Generalized second moment method for advection and diffusion processes
Abstract
A semi-Lagrangian numerical scheme known as the second moment method is generalized to simulate the advection and diffusion processes. By making a correction to the procedure for the diffusion process, the stability and convergence of the method are improved. The generalized method is positive definite and unconditionally stable. Numerical experiments were conducted and compared with the exact solution of the advection-diffusion equation. The condition for convergence of the numerical solutions to the exact solution is determined for the entire range of Courant and Péclet numbers.
Fields of Study & Subjects
Differential Equations and Numerical Methods
Advanced Numerical Methods in Computational Mathematics
Computational Fluid Dynamics and Aerodynamics
Publication details
- Journal / source
- CRC Press eBooks
- Pages
- 357–362
- Publication date
- 12 February 2026
- Language
- EN
- Document type
- Book chapter