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A Multilevel Finite Difference Scheme for One‐Dimensional Burgers Equation Derived from the Lattice Boltzmann Method

https://doi.org/10.1155/2012/925920
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What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1006/jcph.1994.1181openalex-snapshot
Fully-Lagrangian and Lattice-Boltzmann Methods for Solving Systems of Conservation Equations
inferredcites →https://doi.org/10.1006/jcph.2000.6486openalex-snapshot
A Lattice Boltzmann Equation for Waves
inferredcites →https://doi.org/10.1006/jcph.2000.6491openalex-snapshot
Convection-Diffusion Lattice Boltzmann Scheme for Irregular Lattices
inferredcites →https://doi.org/10.1007/978-3-662-08276-8openalex-snapshot
Lattice Boltzmann Methods for Shallow Water Flows
inferredcites →https://doi.org/10.1007/s10955-010-0004-yopenalex-snapshot
An Accurate Multi-level Finite Difference Scheme for 1D Diffusion Equations Derived from the Lattice Boltzmann Method
inferredcites →https://doi.org/10.1016/0370-1573(92)90090-mopenalex-snapshot
The lattice Boltzmann equation: theory and applications
inferredcites →https://doi.org/10.1016/j.amc.2006.02.020openalex-snapshot
A lattice Boltzmann model for reaction dynamical systems with time delay
inferredcites →https://doi.org/10.1016/j.amc.2009.05.047openalex-snapshot
A new lattice Boltzmann model for the laplace equation
inferredcites →https://doi.org/10.1016/j.apm.2007.06.033openalex-snapshot
A novel lattice Boltzmann model for the Poisson equation
inferredcites →https://doi.org/10.1016/j.cam.2006.08.002openalex-snapshot
Lattice Boltzmann model for two-dimensional unsteady Burgers’ equation
inferredcites →https://doi.org/10.1016/j.cam.2007.03.010openalex-snapshot
Numerical solution of one-dimensional Burgers’ equation using reproducing kernel function
inferredcites →https://doi.org/10.1016/j.cnsns.2010.02.025openalex-snapshot
Numerical solutions of two-dimensional Burgers’ equations by lattice Boltzmann method
inferredcites →https://doi.org/10.1016/j.cpc.2008.12.027openalex-snapshot
A lattice Boltzmann model for the Korteweg–de Vries equation with two conservation laws
inferredcites →https://doi.org/10.1016/j.physa.2008.04.002openalex-snapshot
Lattice Boltzmann method for one and two-dimensional Burgers equation
inferredcites →https://doi.org/10.1016/s0065-2156(08)70100-5openalex-snapshot
A Mathematical Model Illustrating the Theory of Turbulence
inferredcites →https://doi.org/10.1023/a:1023273603637openalex-snapshot
Fully Lagrangian and Lattice Boltzmann Methods for the Advection-Diffusion Equation
inferredcites →https://doi.org/10.1063/1.464316openalex-snapshot
Lattice Boltzmann computations for reaction-diffusion equations
inferredcites →https://doi.org/10.1090/s0025-5718-1953-0059077-7openalex-snapshot
Stability conditions in the numerical treatment of parabolic differential equations
inferredcites →https://doi.org/10.1103/physreve.56.6811openalex-snapshot
Theory of the lattice Boltzmann method: From the Boltzmann equation to the lattice Boltzmann equation
inferredcites →https://doi.org/10.1103/physreve.80.026706openalex-snapshot
Lattice Boltzmann model for wave propagation
inferredcites →https://doi.org/10.1103/physrevlett.56.1505openalex-snapshot
Lattice-Gas Automata for the Navier-Stokes Equation
inferredcites →https://doi.org/10.1103/physrevlett.61.2332openalex-snapshot
Use of the Boltzmann Equation to Simulate Lattice-Gas Automata
inferredcites →https://doi.org/10.1126/science.1085048openalex-snapshot
Extended Boltzmann Kinetic Equation for Turbulent Flows
inferredcites →https://doi.org/10.1137/0732062openalex-snapshot
Convergence of Convective–Diffusive Lattice Boltzmann Methods
inferredcites →https://doi.org/10.1146/annurev.fluid.30.1.329openalex-snapshot
LATTICE BOLTZMANN METHOD FOR FLUID FLOWS
inferredcites →https://doi.org/10.1146/fluid.698openalex-snapshot
Annual Review of Fluid Mechanics
inferredcites →https://doi.org/10.1175/1520-0493(1915)43<163:srrotm>2.0.co;2openalex-snapshot
SOME RECENT RESEARCHES ON THE MOTION OF FLUIDS
inferredcites →https://doi.org/10.1299/jsmeb.44.45openalex-snapshot
The Lattice BGK Model for the Poisson Equation
inferredcites →https://doi.org/10.2307/2002754openalex-snapshot
Stability Conditions in the Numerical Treatment of Parabolic Differential Equations
inferredcites →https://doi.org/10.2307/2280580openalex-snapshot
Mathematical Tables and Other Aids to Computation.

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

inferred← citeshttps://doi.org/10.2139/ssrn.4479918openalex-extracted
A General Fourth-Order Mesoscopic Multiple-Relaxation-Time Lattice Boltzmann Model and Equivalent Macroscopic Finite-Difference Scheme for Two-Dimensional Diffusion Equations
inferred← citeshttps://doi.org/10.2139/ssrn.4607624openalex-extracted
The Macroscopic Finite-Difference Scheme and Modified Equations of the General Propagation Multiple-Relaxation-Time Lattice Boltzmann Model
inferred← citeshttps://doi.org/10.1002/mma.9255openalex-snapshot
A multiple‐relaxation‐time lattice Boltzmann model for Burgers equation
inferred← citeshttps://doi.org/10.1007/s10915-014-9827-zopenalex-snapshot
An Efficient Lattice Boltzmann Model for Steady Convection–Diffusion Equation
inferred← citeshttps://doi.org/10.1007/s40314-021-01692-3openalex-snapshot
An efficient Strang splitting technique combined with the multiquadric-radial basis function for the Burgers’ equation
inferred← citeshttps://doi.org/10.1016/j.amc.2017.12.027openalex-snapshot
Linear Bhatnagar–Gross–Krook equations for simulation of linear diffusion equation by lattice Boltzmann method
inferred← citeshttps://doi.org/10.1016/j.jcp.2024.113045openalex-snapshot
A general fourth-order mesoscopic multiple-relaxation-time lattice Boltzmann model and its macroscopic finite-difference scheme for two-dimensional diffusion equations
inferred← citeshttps://doi.org/10.1016/j.jcp.2025.113831openalex-snapshot
Regularized lattice Boltzmann method based maximum principle and energy stability preserving finite-difference scheme for the Allen-Cahn equation
inferred← citeshttps://doi.org/10.1080/00207160.2014.927059openalex-snapshot
On two linearized difference schemes for Burgers’ equation
inferred← citeshttps://doi.org/10.1088/1755-1315/158/1/012022openalex-snapshot
Revenue management of air cargo service in theory and practice
inferred← citeshttps://doi.org/10.1103/61zg-dmhhopenalex-snapshot
Equilibrium-distribution-function-based mesoscopic finite-difference methods for partial differential equations: Modeling and analysis
inferred← citeshttps://doi.org/10.1103/physreve.104.015312openalex-snapshot
Multiple-relaxation-time lattice Boltzmann model-based four-level finite-difference scheme for one-dimensional diffusion equations
inferred← citeshttps://doi.org/10.1103/physreve.107.055305openalex-snapshot
Fourth-order multiple-relaxation-time lattice Boltzmann model and equivalent finite-difference scheme for one-dimensional convection-diffusion equations
inferred← citeshttps://doi.org/10.1103/physreve.109.025301openalex-snapshot
Macroscopic finite-difference scheme based on the mesoscopic regularized lattice-Boltzmann method
inferred← citeshttps://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
inferred← citeshttps://doi.org/10.1134/s1995080225610914openalex-snapshot
Multiple Relaxation Time Lattice Boltzmann Model for Anisotropic Allen–Cahn Diffusion and Applications to Vessel Segmentation
inferred← citeshttps://doi.org/10.2139/ssrn.4946572openalex-snapshot
Regularized Lattice Boltzmann Method Based Maximum Principle and Energy Stability Preserving Finite-Difference Scheme for the Allen-Cahn Equation
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