Domain mappings for the numerical solution of partial differential equations

✍ Scribed by William L. Oberkampf

• Publisher: John Wiley and Sons
• Year: 1976
• Tongue: English
• Weight: 588 KB
• Volume: 10
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/nme.1620100116

✦ Synopsis

Abstract

Independent variable transformations of partial differential equations are examined with regard to their use in numerical solutions. Systems of first order and second order partial differential equations in conservative and nonconservative form are considered. These general equations are transformed using generalized mapping functions and important computational features of the transformed equations are discussed. Examples of mappings which regularize domains are given involving various types of partial differential equations. These mappings are of particular importance in finite difference approximations because of the ease with which a mesh can be adapted to regions formed by co‐ordinate lines.