Convergence analysis for second‐order accurate schemes for the periodic nonlocal Allen‐Cahn and Cahn‐Hilliard equations
Sign Up to like & getrecommendations! Published in 2017 at "Mathematical Methods in The Applied Sciences"
DOI: 10.1002/mma.4497
Abstract: In this paper, we provide a detailed convergence analysis for fully discrete second-order (in both time and space) numerical schemes for nonlocal Allen-Cahn and nonlocal Cahn-Hilliard equations. The unconditional unique solvability and energy stability ensures… read more here.
Keywords: nonlocal allen; allen cahn; convergence analysis; cahn ... See more keywords
Error estimate of the finite volume scheme for the Allen–Cahn equation
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DOI: 10.1007/s10543-017-0687-4
Abstract: The Allen–Cahn equation originates in the phase field formulation of phase transition phenomena. It is a reaction-diffusion ODE with a nonlinear reaction term which allows the formation of a diffuse phase interface. We first introduce… read more here.
Keywords: cahn equation; finite volume; scheme; allen cahn ... See more keywords
Second Order Linear Energy Stable Schemes for Allen-Cahn Equations with Nonlocal Constraints
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DOI: 10.1007/s10915-019-00946-x
Abstract: We present a set of linear, second order, unconditionally energy stable schemes for the Allen-Cahn equation with nonlocal constraints that preserves the total volume of each phase in a binary material system. The energy quadratization… read more here.
Keywords: nonlocal constraints; energy; second order; allen cahn ... See more keywords
Energy minimisers of prescribed winding number in an S1-valued nonlocal Allen-Cahn type model
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DOI: 10.1016/j.aim.2019.106819
Abstract: Abstract We study a variational model for transition layers with an underlying functional that combines an Allen-Cahn type structure with an additional nonlocal interaction term. A transition layer is represented by a map from R… read more here.
Keywords: prescribed winding; cahn type; model; allen cahn ... See more keywords
An Allen–Cahn equation based on an unconstrained order parameter and its Cahn–Hilliard limit
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2021.125486
Abstract: Abstract Our aim in this paper is to study an Allen–Cahn model based on a microforce balance and an unconstrained order parameter. We obtain the existence, uniqueness and regularity of solutions and prove that the… read more here.
Keywords: order parameter; cahn hilliard; parameter; allen cahn ... See more keywords
A practical adaptive grid method for the Allen–Cahn equation
Sign Up to like & getrecommendations! Published in 2021 at "Physica A: Statistical Mechanics and its Applications"
DOI: 10.1016/j.physa.2021.125975
Abstract: Abstract We present a simple and practical adaptive finite difference method for the Allen–Cahn (AC) equation in the two-dimensional space. We use a temporally adaptive narrow band domain embedded in the uniform discrete rectangular domain.… read more here.
Keywords: practical adaptive; cahn equation; method; equation ... See more keywords
Entire solutions originating from monotone fronts to the Allen–Cahn equation
Sign Up to like & getrecommendations! Published in 2018 at "Physica D: Nonlinear Phenomena"
DOI: 10.1016/j.physd.2018.04.003
Abstract: Abstract In this paper, we study entire solutions of the Allen–Cahn equation in one-dimensional Euclidean space. This equation is a scalar reaction–diffusion equation with a bistable nonlinearity. It is well-known that this equation admits three… read more here.
Keywords: originating monotone; cahn equation; solutions originating; allen cahn ... See more keywords
Comparison of operator splitting schemes for the numerical solution of the Allen-Cahn equation
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DOI: 10.1063/1.5126651
Abstract: In this paper, we have analyzed the first- and second-order operator splitting schemes for the numerical solution of the Allen-Cahn equation. Different possibilities are considered for the derivation of the schemes. The numerical errors are… read more here.
Keywords: splitting schemes; numerical solution; solution allen; allen cahn ... See more keywords
The stability of the equilibria of the Allen–Cahn equation with fractional diffusion
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DOI: 10.1080/00036811.2017.1399360
Abstract: ABSTRACT This paper is mainly concerned with the stability of the equilibria of the Allen–Cahn equation where the standard Laplacian diffusion is replaced by the fractional Laplacian diffusion. We shall show that the state is… read more here.
Keywords: diffusion; cahn equation; stability equilibria; equilibria allen ... See more keywords
Regularity of solutions to 1D compressible Navier–Stokes–Allen–Cahn system
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DOI: 10.1080/00036811.2019.1668554
Abstract: In this paper, we investigate the compressible Navier–Stokes equations coupled with an Allen–Cahn phase field description, which describes two-phase patterns in a flowing liquid including phase transformations. Our purpose is to establish the regularity of… read more here.
Keywords: compressible navier; stokes allen; allen cahn; cahn system ... See more keywords
Structural topology optimization through implicit boundary evolution based on the Allen–Cahn equation
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DOI: 10.1080/0305215x.2019.1705288
Abstract: ABSTRACT An improved phase-field method based on the Allen–Cahn (AC) equation is proposed for topology optimization to obtain the optimized structure with a smooth and clear boundary. In the proposed method, the design structure is… read more here.
Keywords: based allen; phase field; allen cahn; topology ... See more keywords