Two magnetohydrodynamic models will be developed to study non-thermal heating, the generation of directed plasma flows, and energetic particle acceleration processes in solar and stellar atmospheres. A critical component of both simulations will be a realistic description of transport processes in the form of anisotropic tensors for electric and thermal conductivities, as well as viscosity. Such a treatment is necessary when magnetized plasma is neither in a collisionless, nor collision-dominated regime. One model will describe the propagation of small amplitude waves in two spatial dimensions with special emphasis on the role of Pedersen currents in heating the plasma where ions are "magnetized" (i.e., the product of the cyclotron frequency and the collision time is of order unity). The second model will treat time-dependent shock formation in one spatial dimension and its impact on heating and the formation of supersonic jets.
