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Regularized Lattice Boltzmann Method Based Maximum Principle and Energy Stability Preserving Finite-Difference Scheme for the Allen-Cahn Equation

https://doi.org/10.2139/ssrn.4946572
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A finite difference interpretation of the lattice Boltzmann method
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The Lattice Boltzmann Method: Principles and Practice
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Numerical analysis of the Allen-Cahn equation and approximation for mean curvature flows
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Finite Difference formulation of any lattice Boltzmann scheme
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Numerical Analysis of Fully Discretized Crank–Nicolson Scheme for Fractional-in-Space Allen–Cahn Equations
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Arbitrarily High-Order Maximum Bound Preserving Schemes with Cut-off Postprocessing for Allen–Cahn Equations
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Stabilized Exponential-SAV Schemes Preserving Energy Dissipation Law and Maximum Bound Principle for The Allen–Cahn Type Equations
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A Cole–Hopf Transformation Based Fourth-Order Multiple-Relaxation-Time Lattice Boltzmann Model for the Coupled Burgers’ Equations
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Analysis of Lattice Boltzmann Initialization Routines
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An Accurate Multi-level Finite Difference Scheme for 1D Diffusion Equations Derived from the Lattice Boltzmann Method
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On the preserving of the maximum principle and energy stability of high-order implicit-explicit Runge-Kutta schemes for the space-fractional Allen-Cahn equation
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M-Matrix Theory and Recent Results in Numerical Linear Algebra
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Numerical analysis of a stabilized Crank–Nicolson/Adams–Bashforth finite difference scheme for Allen–Cahn equations
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A maximum-principle preserving and unconditionally energy-stable linear second-order finite difference scheme for Allen–Cahn equations
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Geometrical image segmentation by the Allen–Cahn equation
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Numerical analysis and applications of explicit high order maximum principle preserving integrating factor Runge-Kutta schemes for Allen-Cahn equation
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A second-order unconditionally stable method for the anisotropic dendritic crystal growth model with an orientation-field
inferredcites →https://doi.org/10.1016/j.cam.2018.02.026openalex-snapshot
An explicit hybrid finite difference scheme for the Allen–Cahn equation
inferredcites →https://doi.org/10.1016/j.camwa.2009.02.022openalex-snapshot
Smooth initialization of lattice Boltzmann schemes
inferredcites →https://doi.org/10.1016/j.camwa.2020.04.007openalex-snapshot
The numerical solutions for the energy-dissipative and mass-conservative Allen–Cahn equation
inferredcites →https://doi.org/10.1016/j.compfluid.2022.105735openalex-snapshot
Discrete effects on the source term for the lattice Boltzmann modelling of one-dimensional reaction–diffusion equations
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The scalar auxiliary variable (SAV) approach for gradient flows
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Initialisation from lattice Boltzmann to multi-step Finite Difference methods: Modified equations and discrete observability
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A second-order maximum bound principle preserving operator splitting method for the Allen–Cahn equation with applications in multi-phase systems
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Stability analysis for a maximum principle preserving explicit scheme of the Allen–Cahn equation
inferredcites →https://doi.org/10.1017/s0956792515000200openalex-snapshot
Mean curvature flow by the Allen–Cahn equation
inferredcites →https://doi.org/10.1051/m2an/2023008openalex-snapshot
Rigorous derivation of the macroscopic equations for the lattice Boltzmann method via the corresponding Finite Difference scheme
inferredcites →https://doi.org/10.1093/oso/9780198503989.001.0001openalex-snapshot
The Lattice Boltzmann Equation for Fluid Dynamics and Beyond
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Multiple-relaxation-time lattice Boltzmann method for the Navier-Stokes and nonlinear convection-diffusion equations: Modeling, analysis, and elements
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Multiple-relaxation-time lattice Boltzmann model-based four-level finite-difference scheme for one-dimensional diffusion equations
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Improved hybrid Allen-Cahn phase-field-based lattice Boltzmann method for incompressible two-phase flows
inferredcites →https://doi.org/10.1103/physreve.109.025301openalex-snapshot
Macroscopic finite-difference scheme based on the mesoscopic regularized lattice-Boltzmann method
inferredcites →https://doi.org/10.1103/physreve.109.065305openalex-snapshot
Macroscopic finite-difference scheme and modified equations of the general propagation multiple-relaxation-time lattice Boltzmann model
inferredcites →https://doi.org/10.1103/physreve.92.043311openalex-snapshot
Regularized lattice Boltzmann model for a class of convection-diffusion equations
inferredcites →https://doi.org/10.1137/18m118236xopenalex-snapshot
Maximum Principle Preserving Exponential Time Differencing Schemes for the Nonlocal Allen--Cahn Equation
inferredcites →https://doi.org/10.1137/19m1264412openalex-snapshot
Energy-Decaying Extrapolated RK--SAV Methods for the Allen--Cahn and Cahn--Hilliard Equations
inferredcites →https://doi.org/10.1137/19m1289157openalex-snapshot
On Energy Stable, Maximum-Principle Preserving, Second-Order BDF Scheme with Variable Steps for the Allen--Cahn Equation
inferredcites →https://doi.org/10.1137/20m1333456openalex-snapshot
Arbitrarily High-Order Exponential Cut-Off Methods for Preserving Maximum Principle of Parabolic Equations
inferredcites →https://doi.org/10.1137/20m1340678openalex-snapshot
Stabilized Integrating Factor Runge--Kutta Method and Unconditional Preservation of Maximum Bound Principle
inferredcites →https://doi.org/10.1137/21m1446496openalex-snapshot
Generalized SAV-Exponential Integrator Schemes for Allen--Cahn Type Gradient Flows
inferredcites →https://doi.org/10.1137/21m144877xopenalex-snapshot
A New Lagrange Multiplier Approach for Constructing Structure Preserving Schemes, II. Bound Preserving
inferredcites →https://doi.org/10.1137/22m1475120openalex-snapshot
A Diffuse-Domain Phase-Field Lattice Boltzmann Method for Two-Phase Flows in Complex Geometries
inferredcites →https://doi.org/10.1142/8806openalex-snapshot
Lattice Boltzmann Method and Its Applications in Engineering
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A Multilevel Finite Difference Scheme for One‐Dimensional Burgers Equation Derived from the Lattice Boltzmann Method
inferredcites →https://doi.org/10.26804/capi.2019.03.01openalex-snapshot
A brief review of the phase-field-based lattice Boltzmann method for multiphase flows
inferredcites →https://doi.org/10.4208/cicp.040913.220115aopenalex-snapshot
On Initial Conditions for the Lattice Boltzmann Method
inferredcites →https://doi.org/10.4208/cicp.301110.040811aopenalex-snapshot
Phase-Field Models for Multi-Component Fluid Flows
inferredcites →https://doi.org/10.4208/jcm.1603-m2014-0017openalex-snapshot
Implicit-Explicit Scheme for the Allen-Cahn Equation Preserves the Maximum Principle
inferredcites →https://doi.org/10.4310/cms.2016.v14.n6.a3openalex-snapshot
On the maximum principle preserving schemes for the generalized Allen–Cahn equation
inferredcites →https://doi.org/10.4310/jdg/1214454300openalex-snapshot
Convergence of the Allen-Cahn equation to Brakke's motion by mean curvature
inferredcites →https://doi.org/10.48550/arxiv.2302.07558openalex-snapshot
Initialisation from lattice Boltzmann to multi-step Finite Difference methods: modified equations and discrete observability
inferredcites →https://doi.org/10.7494/cmms.2020.4.0732openalex-snapshot
An accuracy analysis of the cascaded lattice Boltzmann method for the 1D advection-diffusion equation
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