Conservation form in computational magnetohydrodynamics

The question of whether or not to use a conservation form of the internal energy equation in computational magnetohydrodynamics is considered. Conservation errors resulting from both spatial and temporal difference methods are demonstrated, and means of eliminating the spatial errors and reducing the temporal ones are discussed. It is shown that only in the limit Δt → 0 can a nonconservation form of the internal energy equation be used without destroying in the finite difference equations any of the conservation properties of the magnetohydrodynamic partial differential equations