We propose a class of up to fourth-order maximum-principle-preserving and mass-conserving schemes for the conservative Allen-Cahn equation equipped with a non-local Lagrange multiplier.Based on the second-order finite...We propose a class of up to fourth-order maximum-principle-preserving and mass-conserving schemes for the conservative Allen-Cahn equation equipped with a non-local Lagrange multiplier.Based on the second-order finite-difference semidiscretization in the spatial direction,the integrating factor Runge-Kutta schemes are applied in the temporal direction.Theoretical analysis indicates that the proposed schemes conserve mass and preserve the maximum principle under reasonable time step-size restriction,which is independent of the space step size.Finally,the theoretical analysis is verified by several numerical examples.展开更多
The authors are concerned with the sharp interface limit for an incompressible Navier-Stokes and Allen-Cahn coupled system in this paper.When the thickness of the diffuse interfacial zone,which is parameterized by ε,...The authors are concerned with the sharp interface limit for an incompressible Navier-Stokes and Allen-Cahn coupled system in this paper.When the thickness of the diffuse interfacial zone,which is parameterized by ε,goes to zero,they prove that a solution of the incompressible Navier-Stokes and Allen-Cahn coupled system converges to a solution of a sharp interface model in the L^(∞)(L^(2))∩L^(2)(H^(1))sense on a uniform time interval independent of the small parameterε.The proof consists of two parts:One is the construction of a suitable approximate solution and another is the estimate of the error functions in Sobolev spaces.Besides the careful energy estimates,a spectral estimate of the linearized operator for the incompressible Navier-Stokes and Allen-Cahn coupled system around the approximate solution is essentially used to derive the uniform estimates of the error functions.The convergence of the velocity is well expected due to the fact that the layer of the velocity across the diffuse interfacial zone is relatively weak.展开更多
基金the National Key R&D Program of China(No.2020YFA0709800)the National Key Project(No.GJXM92579)the National Natural Science Foundation of China(No.12071481)。
文摘We propose a class of up to fourth-order maximum-principle-preserving and mass-conserving schemes for the conservative Allen-Cahn equation equipped with a non-local Lagrange multiplier.Based on the second-order finite-difference semidiscretization in the spatial direction,the integrating factor Runge-Kutta schemes are applied in the temporal direction.Theoretical analysis indicates that the proposed schemes conserve mass and preserve the maximum principle under reasonable time step-size restriction,which is independent of the space step size.Finally,the theoretical analysis is verified by several numerical examples.
基金supported by the National Natural Science Foundation of China(Nos.12271359,11831003,12161141004,11631008)Shanghai Science and Technology Innovation Action Plan(No.20JC1413000)+3 种基金the National Key R&D Program(No.2020YFA0712200)the National Key Project(No.GJXM92579)the Sino-German Science Center(No.GZ 1465)the ISF-NSFC Joint Research Program(No.11761141008)。
文摘The authors are concerned with the sharp interface limit for an incompressible Navier-Stokes and Allen-Cahn coupled system in this paper.When the thickness of the diffuse interfacial zone,which is parameterized by ε,goes to zero,they prove that a solution of the incompressible Navier-Stokes and Allen-Cahn coupled system converges to a solution of a sharp interface model in the L^(∞)(L^(2))∩L^(2)(H^(1))sense on a uniform time interval independent of the small parameterε.The proof consists of two parts:One is the construction of a suitable approximate solution and another is the estimate of the error functions in Sobolev spaces.Besides the careful energy estimates,a spectral estimate of the linearized operator for the incompressible Navier-Stokes and Allen-Cahn coupled system around the approximate solution is essentially used to derive the uniform estimates of the error functions.The convergence of the velocity is well expected due to the fact that the layer of the velocity across the diffuse interfacial zone is relatively weak.
