High-order and mass conservative methods for the conservative Allen-Cahn equation. (English) Zbl 1359.65216
Summary: The conservative Allen-Cahn (AC) equation has been studied analytically and numerically. Our mathematical analysis and numerical experiment, however, show that previous numerical methods are not second-order accurate in time and/or do not conserve the initial mass. The aim of this paper is to propose high-order and mass conservative methods for solving the conservative AC equation. In the methods, we discretize the conservative AC equation by using a Fourier spectral method in space and first-, second-, and third-order implicit-explicit Runge-Kutta schemes in time. We show that the methods inherit the mass conservation. Numerical experiments are presented demonstrating the accuracy and efficiency of proposed methods.
MSC:
| 65M70 | Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs |
| 80A22 | Stefan problems, phase changes, etc. |
| 82C26 | Dynamic and nonequilibrium phase transitions (general) in statistical mechanics |
Keywords:
conservative Allen-Cahn equation; high-order method; mass conservative method; Fourier spectral methodReferences:
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