Multiple-Relaxation-Time Lattice Boltzmann scheme for fractional advection–diffusion equation

Autor: Amina Younsi, Alain Cartalade, Marie-Christine Néel
Přispěvatelé: Département de Modélisation des Systèmes et Structures (DM2S), CEA-Direction de l'Energie Nucléaire (CEA-DEN), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay, FRAMATOME-ANP, Environnement Méditerranéen et Modélisation des Agro-Hydrosystèmes (EMMAH), Avignon Université (AU)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), CEA-Direction des Energies (ex-Direction de l'Energie Nucléaire) (CEA-DES (ex-DEN))
Jazyk: angličtina
Rok vydání: 2019
Předmět:
Anisotropic diffusion
Lattice Boltzmann method
Lattice Boltzmann methods
General Physics and Astronomy
FOS: Physical sciences
01 natural sciences
Multiple-Relaxation-Time
010305 fluids & plasmas
Stable Process
[PHYS.PHYS.PHYS-COMP-PH]Physics [physics]/Physics [physics]/Computational Physics [physics.comp-ph]
symbols.namesake
0103 physical sciences
FOS: Mathematics
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
Tensor
Mathematics - Numerical Analysis
010306 general physics
Fractional Advection-Diffusion Equation
Physics
Partial differential equation
Numerical analysis
Mathematical analysis
Numerical Analysis (math.NA)
Computational Physics (physics.comp-ph)
Random walk
Nonlinear Sciences::Cellular Automata and Lattice Gases
Hardware and Architecture
Dirichlet boundary condition
Random Walk
symbols
Convection–diffusion equation
Physics - Computational Physics
Zdroj: Computer Physics Communications
Computer Physics Communications, Elsevier, 2019, 234, pp.40-54. ⟨10.1016/j.cpc.2018.08.005⟩
Computer Physics Communications, 2019, 234, pp.40-54. ⟨10.1016/j.cpc.2018.08.005⟩
ISSN: 0010-4655
DOI: 10.1016/j.cpc.2018.08.005⟩
Popis: Partial differential equations (p.d.e) equipped of spatial derivatives of fractional order capture anomalous transport behaviors observed in diverse fields of Science. A number of numerical methods approximate their solutions in dimension one. Focusing our effort on such p.d.e. in higher dimension with Dirichlet boundary conditions, we present an approximation based on Lattice Boltzmann Method with Bhatnagar-Gross-Krook (BGK) or Multiple-Relaxation-Time (MRT) collision operators. First, an equilibrium distribution function is defined for simulating space-fractional diffusion equations in dimensions 2 and 3. Then, we check the accuracy of the solutions by comparing with i) random walks derived from stable L\'evy motion, and ii) exact solutions. Because of its additional freedom degrees, the MRT collision operator provides accurate approximations to space-fractional advection-diffusion equations, even in the cases which the BGK fails to represent because of anisotropic diffusion tensor or of flow rate destabilizing the BGK LBM scheme.
Comment: Final version accepted in Computer Physics Communications. 23 pages, 25 figures
Databáze: OpenAIRE
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