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Energy-stable Runge–Kutta schemes for gradient flow models using the energy quadratization approach
- Source :
- Applied Mathematics Letters. 94:224-231
- Publication Year :
- 2019
- Publisher :
- Elsevier BV, 2019.
-
Abstract
- In this letter, we present a novel class of arbitrarily high-order and unconditionally energy-stable algorithms for gradient flow models by combining the energy quadratization (EQ) technique and a specific class of Runge–Kutta (RK) methods, which is named the EQRK schemes. First of all, we introduce auxiliary variables to transform the original model into an equivalent system, with the transformed free energy a quadratic functional with respect to the new variables and the modified energy dissipative law is conserved. Then a special class of RK methods is employed for the reformulated system to arrive at structure-preserving time-discrete schemes. Along with rigorous proofs, numerical experiments are presented to demonstrate the accuracy and unconditionally energy-stability of the EQRK schemes.
- Subjects :
- Class (set theory)
Applied Mathematics
010102 general mathematics
Mathematical proof
01 natural sciences
010101 applied mathematics
Auxiliary variables
Runge–Kutta methods
Dissipative system
Applied mathematics
0101 mathematics
Balanced flow
Energy (signal processing)
Quadratic functional
Mathematics
Subjects
Details
- ISSN :
- 08939659
- Volume :
- 94
- Database :
- OpenAIRE
- Journal :
- Applied Mathematics Letters
- Accession number :
- edsair.doi...........fa2a580c43fc4de09fecb265bea74225