A generalized SAV approach with relaxation for dissipative systems

Abstract

The scalar auxiliary variable (SAV) approach \cite{shen2018scalar} and its generalized version GSAV proposed in \cite{huang2020highly} are very popular methods to construct efficient and accurate energy stable schemes for nonlinear dissipative systems. However, the discrete value of the SAV is not directly linked to the free energy of the dissipative system, and may lead to inaccurate solutions if the time step is not sufficiently small. Inspired by the relaxed SAV method proposed in \cite{jiang2022improving} for gradient flows, we propose in this paper a generalized SAV approach with relaxation (R-GSAV) for general dissipative systems. The R-GSAV approach preserves all the advantages of the GSAV appraoch, in addition, it dissipates a modified energy that is directly linked to the original free energy. We prove that the $k$-th order implicit-explicit (IMEX) schemes based on R-GSAV are unconditionally energy stable, and we carry out a rigorous error analysis for $k=1,2,3,4,5$. We present ample numerical results to demonstrate the improved accuracy and effectiveness of the R-GSAV approach.

References in corpus (2)

• Improving the Accuracy and Consistency of the Scalar Auxiliary Variable (SAV) Method with Relaxation
• Implicit-explicit BDF $k$ SAV schemes for general dissipative systems and their error analysis

Cited by in corpus (8)

• Efficient finite element schemes for a phase field model of two-phase incompressible flows with different densities
• The Deep Minimizing Movement Scheme
• A general class of linear unconditionally energy stable schemes for the gradient flows
• Stability and convergence of relaxed scalar auxiliary variable schemes for Cahn-Hilliard systems with bounded mass source
• The effect of contact angle hysteresis on a droplet in a viscoelastic two-phase system
• A Relaxed Lagrange Multiplier Approach for Phase Field Models
• A convergent stochastic scalar auxiliary variable method
• Analysis and numerical simulation of a generalized compressible Cahn-Hilliard-Navier-Stokes model with friction effects