Global Constraints Preserving Scalar Auxiliary Variable Schemes for Gradient Flows

We develop several efficient numerical schemes which preserve exactly the global constraints for constrained gradient flows. Our schemes are based on the scalar auxiliary variable (SAV) approach combined with the Lagrangian multiplier approach. They are as efficient as the SAV schemes for unconstrained gradient flows, i.e., only require solving linear equations with constant coefficients at each time step plus an additional nonlinear algebraic system which can be solved at negligible cost, can be unconditionally energy stable, and preserves exactly the global constraints for constrained gradient flows. Ample numerical results for phase-field vesicle membrane and optimal partition models are presented to validate the effectiveness and accuracy of the proposed numerical schemes.