Vector potential-based MHD solver for non-periodic flows using Fourier continuation expansions

Effect of electromagnetic boundary conditions on the onset of small-scale dynamos driven by convection

“…We studied the problem of attaining a dynamo state in a channel filled with a conducting fluid undergoing turbulent Rayleigh-Bénard convection. To this purpose, we performed multiple direct numerical simulations of the Boussinesq approximation to the MHD equations, utilizing a versatile numerical method with spectral convergence in the bulk of the flow, and very high order convergence near the boundaries [27]. We analyzed the growth or decay of an initially small and random magnetic field as a function of time, determining the critical magnetic Reynolds number Rm crit for which self-sustaining dynamo action becomes feasible for three electromagnetic boundary conditions at the floor and the top of the channel at fixed Ra, and then by varying Ra for a fixed boundary condition.…”

“…(1) to (3). The simulations are performed using the SPECTER parallel pseudo-spectral code [26,27], freely available at [35]. The equations are evolved in time using a double-precision second-order Runge-Kutta method.…”

“…The absence of magnetic monopoles (∇ • b = 0) is enforced to machine accuracy by evolving in time the vector potential a in the Coulomb gauge, defined by ∇ × a = b and ∇ • a = 0. Particularly relevant in the context of this study, SPECTER can implement different kinds of electromagnetic boundary conditions while retaining the cuasi-spectral convergence properties aforementioned [27] (as a reference, typical errors are (∇ • b) 2 < 10 −30 , while quadratic errors in the magnetic boundary conditions are of O(10 −10 ) or smaller). Previous studies of convective dynamos, using other numerical methods or simplified boundary conditions, can be found, e.g., in Refs.…”

“…[25,[37][38][39][40]. For more details of the high-order method used here, or for the full implementation of the electromagnetic boundary conditions, see [27].…”

“…In this letter we present a detailed numerical study of the influence of electromagnetic boundary conditions in the minimum magnetic Reynolds number required to observe dynamo action on a convecting flow forced by a temperature gradient. To this purpose direct numerical simulations (DNSs) of the three-dimensional (3D) non-linear MHD equations are employed, using a numerical method which guarantees quasi-spectral convergence for several types of boundary conditions while enforcing a solenoidal magnetic field to machine precision in non-trivial geometries [26,27]. In particular, perfectly conducting or vacuum electromagnetic conditions are considered at the boundaries, together with a combination of both scenarios.…”