Global Constraints Preserving Scalar Auxiliary Variable Schemes for Gradient Flows

2020/01/01 by Qing Cheng, Jie Shen
Computer Science · Engineering · Materials Science · #Fluid Dynamics and Thin Films #Nonlinear Dynamics and Pattern Formation #Solidification and crystal growth phenomena

paper · doi:10.1137/19m1306221

openalex publication_date 2020/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

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.

Citations

• Analysis and Approximation of Nonlocal Diffusion Problems with Volume Constraints
• Multiple Scalar Auxiliary Variable (MSAV) Approach and its Application to the Phase-Field Vesicle Membrane Model
• A New Class of Efficient and Robust Energy Stable Schemes for Gradient Flows

Related

• Global constraints preserving SAV schemes for gradient flows
• The generalized scalar auxiliary variable approach (G-SAV) for gradient flows
• A New Scalar Auxiliary Variable Approach for Gradient Flows
• A weighted scalar auxiliary variable method for solving gradient flows: bridging the nonlinear energy-based and Lagrange multiplier approaches
• Multiple Scalar Auxiliary Variable (MSAV) Approach and its Application to the Phase-Field Vesicle Membrane Model