scholarly journals Arbitrarily high-order unconditionally energy stable SAV schemes for gradient flow models

2020 ◽  
Vol 249 ◽  
pp. 107033 ◽  
Author(s):  
Yuezheng Gong ◽  
Jia Zhao ◽  
Qi Wang
Keyword(s):  
Gradient Flow ◽  
High Order ◽  
Flow Models ◽  
Energy Stable

A New Class of High-Order Energy Stable Flux Reconstruction Schemes

2010 ◽  
Vol 47 (1) ◽  
pp. 50-72 ◽  
Author(s):  
P. E. Vincent ◽  
P. Castonguay ◽  
A. Jameson
Keyword(s):  
High Order ◽  
Flux Reconstruction ◽  
New Class ◽  
Order Energy ◽  
Energy Stable

scholarly journals A High-Order Convex Splitting Method for a Non-Additive Cahn–Hilliard Energy Functional

Mathematics ◽  
2019 ◽  
Vol 7 (12) ◽  
pp. 1242 ◽  
Author(s):  
Hyun Geun Lee ◽  
Jaemin Shin ◽  
June-Yub Lee
Keyword(s):  
Splitting Method ◽  
Partition Of Unity ◽  
Energy Functional ◽  
High Order ◽  
Third Order ◽  
Energy Functionals ◽  
Runge Kutta Method ◽  
Highly Nonlinear ◽  
Convex Splitting ◽  
Energy Stable

Various Cahn–Hilliard (CH) energy functionals have been introduced to model phase separation in multi-component system. Mathematically consistent models have highly nonlinear terms linked together, thus it is not well-known how to split this type of energy. In this paper, we propose a new convex splitting and a constrained Convex Splitting (cCS) scheme based on the splitting. We show analytically that the cCS scheme is mass conserving and satisfies the partition of unity constraint at the next time level. It is uniquely solvable and energy stable. Furthermore, we combine the convex splitting with the specially designed implicit–explicit Runge–Kutta method to develop a high-order (up to third-order) cCS scheme for the multi-component CH system. We also show analytically that the high-order cCS scheme is unconditionally energy stable. Numerical experiments with ternary and quaternary systems are presented, demonstrating the accuracy, energy stability, and capability of the proposed high-order cCS scheme.

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