We propose a second order, fully semi-Lagrangian method for the numerical solution of systems of advection-diffusion-reaction equations, which is based on a semi-Lagrangian approach to approximate in time both the advective and the diffusive terms. The proposed method allows to use large time steps, while avoiding the solution of large linear systems, which would be required by implicit time discretization techniques. Standard interpolation procedures are used for the space discretization on structured and unstructured meshes. A novel extrapolation technique is proposed to enforce second-order accurate Dirichlet boundary conditions. We include a theoretical analysis of the scheme, along with numerical experiments which demonstrate the effectiveness of the proposed approach and its superior efficiency with respect to more conventional explicit and implicit time discretizations.
Second Order Fully Semi-Lagrangian Discretizations of Advection-Diffusion-Reaction Systems / Bonaventura, Luca; Calzola, Elisa; Carlini, Elisabetta; Ferretti, Roberto. - In: JOURNAL OF SCIENTIFIC COMPUTING. - ISSN 1573-7691. - 88:(2021). [10.1007/s10915-021-01518-8]
Second Order Fully Semi-Lagrangian Discretizations of Advection-Diffusion-Reaction Systems
Elisa Calzola;Elisabetta Carlini;Roberto Ferretti
2021
Abstract
We propose a second order, fully semi-Lagrangian method for the numerical solution of systems of advection-diffusion-reaction equations, which is based on a semi-Lagrangian approach to approximate in time both the advective and the diffusive terms. The proposed method allows to use large time steps, while avoiding the solution of large linear systems, which would be required by implicit time discretization techniques. Standard interpolation procedures are used for the space discretization on structured and unstructured meshes. A novel extrapolation technique is proposed to enforce second-order accurate Dirichlet boundary conditions. We include a theoretical analysis of the scheme, along with numerical experiments which demonstrate the effectiveness of the proposed approach and its superior efficiency with respect to more conventional explicit and implicit time discretizations.File | Dimensione | Formato | |
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