TY - JOUR
T1 - Stability of High Order Finite Difference Schemes with Implicit-Explicit Time-Marching for Convection-Diffusion and Convection-Dispersion Equations
AU - Tan , Meiqi
AU - Cheng , Juan
AU - Shu , Chi-Wang
JO - International Journal of Numerical Analysis and Modeling
VL - 3
SP - 362
EP - 383
PY - 2021
DA - 2021/03
SN - 18
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/18730.html
KW - Convection-diffusion equation, convection-dispersion equation, stability, IMEX,
finite difference, Fourier method.
AB - <p style="text-align: justify;">The main purpose of this paper is to analyze the stability of the implicit-explicit
(IMEX) time-marching methods coupled with high order finite difference spatial discretization
for solving the linear convection-diffusion and convection-dispersion equations in one dimension.
Both Runge-Kutta and multistep IMEX methods are considered. Stability analysis is performed
on the above mentioned schemes with uniform meshes and periodic boundary condition by the aid
of the Fourier method. For the convection-diffusion equations, the result shows that the high order
IMEX finite difference schemes are subject to the time step restriction $∆t ≤$ max{$τ_0, c∆x$}, where $τ_0$ is a positive constant proportional to the diffusion coefficient and c is the Courant number. For
the convection-dispersion equations, we show that the IMEX finite difference schemes are stable
under the standard CFL condition $∆t ≤ c∆x$. Numerical experiments are also given to verify the
main results.<br/></p>