2017/06/28 by Alain Cartalade, Cartalade, Alain, Amina Younsi +3
Engineering · Mathematics · #Lattice Boltzmann Simulation Studies #Fractional Differential Equations Solutions #Heat and Mass Transfer in Porous Media
paper · pdf · doi:10.48550/arxiv.1706.09161
Partial differential equations (p.d.e) equipped of spatial derivatives of\nfractional order capture anomalous transport behaviors observed in diverse\nfields of Science. A number of numerical methods approximate their solutions in\ndimension one. Focusing our effort on such p.d.e. in higher dimension with\nDirichlet boundary conditions, we present an approximation based on Lattice\nBoltzmann Method with Bhatnagar-Gross-Krook (BGK) or Multiple-Relaxation-Time\n(MRT) collision operators. First, an equilibrium distribution function is\ndefined for simulating space-fractional diffusion equations in dimensions 2 and\n3. Then, we check the accuracy of the solutions by comparing with i) random\nwalks derived from stable L 'evy motion, and ii) exact solutions. Because of\nits additional freedom degrees, the MRT collision operator provides accurate\napproximations to space-fractional advection-diffusion equations, even in the\ncases which the BGK fails to represent because of anisotropic diffusion tensor\nor of flow rate destabilizing the BGK LBM scheme.\n