Three-dimensional magnetic reconnection simulations using the Eulerian Conservative High Order (ECHO) code

Magnetic reconnection and shear driven instabilities are pervasive phenomena in the heliosphere and in astrophysical plasmas in general. Magnetic reconnection and instabilities require the use of high-order numerical approximations to study their linear and non-linear evolution. At the same time, in compressible MHD the dynamical activity following reconnection processes leads to formation of discontinuous modes which should be treated by shock-capturing numerical schemes. For this purpose we have designed an Eulerian Conservative High Order (ECHO) code in which, i) explicit diffusivity is taken into account, ii) high-order numerical approximations of flux derivatives are included and iii) shock-capturing algorithms are employed in managing flux discontinuities. This code has been applied successfully in studying the linear and non-linear 3D evolution of the tearing instability and in following the 3D evolution of a current sheet embedded in a sheared flow.