✦ LIBER ✦

AN ACCURATE FINITE DIFFERENCE SCHEME FOR SOLVING CONVECTION-DOMINATED DIFFUSION EQUATIONS

✍ Scribed by Ch. H. Bruneau; P. Fabrie; P. Rasetarinera

Publisher: John Wiley and Sons
Year: 1997
Tongue: English
Weight: 327 KB
Volume: 24
Category: Article
ISSN: 0271-2091
DOI: 10.1002/(sici)1097-0363(19970130)24:2<169::aid-fld486>3.0.co;2-j

No coin nor oath required. For personal study only.

✦ Synopsis

Approximating convection-dominated diffusion equations requires a very accurate scheme for the convection term. The most famous is the method of backward characteristics, which is very precise when a good interpolation procedure is used. However, this method is difficult to implement in 2D or 3D. The goal of this paper is to show that it is possible to construct finite difference schemes almost as accurate as the method of characteristics. Starting from a family of second-and third-order Lax-Wendroff-type schemes, a TVD and L ? - stable scheme that is easy to implement in higher dimensions is constucted. Numerical tests are performed on various model problems whose solution is known and on classical problems. Comparisons with some other limiter schemes and the method of characteristics are discussed.

📜 SIMILAR VOLUMES

An explicit fourth-order compact finite

An explicit fourth-order compact finite difference scheme for three-dimensional convection-diffusion equation

✍ Zhang, Jun 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 141 KB 👁 2 views

We present an explicit fourth-order compact ®nite dierence scheme for approximating the threedimensional convection±diusion equation with variable coecients. This 19-point formula is de®ned on a uniform cubic grid. We compare the advantages and implementation costs of the new scheme with the standar

Nonstandard finite difference schemes fo

Nonstandard finite difference schemes for reaction-diffusion equations

✍ Ronald E. Mickens 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 270 KB 👁 1 views

We construct finite difference schemes for a particular class of one-space dimension, nonlinear reactiondiffusion PDEs. The use of nonstandard finite difference methods and the imposition of a positivity condition constrain the schemes to be explicit and allow the determination of functional relatio

Nonstandard finite difference schemes fo

Nonstandard finite difference schemes for reaction--diffusion equations having linear advection

✍ Ronald E. Mickens 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 48 KB

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

A finite difference scheme for solving t

A finite difference scheme for solving the heat transport equation at the microscale

✍ Weizhong Dai; Raja Nassar 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 134 KB 👁 2 views

Heat transport at the microscale is of vital importance in microtechnology applications. In this study, we develop a finite difference scheme of the Crank-Nicholson type by introducing an intermediate function for the heat transport equation at the microscale. It is shown by the discrete energy meth

An accurate semi-analytic finite differe

An accurate semi-analytic finite difference scheme for two-dimensional elliptic problems with singularities

✍ Z. Yosibash; M. Arad; A. Yakhot; G. Ben-Dor 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 484 KB 👁 1 views

A high-order semi-analytic finite difference scheme is presented to overcome degradation of numerical performance when applied to two-dimensional elliptic problems containing singular points. The scheme, called Least-Square Singular Finite Difference Scheme (L-S SFDS), applies an explicit functional

A note on second-order finite-difference

A note on second-order finite-difference schemes on uniform meshes for advection--diffusion equations

✍ Daniele Funaro 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 85 KB 👁 2 views

An artificial-viscosity finite-difference scheme is introduced for stabilizing the solutions of advectiondiffusion equations. Although only the linear one-dimensional case is discussed, the method is easily susceptible to generalization. Some theory and comparisons with other well-known schemes are