Journal Article10.1002/NME.1620260711
A third-order semi-implicit finite difference method for solving the one-dimensional convection-diffusion equation
B. J. Noye,Hwee Huat Tan +1 more
90
About: This article is published in International Journal for Numerical Methods in Engineering. The article was published on 01 Jul 1988. The article focuses on the topics: Numerical solution of the convection–diffusion equation & Convection–diffusion equation.
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Citations
High order ADI method for solving unsteady convection-diffusion problems
Samir Karaa,Jun Zhang +1 more
TL;DR: A high order alternating direction implicit (ADI) solution method for solving unsteady convection-diffusion problems and it is shown through a discrete Fourier analysis that the method is unconditionally stable for 2D problems.
215
A class of higher order compact schemes for the unsteady two‐dimensional convection–diffusion equation with variable convection coefficients
TL;DR: In this article, a class of higher order compact (HOC) schemes with weighted time discretization for the two-dimensional unsteady convection-diffusion equation with variable convection coefficients was developed.
194
Extension of high‐order compact schemes to time‐dependent problems
W. F. Spotz,Graham F. Carey +1 more
TL;DR: In this paper, the authors present an extension of their previous approaches for steady-state higher-order compact (HOC) difference methods to time-dependent problems, and a stability analysis is provided for transient convection-diffusion in 1D and transient diffusion in 2D.
134
Physics-Informed Neural Network Method for Forward and Backward Advection-Dispersion Equations
TL;DR: In this paper, the authors proposed a discretization-free approach based on the physics-informed neural network (PINN) method for solving coupled advection dispersion and Darcy flow equations with space-dependent hydraulic conductivity.
90
Implicit finite difference techniques for the advection-diffusion equation using spreadsheets
TL;DR: By changing only the values of temporal and spatial weighted parameters with ADEISS implementation, solutions are implicitly obtained for the BTCS, Upwind and Crank-Nicolson schemes by using iterative spreadsheet solution technique.
65
References
Finite-difference methods for partial differential equations
George E. Forsythe,Wolfgang R. Wasow +1 more
- 01 Jan 1960
1.3K
The modified equation approach to the stability and accuracy analysis of finite-difference methods
R. F. Warming,B.J Hyett +1 more
TL;DR: In this paper, the stability and accuracy of finite-difference approximations to simple linear PDEs are analyzed by studying the modified partial differential equation, which is derived by first expanding each term of a difference scheme in a Taylor series and then eliminating time derivatives higher than first order by certain algebraic manipulations.
610