A result of convergence for a mono-dimensional two-velocities lattice Boltzmann scheme Article Swipe
Related Concepts
Mathematics
Mathematical analysis
Burgers' equation
Lattice Boltzmann methods
Maximum entropy probability distribution
Partial differential equation
Hyperbolic partial differential equation
Entropy (arrow of time)
Applied mathematics
Boltzmann equation
Physics
Principle of maximum entropy
Mechanics
Thermodynamics
Statistics
Filipa Caetano
,
François Dubois
,
Benjamin Graille
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.3934/dcdss.2023072
· OA: W2947280453
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.3934/dcdss.2023072
· OA: W2947280453
We consider a mono-dimensional two-velocities scheme used to approximate the\nsolutions of a scalar hyperbolic conservative partial differential equation. We\nprove the convergence of the discrete solution toward the unique entropy\nsolution by first estimating the supremum norm and the total variation of the\ndiscrete solution, and second by constructing a discrete kinetic\nentropy-entropy flux pair being given a continuous entropy-entropy flux pair of\nthe hyperbolic system. We finally illustrate our results with numerical\nsimulations of the advection equation and the Burgers equation.\n
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