𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The two-dimensional streamline upwind scheme for the convection–reaction equation

✍ Scribed by Tony W. H. Sheu; H. Y. Shiah

Publisher
John Wiley and Sons
Year
2001
Tongue
English
Weight
221 KB
Volume
35
Category
Article
ISSN
0271-2091

No coin nor oath required. For personal study only.

✦ Synopsis

This paper is concerned with the development of the finite element method in simulating scalar transport, governed by the convection-reaction (CR) equation. A feature of the proposed finite element model is its ability to provide nodally exact solutions in the one-dimensional case. Details of the derivation of the upwind scheme on quadratic elements are given. Extension of the one-dimensional nodally exact scheme to the two-dimensional model equation involves the use of a streamline upwind operator. As the modified equations show in the four types of element, physically relevant discretization error terms are added to the flow direction and help stabilize the discrete system. The proposed method is referred to as the streamline upwind Petrov-Galerkin finite element model. This model has been validated against test problems that are amenable to analytical solutions. In addition to a fundamental study of the scheme, numerical results that demonstrate the validity of the method are presented.

📜 SIMILAR VOLUMES

Multidimensional upwind schemes for the
Multidimensional upwind schemes for the shallow water equations
✍ H. Paillère; G. Degrez; H. Deconinck 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 359 KB 👁 2 views

A multidimensional discretisation of the shallow water equations governing unsteady free-surface flow is proposed. The method, based on a residual distribution discretisation, relies on a characteristic eigenvector decomposition of each cell residual, and the use of appropriate distribution schemes.

A THIRD-ORDER NUMERICAL SCHEME WITH UPWI
A THIRD-ORDER NUMERICAL SCHEME WITH UPWIND WEIGHTING FOR SOLVING THE SOLUTE TRANSPORT EQUATION
✍ KANGLE HUANG; JIŘÍ ŠIMŮNEK; M. TH. VAN GENUCHTEN 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 273 KB 👁 2 views

Solute transport in the subsurface is generally described quantitatively with the convection-dispersion transport equation. Accurate numerical solutions of this equation are important to ensure physically realistic predictions of contaminant transport in a variety of applications. An accurate third-

Colocated schemes for the incompressible
Colocated schemes for the incompressible Navier–Stokes equations on non-smooth grids for two-dimensional problems
✍ C. Moulinec; P. Wesseling 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 172 KB 👁 2 views

The accuracy of colocated finite volume schemes for the incompressible Navier -Stokes equations on non-smooth curvilinear grids is investigated. A frequently used scheme is found to be quite inaccurate on non-smooth grids. In an attempt to improve the accuracy on such grids, three other schemes are

Nonstandard methods for the convective t
Nonstandard methods for the convective transport equation with nonlinear reactions
✍ Hristo V. Kojouharov; Benito M. Chen 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 454 KB 👁 1 views

A new nonstandard Lagrangian method is constructed for the one-dimensional, transient convective transport equation with nonlinear reaction terms. An ''exact'' time-stepping scheme is developed with zero local truncation error with respect to time. The scheme is based on nonlocal treatment of nonlin

A Riemann solver for the two-dimensional
A Riemann solver for the two-dimensional MHD equations
✍ Necdet Aslan; Terry Kammash 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 212 KB 👁 2 views

This paper presents how the equations of magnetohydrodynamics (MHD) in primitive form should be written in conservative form with the inclusion of a divergence source along with a divergence wave and how a physically correct sonic ®x can be embedded directly in the ¯uxes. The numerical scheme was ap