  In this paper, we consider a novel auxiliary variable method to obtain energy
stable schemes for gradient flows. The auxiliary variable based on energy
bounded above does not limited to the hypothetical conditions adopted in
previous approaches. We proved the unconditional energy stability for all the
semi-discrete schemes carefully and rigorously. The novelty of the proposed
schemes is that the computed values for the functional in square root are
guaranteed to be positive. This method, termed novel auxiliary energy variable
(NAEV) method does not consider any bounded below restrictions any longer.
However, these restrictions are necessary in invariant energy quadratization
(IEQ) and scalar auxiliary variable (SAV) approaches which are very popular
methods recently. This property of guaranteed positivity is not available in
previous approaches. A comparative study of classical SAV and NAEV approaches
is considered to show the accuracy and efficiency. Finally, we present various
2D numerical simulations to demonstrate the stability and accuracy.
