We extend previous work on nonstandard finite difference schemes for one-space dimension, nonlinear reaction-diffusion PDEs to the case where linear advection is included. The use of a positivity condition allows the determination of a functional relation between the time and space step-sizes, and p
ADER Schemes for Nonlinear Systems of Stiff Advection–Diffusion–Reaction Equations
✍ Scribed by Arturo Hidalgo; Michael Dumbser
- Publisher
- Springer US
- Year
- 2010
- Tongue
- English
- Weight
- 827 KB
- Volume
- 48
- Category
- Article
- ISSN
- 0885-7474
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
For reaction-diffusion-advection equations, the stiffness from the reaction and diffusion terms often requires very restricted time step size, while the nonlinear advection term may lead to a sharp gradient in localized spatial regions. It is challenging to design numerical methods that can efficien
A family of ELLAM (Eulerian-Lagrangian localized adjoint method) schemes is developed and analyzed for linear advection-diffusion-reaction transport partial differential equations with any combination of inflow and outflow Dirichlet, Neumann, or flux boundary conditions. The formulation uses space-t
An important class of physical phenomena in acoustics, #uid dynamics, and the transport of contaminants can be modelled by the partial di!erential equation [1}3]