), 𝛿 was picked as the local element diameter.…”