We propose in this paper three generalized auxiliary scalar variable (G-SAV) approaches for developing, efficient energy stable numerical schemes for gradient systems. The first two G-SAV approaches allow a range of functions in the definition of the SAV variable, furthermore, the second G-SAV approach only requires the total free energy to be bounded from below as opposed to the requirement that the nonlinear part of the free energy to be bounded from below. On the other hand, the third G-SAV approach is unconditionally energy stable with respect to the original free energy as opposed to a modified energy. Ample numerical results for various gradient systems are presented to validate the effectiveness and accuracy of the proposed G-SAV approaches.
All Science Journal Classification (ASJC) codes
- Computational Mathematics
- Applied Mathematics